Mathematics self-efficacy, self-concept and anxiety in relation to Mathematics achievement: The case of Kafa Zone School adolescents, Ethiopia

Belay Woldemichael; Tesfaye Semela; Abraham Tulu

doi:10.12688/f1000research.142779.1

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Research Article

Mathematics self-efficacy, self-concept and anxiety in relation to Mathematics achievement: The case of Kafa Zone School adolescents, Ethiopia

[version 1; peer review: 1 approved with reservations, 2 not approved]

Belay Woldemichael ¹, Tesfaye Semela², Abraham Tulu¹

PUBLISHED 23 Nov 2023

Author details Author details

¹ Department of Teacher Education, College of Education, Hawassa University, Awassa, Southern Nations, Nationalities, and People's Region, Ethiopia
² Institute of Policy & Development Research (IPDR) & College of Education, Hawassa University, Hawassa, Southern Nations, Nationalities, and People's Region, Ethiopia

Belay Woldemichael
Roles: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Resources, Software, Writing – Original Draft Preparation, Writing – Review & Editing

Tesfaye Semela
Roles: Investigation, Methodology, Supervision, Validation, Visualization

Abraham Tulu
Roles: Methodology, Supervision

OPEN PEER REVIEW

REVIEWER STATUS

Abstract

Background

It is significant to investigate students’ mathematical self-efficacy, self-concept and anxiety constructs since they have an effect on not only the process of acquiring mathematics, and academic achievement but also potential professional choices and general welfare. This study was aimed at exploring the effects of mathematical self-beliefs, namely self-concept, self-efficacy, and math anxiety on the mathematics achievement of high school adolescents.

Methods

The sample contains 384 randomly selected grade 12 students (M=199, F= 185) from three preparatory schools in Kafa zone. Tools were adapted from Butler (2016) and Al Mutawah (2015). The Mathematics Achievement Test (MAT) was administered to get information on mathematics achievement. Confirmatory factor analysis along with structural equation modeling was used to analyze the data.

Results

The results reveal that self-concept and self-efficacy have a positive and significant association with math achievement whereas anxiety has a negative relationship with math achievement but is not significant.

Conclusions

From the results, we conclude that self-concept and self-efficacy have significant and positive effects on mathematics achievement. We recommend that every concerned body should pay concerted effort to these motivational variables so as to encourage students’ achievements in mathematics.

Keywords

Self Efficacy, Self Concept, Anxiety, Mathemtics Achievement

Corresponding author: Belay Woldemichael

Competing interests: No competing interests were disclosed.

Grant information: The author(s) declared that no grants were involved in supporting this work.

Copyright: © 2023 Woldemichael B et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite: Woldemichael B, Semela T and Tulu A. Mathematics self-efficacy, self-concept and anxiety in relation to Mathematics achievement: The case of Kafa Zone School adolescents, Ethiopia [version 1; peer review: 1 approved with reservations, 2 not approved]. F1000Research 2023, 12:1494 (https://doi.org/10.12688/f1000research.142779.1) First published: 23 Nov 2023, 12:1494 (https://doi.org/10.12688/f1000research.142779.1) Latest published: 23 Nov 2023, 12:1494 (https://doi.org/10.12688/f1000research.142779.1)

Introduction

Self-concept is how persons observe and assess themselves: questions such as “Who am I?”, “What type of individual am I?” and “Am I good at Mathematics?” are the foci of self-concept (Hattie, 1992). Self-concept in this study is students’ own measure of how good they are at mathematics. “Self-efficacy can be understood as the individual’s conviction that he or she is capable of successfully performing a specific given task” (Bandura, 1997). This implies that self-efficacy is the measure of how much students believe they can perform a specific task in mathematics, for example linear equation, quadratic equation, or specific math, successfully. In this regard, students can measure the degree of their self-efficacy by asking themselves questions such as “Can I do this task?” or “Can I solve linear equation?”.

Self-concept is more general than self-efficacy. For example, self-concept is the value that students give to themselves in regard to their abilities in mathematics. There are students who do not have much confidence in their mathematics performance. Such students have less self-concept on mathematics than students who believe themselves that they are good in mathematics. Whereas in the case of self-efficacy students think themselves and value their performance on a specific task or content within mathematics such as linear equation, trigonometry, limits and continuity, derivatives, integration, and so on. Mathematics anxiety is a feeling of worry or fear that might arise when solving mathematical problems (Richardson and Suinn, 1972, p. 551).

Our dynamic globe is becoming more economically competitive and doors of opportunity are closing for students who have difficulty in mathematics. Investigative opinion and math know-how are requisite in many areas of occupations and students who are good in mathematics attain such occupations. As per Brown (2014), mathematical proficiency is very important in daily life, as well as for achievement in our ever-changing industrial society. Basic mathematics skills are required in daily situations. Moreover, higher levels of employability are related to proficiency in mathematics (Finnie and Meng, 2006). Meece, Wigfield, and Eccles (1990) argued that well-built mathematical backgrounds are decisive for a lot of careers in our challenging technological world. There are numerous factors which have an effect on students’ success in schools of Ethiopia. Math self-concept, self-efficacy and math anxiety are the main factors that influence mathematics achievement. Kiamanesh et al. (2004), for example, designate that math self-concept, self-efficacy and math anxiety are the main factors of math achievement. Zivkovic et al. (2023) also declare that there is significant influence of math anxiety and math self-efficacy on math performance.

In Ethiopia, as pupils’ low academic-achievement and low pass rates as well as high dropouts were serious problems (Tamire, 1997; Adem, 2005; Tesfaye, 2007) many studies in Ethiopia have focused on factors affecting students’ academic achievement in Ethiopia. Even though self-efficacy, self-concept and anxiety constructs significantly influence learning (Uzun, Gelbal, and Ogretmen, 2010), no study has been conducted in relation to these self-beliefs and anxiety constructs concerning mathematics as well as academic achievement in the case of Ethiopia. Thus, this study will offer insight for every stakeholder on effects of self-concept, self–efficacy and anxiety on mathematics achievement in the case of high school students. That is, the study will provide information to students, parents, teachers and the administrative bodies including the curriculum and policy designers, education leaders, ministry of education and the government concerning the relationship among self-efficacy, self-concept, and anxiety constructs for mathematics and academic achievement.

As mathematics is very important for daily life and for the development of a country, and since the achievement of math were highly influenced by math anxiety, math self-concept and math self-efficacy, it is essential to check the effect of these constructs in the case of Ethiopian students. This is why we aimed to investigate the influence of self-efficacy, self-concept and anxiety related to mathematics, and its effect on pupils’ success in mathematics in the Kafa zone, Ethiopia.

Problem statement

Klee, Miller, and Buehl (2022) conducted a study on self-efficacy, self-concept, and anxiety related to mathematics. The result pointed out that least mathematics self-concept and least mathematics self-efficacy frequently exhibit elevated mathematics anxiety. Hiller, Kitsantas, and Poulou (2022) investigated that anxiety and self-efficacy related to mathematics are high forecasters of mathematics achievement. The result of a study conducted by Du, Qin, Wang, and Xin (2021) revealed that there are reciprocal relations amongst mathematics interest (MI), mathematics anxiety (MA), mathematics self-efficacy (MSE) and mathematics achievement of primary school students. Zhang, Zhao, and Kong (2019) conducted a meta-analytic study on the relationship between math anxiety and math performance. The outcome of this study signifies that a negative relationship arises between math performance and mathematics anxiety. The relationship was strong in investigations that concerned students in Asia whereas the relationship was weak in investigations which engage European students. Moreover, the connection was strong in investigations concerning a senior-high-school grouping, while it was weakest in the studies within an elementary group.

As per Arens, Frenzel, and Goetz (2022), past self-concept related to math was positively connected to a following self-efficacy related to math whereas past self-efficacy related to math was not connected to a succeeding math-self-concept. In view of math grades, reverse relations might be establishing for math self-concept. Math self-efficacy and math grades indicated a one directional relationship with previous math grades being associated to a following math self-efficacy. Despite all these factors, little is known about mathematics achievement in relation to the linear combination of self-efficacy, self-concept and anxiety related to math in the case of high schools in Ethiopia, especially in the Kafa Zone; Hence, the need for this study to be undertaken. Thus, this study is aimed at investigating the relationship between self-efficacy, self-concept, and anxiety with success in mathematics for high school students in Kafa Zone.

Research hypothesis

H01: Self-concept has no influence on mathematics achievement in the case of the Kafa zone, Ethiopia.

H02: Self-efficacy has no influence on achievement in mathematics in the Kafa zone, Ethiopia.

H03: Anxiety has no influence on achievement of mathematics in the Kafa zone, Ethiopia.

Objectives

The main objective of this study is to investigate the effect of self-concept, self-efficacy and anxiety on mathematics achievement and the specific objectives are the following:

• to identify the extent by which anxiety influences mathematics achievement;
• to cognize the effect of self-efficacy on mathematics achievement;
• to examine the effect of self-concept on mathematics achievement.

Methods

Research design

Geographically, Ethiopia is located in the horn of Africa. It is bordered by Eritrea to the north, Djibouti and Somalia to the east, Sudan and south Sudan to the west and Kenya to the south. This study was undertaken on grade 12 high school students in the Kafa zone, Southwestern Ethiopia, in 2023. Primary data was collected by the researchers via questionnaire and math achievement test. Respondent students were approached personally. The study employed quantitative data collected at a single point in time, and the study purpose was to investigate a relationship among variables. We employed a cross-sectional study design with quantitative methods and explanatory purpose. The adaptation and contextualization process for the questionnaire involved items re-development and contextualization, analysis of reliability, and setting up the construct validity of mathematics self-efficacy, mathematics self-concept and mathematics-anxiety items by using exploratory factor analysis. High focus was given to a survey method so as to portray the extent of association between pupils’ self-concept, self- efficacy, and anxiety related to mathematics and their academic performance.

Considerable effort was exerted to prevent the effect of extraneous variables to bias the results of this study. In this regard, the researcher employed proper design, suitable tools of data collection, appropriate methods of data analysis, proper sample size and sample selection techniques so as to prevent the confounding variables to alter the results of the study.

Data sources

The primary data were collected by using self-developed-questionnaires, Mathematics achievement test and interviews.

Measurement of variables

Independent variables

Self-concept: The self-concept in this study is a latent variable measured by using self-developed scale based on the theory of self-concept

Self-efficacy: Is a latent variable measured by self-developed scales based on self-efficacy theory.

Anxiety: Is a latent variable which is measured by using scales developed based on anxiety theory.

Dependent variable

Mathematics achievement: Is an observed variable which is measured by administering Mathematics Achievement Test (MAT).

Sampling

The population of the study was all grade 12 students in the Kafa Zone, Ethiopia. Students were approached personally to complete the questionnaire and to be administered the test. Students were approached in such a way that once the three schools were purposively selected based on their plenty of experience, students were selected from each stratum. The stratification was based on the grade-section of the students. In this regard, 122 grade 12 students were randomly selected from each section of Bishaw Wodeyohanis high school, 131 grade 12 students were randomly selected from each section of Grazmach Pawulos high school, and 131 grade 12 students were randomly selected from each section of Gimo high school. Once these students were selected randomly, the questionnaire together with the mathematics achievement test was distributed in hard copy to each respondent personally by the researcher. It took about one hour for students to complete the questionnaire as well as to take the math achievement test. The questionnaire and the math achievement were provided to students in hard copy, both attached together. Students first completed the questionnaire including their demographic characteristics and then performed on the mathematics achievements test.

It took about one hour for students to complete the questionnaire as well as to take the math achievement test. The questionnaire and the math achievement were provided to students in hard copy, both attached together. Students first completed the questionnaire including their demographic characteristics and then performed on the mathematics achievements test.

This was so that grade 12 students were purposively selected to perform on a mathematics achievement test which includes all chapters of mathematics contents from grade 9 to grade 12. Other grade levels were assumed to be not fit to answer this achievement test. Moreover, grade 12 students were considered to be more equipped to perform on all questions of the math achievement test which encompasses all contents of grade 9 math up to grade 12 math, and to give reliable responses to the adapted and validated questionnaires concerning anxiety, self-efficacy, and self-concept.

Fox, Hunn and Mathers (2009) suggested the following range of population and the corresponding sample size to be to be taken from the given population. That is, given a population size, there is an appropriate sample size to be considered in a study as shown in Table 1 below.

Table 1. Population range and sample size approximation.

Population range	Approximate sample size
1000	278
2000	322
3000	341
5000	357
10,000	370
50,000	381
100,000	383
500,000	384
Infinity	384

Accordingly, the study sample was 384 randomly selected grade 12 students from 3 high schools, namely: Gimbo secondary and preparatory school, Bishaw Woldeyohanis secondary and preparatory school, and Grazmach pawuos secondary and preparatory school in the Kafa Zone, Ethiopia.

Stratified random sampling was employed according to students’ sections. Proportionate respondents were randomly selected from each stratum (section). The stratification was also balanced based on the gender of students.

Conceptual framework

Figure 1. The hypothesized model and the association between the constructs based on theories of self-efficacy, anxiety, and self-concept.

Source: Own design by reading different works of literature.

Data collection

Research instruments

A Likert scale type self-report questionnaire titled, “Self-concept and self-efficacy and anxiety scales towards Mathematics” which was adapted from Butler (2016) and Al Mutawah (2015) in which the students were asked to rate. The mathematics self-concept, self-efficacy, and anxiety scale was adapted and then contextualized in the context of Ethiopia (Woldemichael, 2023). In this regard, 25 items of self-concept and 25 items of self-efficacy scales were adapted from Butler (2016) whereas 26-items of the anxiety scale were adapted from Al Mutawah (2015). The questionnaire and MAT file was presented in a data repository (Woldemichael, 2023). The factor analysis along with the structural equation modeling was employed to validate the adapted questionnaire.

The mathematics achievement test was the other instrument of data collection (Woldemichael, 2023). A mathematics achievement test encompassing grade nine math up to grade 12 math of the Ethiopian mathematics curriculum, was developed and validated to measure mathematics achievement of students. The test was self-developed and validated by using IRT theory which incorporates item difficulty index, item discrimination index, item-total correlation, as well as item characteristic curve and item information curve. The participants completed the data collection instruments across one class period (about 1 hour) without a break.

Data analysis

The scales were adapted and student survey and other related surveys were employed to re-develop the scale for the Ethiopian context. The explanatory factor analysis (EFA) and confirmatory factor analysis (CFA) of this scale was conducted; the internal consistency coefficient was calculated.

Cohen’s kappa coefficient was calculated to test inter-scorer reliability. The data was entered into SPSS 23, and Stata 13 was used for analysis. All the items pass all psychometric properties of item analysis. Item Response Theory (IRT) was employed for item analysis.

Quantitative analysis was employed. The main data analysis tool employed was the structural equation modeling with the help of STATA13 software. The construct validity in terms of convergent and discriminant validity, as well as internal consistency reliability were checked. The measurement level goodness of fit as well as overall goodness of the fit of the model was investigated. SPSS data can be found under Underlying data (Woldemichael, 2023).

Results

This section incorporates the preliminary analysis including the response rate, descriptive results, and the item analysis for the Mathematics Achievement Test (MAT), and Confirmatory factor Analysis to test the hypothesis.

Response rate

384 questionnaires were distributed to 384 respondents and all of them completed and returned the questionnaire.

Demographic data

The demographic characteristics of the respondents were analyzed in frequency tables in terms of sex, age, grade level, parental education, parental employment status, and parental profession in science.

Table 2 above shows that out of 384 respondents, 185(48.2 %) were female and 199(51.8%) were male. This shows that gender balance was considered as planned in the proposal. The ages of all students were in between 18-25, and all students were from grade 12. Three schools, Bishaw Wodeyohanis, Grazmach Pawulos and Gimbo were selected. Of the respondents, 122(31.8%) were from Bishaw Wodeyohanis school, 131(34.1%) were from Grazmach Pawulos school, and 131(34.1%) were from Gimbo school.

Table 2. Gender, age, school and grade level.

Variable	Characteristics	Frequency	Percent
Gender	Female	185	48.2
	Male	199	51.8
	Total	384	100.0
Age	18-25	384	100.0
School	Bishaw Wodeyohanis	122	31.8
	Grazmach Pawulos	131	34.1
	Gimbo	131	34.1
	Total	384	100.0
Grade-level	Grade 12	384	100.0

Table 3 shows the family background of students in terms of parental education, employment status, and profession in science. The data indicate that majority of respondents were from families whose education level is college diploma, who are not government or self-employed and who have no profession in science.

Table 3. Parental education, parental employment status, and parental profession in science.

Variable		Characteristics	Frequency	Percent
Parental education	Mother’s education	Elementary education and below	74	19.3
		High school	97	25.3
		College diploma	124	32.3
		Higher education	89	23.2
		Total	384	100.0
	Father’s education	Elementary education and below	75	19.5
		High school	92	24.0
		College diploma	136	35.4
		Higher education	81	21.1
		Total	384	100.0
Parental employment status	Mother employment status	Government employed	23	6.0
		Self employed	110	28.6
		Farmer	122	31.8
		Other	129	33.6
		Total	384	100.0
	Father employment status	Government employed	99	25.8
		Self employed	82	21.4
		Farmer	82	21.4
		Other	121	31.5
		Total	384	100.0
Parental profession in science	Mother profession in science	No	243	63.3
		Yes	141	36.7
		Total	384	100.0
	Father profession in science	No	205	53.4
		Yes	179	46.6
		Total	384	100.0

Item analysis for Mathematics achievement Test (MAT)

Evaluation by experts

According to Rubio et al. (2003), face validity is the degree to which a scale or item reveals what it intends to measure and is evaluated by adjudicators who have proficiency in the field of the study being undertaken. Ngo and O’Cass (2009) suggest that specialists specify the theoretical correspondence between the main constructs and the items assessing those constructs. As suggested by Ngo and O’Cass (2012), experts were asked to comment on the correspondence between the main constructs and their particular definition, as well as their significance for the purpose of the study. Accordingly, the nine experts in this study were asked to rate each item as either: 1 = Very weakly represents the Construct, 2 = somewhat weakly represents the Construct, 3 = Unsure, 4 = Somewhat Strongly represents the Construct, 5 = Very strongly represents the Construct.

Yusoff (2019) suggests that the content-validity facts can be confirmed by the content-validity index (CVI). Moreover, as per Yusoff (2019) there are two forms of CVI: CVI for item (I-CVI) and CVI for scale (S-CVI). There are two ways for calculating S-CVI: the average of the I-CVI scores for all items on the scale (S-CVI/Ave) and the proportion of items on the scale that achieve a relevance scale of 4 or 5 by all experts (S-CVI/UA). The calculation of CVI, the relevance rating must be recorded as 1 (relevance scale of 4 or 5) or 0 (relevance scale of 1, 2 or 3). In this study, items with all the experts agreed upon as relevant, which are items with I-CVI = 1 and universal agreement (UA = 1), were accepted for the next step. Accordingly, 31 MAT items were accepted to fit the content.

Cognitive interview

Five students who took the test were asked to determine items with confusing meaning that need modification and deletion. Students responded that there is no such item whose meanings are not matched with the intended meaning to measure the construct and which are confusing. Thus, the cognitive interview result indicated that all the 31 items could be retained.

Item difficulty and discrimination index

The test characteristic curve (TCC) designates that individuals with whichever trait-level could answer the question correctly in such a way that, as depicted in Figure 2, students with lower trait-level, say theta is equal to zero, can have expected score of 10. And students with higher trait lever, say theta is equal to four, can have expected score of 31.

Figure 2. The Test Characteristic Curve (TCC).

The test-information-function curve is helpful for exemplifying the degree to which a test offers diverse quality of information at different trait levels. Since the test information function graph was bell-shaped, as observed in Figure 3, this reveals that the test was discriminating fine amongst students with a variety of trait levels.

Figure 3. The Test Information Curve (TIC).

Figure 4. The scree plot.

Source: SPSS graph from the primary data.

A two parameter IRT model was employed to determine the items’ difficulty and discrimination indices. The results indicated that all items except 6 items (item 1, item 3, item 5, item 7, item 19, and item 23), have an acceptable degree of discrimination and difficulty indices. Thus, only 25 items: item-2, item-4, item-6, item-8, item-9, item-10, item-11, item-12, item-13, item-14, item-15, item-16, item-17, item-18, item-20, item-21, item-22, item-24, item-25, item-26, item-27, item-28, item-29, item-30, and item-31 were retained for the final data collection. That is, the above 25 items, namely item-2, item-4, item-6, item-8, item-9, item-10, item-11, item-12, item-13, item-14, item-15, item-16, item-17, item-18, item-20, item-21, item-22, item-24, item-25, item-26, item-27, item-28, item-29, item-30, and item-31, which have an acceptable level of discriminating and difficulty indices were retained in the final data collection.

Scale validation

Confirmatory factor analysis

Confirmatory factor analysis (CFA) involving structural equation modeling (SEM) was involved for scale validation.

We observe from Table 4 that all self-concept, anxiety and self-efficacy items load to their corresponding factor.

Table 4. Rotated component matrix^a.

	Component
	1	2	3
C14	.684
C7	.678
E10	.669
C17	.659
E12	.637
E2	.555		.441
C3	.551
E21	.550
C4	.530
E20	.417
C23
A16		.800
A8		.749
A3		.744
C24		.687
A21		.678
A27			.834
A23			.785
E1	.428		.667

a Rotation converged in 5 iterations.

Moreover, the scree plot indicate that the inflection point, the point at which the curve changes its concavity, appear after 4 points. Based on Field (2009), this implies that the number of factors = 4-1 = 3. Thus, by the evidence of the scree-plot, we retain the three factors and then we go to the next step.

Structural equation modeling

Measurement level model estimates

As observed from Table 5, all the items of anxiety measure the construct significantly ( $α = 00 < .05)$ as intended.

Table 5. Measurement model estimates anxiety items.

Standardized measurement		Coef.	OIM Std. Err.	Z	[95%Conf. Interval]
E1 <-	Anxiety	.5412593	.0458894	11.79	.4513177	.6312008
E1 <-	_cons	4.942944	.185521	26.64	4.57933	5.306559
A23 <-	Anxiety	.7205062	.0373939	19.27	.6472155	.7937969
A23 <-	_cons	6.397307	.2364158	27.06	5.93394	6.860673
E27 <-	Self_Efficacy	.7932624	.0364542	21.76	.7218135	.8647113
E27 <-	_cons	5.840597	.2168441	26.93	5.415591	6.265604

We observe from Table 6 that the items of self-efficacy are the significant estimators of the construct self-efficacy. All items loaded and contributed to the construct positively and p < 0.05.

Table 6. Measurement model self-efficacy estimates.

Standardized measurement		Coef.	OIM Std. Err.	Z		[95% conf. Interval]
C14 <-	Self_Efficacy	.623136	.362131	17.21	0.000	.5521593	.6941121
C14 <-	_cons	4.097766	.1564253	26.2	0.000	3.79118	4.40435
C7 <-	Self_Efficacy	.612742	.366806	16.7	0.000	.5408492	.6846347
C7 <-	_cons	5.215915	.1950084	26.75	0.000	4.83371	5.59813
E10 <-	Self_Efficacy	.5471888	.405299	13.5	0.000	.4677518	.6266259
E10 <-	_cons	5.687671	.2114851	26.89	0.000	5.27317	6.10218
C17 <-	Self_Efficacy	.649508	.345167	18.82	0.000	.5818565	.71716
C17 <-	_cons	4.495837	.1700662	26.44	0.000	4.16251	4.82916
E12 <-	Self_Efficacy	.4559529	.449275	10.15	0.000	.3678966	.5440092
E12 <-	_cons	6.567794	.2424266	27.09	0.000	6.09265	7.04294
E2<-	Self_Efficacy	.576179	.0387992	14.85	0.000	.50013	.65222
E2<-	_cons	5.7134	.2123874	26.9	0.000	5.29716	6.12971
C3<-	Self_Efficacy	.64198	.0352496	18.21	0.000	.57289	.71107
C3<-	_cons	4.72049	.1778159	26.55	0.000	4.37198	5.06901
E21<-	Self_Efficacy	.62931	.0358089	17.57	0.000	.55913	.6995
E21<-	_cons	4.4459	.1683-513	26.41	0.000	4.11603	4.77595
C4<-	Self_Efficacy	.63818	.035315	18.07	0.000	.56896	.7074
C4<-	_cons	4.2946	.1631545	26.32	0.000	3.97484	4.61439
E20<-	Self_Efficacy	.38492	.0479583	8.03	0.000	.29092	.47892
E20<-	_cons	5.44973	.2031639	26.82	0.000	5.05155	5.84793
C23<-	Self_Efficacy	.458239	.0449285	10.2	0.000	.370181	.546298
C23<-	_cons	4.9903	0.187163	26.66	0.000	4.62346	5.35713

Similarly, we observe from Table 7 that all items of self-concept contributed to the construct self-concept positively and p < 0.05.

Table 7. Measurement model estimate of self-concept.

Standardized measurement		Coef.	OIM Std. Err.	Z	[95% conf. Interval]
A16<-	Self-concept	.8301448	.0239936	34.60	.7831183	.8771714
A16<-	_cons	4.971278	.1864874	26.66	6.605769	5.336786
A8<-	Self-concept	.7705607	.0269939	28.55	.7176536	.8234678
A8<-	_cons	5.042563	.1889643	26.69	4.6722	5.412926
A3<-	Self-concept	.659921	.0350978	18.80	.5911305	.7287115
A3<-	_cons	5.576303	.2075756	26.86	4.6722	5.412926
A21<-	Self-concept	.6443386	.035381	18.21	.5911305	.7287115
A21<-	_cons	5.645731	.2100052	26.88	5.169462	5.983143
C24<-	Self-concept	.5957242	.384403	15.50	.5203825	.6710659
C24<-	_cons	5.268314	.1968245	26.77	4.882545	5.654083

Figure 5 shows the full-fledged model and from this model we acquire the goodness-of-fit statistics, with relative Chi-Square = 756.620; CFI = .780, RMSEA = .097, SRMR = .072, and p = .000, which indicate that there will be certain modification indices (see Table 8).

Figure 5. Fully fledged model.

Figure 6. The modified model.

Source: STATA graph from the primary data.

Table 8. Overall goodness of fit.

Fit statistic	Value description
Likelihood ratio
chi2_ms (165) p > chi2	756.620 model vs. saturated 0.000
chi2_bs (190) P > chi2	2882.480 baseline vs. saturated 0.000
Population error
RMSEA	0.097 Root mean squared error of approximation
90% CI, lower bound	0.090
upper bound	0.104
pclose	0.000 Probability RMSEA <= 0.05
Information criteria
AIC	17350.090 Akaike's information criterion
BIC	17606.882 Bayesian information criterion
Baseline comparison
CFI	0.780 Comparative fit index
TLI	0.747 Tucker-Lewis index
Size of residuals
SRMR	0.072 Standardized root mean squared residual
CD	0.992 Coefficient of determination

Modification indices

Certain modification indices have been employed and after the modification indices, we observe that the model fit the data and the model was free from offending estimates (see Table 9).

Table 9. The modified model goodness of fit.

Fit statistic	Value description
Likelihood ratio
chi2_ms (165) p > chi2	655.147 model vs. saturated 0.000
chi2_bs (190) P > chi2	2882.480 baseline vs. saturated 0.000
Population error
RMSEA	0.089Root mean squared error of approximation
90% CI, lower bound	0.082
upper bound	0.096
pclose	0.000 Probability RMSEA <= 0.05
Information criteria
AIC	17254.617Akaike's information criterion
BIC	17523.260Bayesian information criterion
Baseline comparison
CFI	0.817Comparative fit index
TLI	0.795 Tucker-Lewis index
Size of residuals
SRMR	0.072 Standardized root mean squared residual
CD	0.995 Coefficient of determination

As depicted in Table 9, we get the goodness-of-fit statistics, with relative Chi-Square = 655.147; CFI = .817, RMSEA = .089, SRMR = .072, and p = .000, which indicate that the model is considerably fit for the data.

As depicted in Table 10 above, the two predictors, namely the self-efficacy( $β$ = .17, p = .007 < .05) and self-concept ( $β$ = .30, p = .000 < .05), of math achievement are positively related and significant estimators of mathematics achievement whereas the anxiety ( $β$ = -.018, p = .0785 > .05) is negatively related but not a significant estimator of math achievement.

Table 10. Structural level estimates.

Standardized measurement		Coef.	OIM Std. Err.	Z	$P > \|z\|$	[95%Conf. Interval]
Math_Resut $\leftarrow$	Self_efficacy	. 1749275	.0653928	2.68	0.007	.0467599	.303095
	Self_concept	.3007339	.0613051	4.91	0.000	.1805781	.4208898
	Anxiety	-.018028	.0606	-0.27	0.785	-.147504	.1114466
	_cons	6.291456	.2326869	27.04	0.000	5.835599	6.747514

The result is supported by other studies, for example, Schunk (1991) conducted a similar study on self-efficacy and academic motivation and the result of this study demonstrated that self-efficacy is a better predicator than any other cognitive or affective processes. Hodges (2008) also conducted a study on self-efficacy in the context of online learning and the result of this study suggested that self-efficacy is an applicable forecaster for students’ motivation and performance (Hodges, 2008). Mathematics anxiety has negative influence on students’ mathematics achievement regardless of their true level of mastering mathematics (Ashcraft and Moore, 2009). Relationships of math anxiety and math achievement vary depending on gender and the grade year (Szczygieł, 2020). Academic self-concept plays an important role in increasing students’ academic achievement (Marsh and Martin, 2011). It has been found that there is a positive relationship between mathematics self-concept and mathematical achievement (Thien and Ong, 2015; Bong and Skaalvik, 2003).

Conclusion

The main aim of this study was to identify whether the self-efficacy, self-concept and anxiety around mathematics influence students’ achievement in the subject in the Kafa zone, Ethiopia. Confirmatory factor analysis and structural equation modeling were employed to analyze the data; the results by using factor analysis and structural equation modeling reveal the following findings: All items loaded positively and significantly to their corresponding construct and no item was deleted from the list. The structural equation model indicates that math anxiety has a negative relationship with the math result; whereas self-concept and self-efficacy have a positive relationship with math achievement. Self-efficacy has positive relationship with math achievement and hence has significant influence on math achievement. Math anxiety has a negative relationship with the math result but anxiety did not significantly influence mathematics achievement. The findings supported the claim that self-efficacy and self-concept are significant predictors of math achievement. And the finding does not support the claim that anxiety influences mathematics achievement. From these results we conclude the following based on the research hypothesis:

- Self-concept has significant influence on mathematics achievement in the case of the Kafa zone school adolescents.
- Self-efficacy has significant influence on mathematics achievement in the case of the Kafa zone school adolescents.
- Anxiety has no significant effect on mathematics achievement in the case of the Kafa zone school adolescents.

The results indicate that the two factors namely the self-efficacy and self-concept contributes positively and significantly to mathematics achievement in the case of the Kafa Zone. Whereas the third factor, anxiety has a negative effect on the math achievement but does not significantly influence mathematics achievement of students in the Kafa zone. From these results we recommend that parents, students themselves, teachers, school principals, education officers, curriculum developers, policy workers, and the government should pay special attention to the variables of self-concept, self-efficacy and anxiety. Moreover, other researchers are recommended to incorporate other unexplained variables that influence mathematics achievement.

Consent of participants

The authors affirm that: written consent was obtained from participants; all respondents were told about how their data would be used and published; participants did not object to participate in this research and to be published in the journal article; participants provided informed consent for publication of the data in the journal. The consent form can be found in the date repository (Woldemichael, 2023).

Ethical considerations

The study was conducted following the approval of the PhD dissertation proposal and obtaining ethical clearance by the Office of Vice President for Research and Technology Transfer (VPRTT), Hawassa University. In this regard, the approval was given from College of Education with Reference number: መትት/17/2014 and date October 19/2021.The respondents were free to participate or not to participate in the study at any point in time; Respondents were aware of the aims, reward, risks, and financial support following the study and had the opportunity to refuse to participate; In person identifiable information was not assembled; Bodily, societal, mental and all other types of hurt are kept to an absolute bare minimum.

Data availability

Underlying data

OSF:Self-Efficacy, Self-Concept and Anxiety. https://doi.org/10.17605/OSF.IO/5NDTU (Woldemichael, 2023)

This project contains the following underlying data:

- data BCE.2sav.sav

Extended data

This project contains the following extended data:

- questionnaire and MAT.docx
- Signed Informed Consent.docx

Data are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0).

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Version 1

VERSION 1 PUBLISHED 23 Nov 2023

Author details Author details

¹ Department of Teacher Education, College of Education, Hawassa University, Awassa, Southern Nations, Nationalities, and People's Region, Ethiopia
² Institute of Policy & Development Research (IPDR) & College of Education, Hawassa University, Hawassa, Southern Nations, Nationalities, and People's Region, Ethiopia

Belay Woldemichael
Roles: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Resources, Software, Writing – Original Draft Preparation, Writing – Review & Editing

Tesfaye Semela
Roles: Investigation, Methodology, Supervision, Validation, Visualization

Abraham Tulu
Roles: Methodology, Supervision

Competing interests

No competing interests were disclosed.

Grant information

The author(s) declared that no grants were involved in supporting this work.

Article Versions (1)

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Published: 23 Nov 2023, 12:1494

https://doi.org/10.12688/f1000research.142779.1

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Woldemichael B, Semela T and Tulu A. Mathematics self-efficacy, self-concept and anxiety in relation to Mathematics achievement: The case of Kafa Zone School adolescents, Ethiopia [version 1; peer review: 1 approved with reservations, 2 not approved]. F1000Research 2023, 12:1494 (https://doi.org/10.12688/f1000research.142779.1)

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Open Peer Review

Current Reviewer Status: ?

Key to Reviewer Statuses VIEW HIDE

ApprovedThe paper is scientifically sound in its current form and only minor, if any, improvements are suggested

Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.

Not approvedFundamental flaws in the paper seriously undermine the findings and conclusions

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Reviewer Report 13 May 2024

Jones Apawu, University of Education Winneba, Winneba, Central, Ghana

Approved with Reservations

https://doi.org/10.5256/f1000research.156364.r258018

I have thoroughly read through the manuscript have fashioned my report under the following headings:

Abstract:
The research design and population are missing in the abstract.

Introduction:

Once you

I have thoroughly read through the manuscript have fashioned my report under the following headings:

Abstract:
The research design and population are missing in the abstract.

Introduction:

Once you have a direct quotation, the page number(s) must be provided and vice versa. On page 3, line 3 from the top, no page number was provided for this quotation “Self-efficacy can be understood as the individual’s conviction that he or she is capable of successfully performing a specific given task” (Bandura, 1997).
On page 3, line 14 from the top, page number was provided without any quotes on any text (see Richardson and Suinn, 1972, p. 551).
On page 3, line 27 from the top, the parenthetical citations should be arranged in alphabetical order (i.e. Tamire, 1997; Adem, 2005; Tesfaye, 2007 should be Adem, 2005; Tamire, 1997; Tesfaye, 2007). There are others in the manuscript.
On page 4, the subheading should be "Research hypotheses" not "Research hypothesis" since there were three (3) hypotheses that were formulated. H01, H02 and H03 should be H₀₁, H₀₂, H₀₃.
The "Objectives" subheading should come before the "Research hypotheses".

Methods:

On page 4, the subheading "Research design" should be deleted since the writings are not only about research design.
On page 4, line 10 from the bottom, "…the researcher..." should be "…the researchers..." since the manuscript has three (3) authors.
On page 4, line 17, the "quantitative methods" in my opinion should be reconciled with interviews under the subheading "Data sources".
Sampling heading on page 5 should be "Population and sampling".
On page 5 the population should be stated explicitly. For instance, the population of Ethiopia is 128,911,361 but not a description of e.g., all the people in Ethiopia. On page 5, how did the authors arrive at 122, 131, and 131 grade 12 students?
The following sentences, i.e. "Once these students were selected randomly, the questionnaire together with the mathematics achievement test was distributed in hard copy to each respondent personally by the researcher. It took about one hour for students to complete the questionnaire as well as to take the math achievement test. The questionnaire and the math achievement were provided to students in hard copy, both attached together. Students first completed the questionnaire including their demographic characteristics and then performed on the mathematics achievements test. It took about one hour for students to complete the questionnaire as well as to take the math achievement test. The questionnaire and the math achievement were provided to students in hard copy, both attached together. Students first completed the questionnaire including their demographic characteristics and then performed on the mathematics achievements test." should not be under "Population and sampling". This sentence, "This was so that grade 12 students were purposively selected to perform on a mathematics achievement test which includes all chapters of mathematics contents from grade 9 to grade 12." is not clear. The subheading "Population and sampling" must be written again making sure that things not relating to population and sampling are not included.
The authors should avoid vague pointers such as below, above, s/he, etc. For instance, on page 5, line 6 from the bottom, below after Table 1 should be deleted.
On page 5, line 1 from the bottom, the sentence "The stratification was also balanced based on the gender of students" is not clear. From Table 1, does it mean the population of the three (3) schools is 500,000 or more?
On page 6, there is a conceptual framework which I think the authors should have a brief write-up on it and it must come after the "Research hypotheses" subheading.
On page 6, lines 6 and 7 under "Research instruments", "... questionnaire and MAT file was ..." should be "... questionnaire and MAT file were ...". The sentence "The factor analysis along with the structural equation modeling was employed to validate the adapted questionnaire" under "Research instruments" seems inappropriate since factor analysis and SEM are not research instruments.
On page 6, line 10 under "Research instruments", IRT should be in full and abbreviated in parentheses since it is the first usage.
On page 6, line 7 from the bottom, for the sentence, “The data was entered into SPSS 23, and Stata 13 was used for analysis” should be made clearer. One software is used for data entering the other one without data is used for data analysis. SPSS 23 should be IBMSPSS 23.
On page 6, line 1 from the bottom, … “SPSS data” is not clear.
To make write-ups fit well, the authors should have paragraphs under the heading Methods since there were instances write-ups do not fit under some subheadings.
Pilot testing of the instruments was conspicuously missing.

Results:

On page 7, line 9 from the top, above should be deleted after Table 2.
What was the motivation for demographic data. In my opinion, demographic data is not necessary because there was no research question and/or research hypothesis that needed demographic results. Consequently, Tables 2 and 3 are not necessary.
There should be a preamble under “Item analysis for Mathematics achievement Test (MAT)”.
Write-ups under “Item analysis for Mathematics achievement Test (MAT)” up to before scale validation fit under Methods.
On page 10, the sentence “That is, the above 25 items, namely item-2, item-4, item-6, item-8, item-9, item-10, item-11, item-12, item-13, item-14, item-15, item-16, item-17, item-18, item-20, item-21, item-22, item-24, item-25, item-26, item-27, item-28, item-29, item-30, and item-31” should be deleted because it is a repetition.
On page 10, line 2 from the top, “because they met the acceptable level of discriminating and difficulty indices” should come after collection.
On page 10, line 1 on top of Table 4 do not reconcile with “In this regard, 25 items of self-concept and 25 items of self-efficacy scales were adapted from Butler (2016) whereas 26-items of the anxiety scale were adapted from Al Mutawah (2015).” On page 6, lines 4 and 5 under “Research instruments”.
The authors should have a preamble under “Structural equation modeling”.
On page 11, line 1 under “Measurement level model estimates”, (α=00<.05) should be relooked at and corrected.

Conclusion:

The conclusion heading should be “Conclusions and recommendations”.
On page 15, line 11 under “Conclusion”, hypothesis should be hypotheses.
Consent of participants write-ups should be part of Methods.

In-text citations and references list:

The authors should situate in-text citations and the references list in known style of referencing. The style used in the manuscript seems to have the lens of APA referencing which was not followed judiciously.
The references list should be reformatted with the lens of APA style of referencing.
The authors should arrange the references list in alphabetical order. For instance, “Hodges CB: Self-efficacy in the context of online learning environments: A review of the literature and directions for research. Perform. Improv. Q. 2008; 20(3-4): 7–25” should come before “Kiamanesh AR, Hejazi E, Esfahani ZN: The role of math self-efficacy, math self-concept, perceived usefulness of mathematics and math anxiety in math achievement. Proceedings of the 3rd International Biennial SELF Research Conference, Self-Concept, Motivation and Identity: Where to from here. 2004.”
The authors can peruse the basics of APA style of referencing from https://libguides.csudh.edu/ld.php?content_id=52097964

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Yes
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Mathematics Education in general, ICT integration into the teaching and learning of mathematics, differentiated instruction, TPACK

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

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Reviewer Report 17 Apr 2024

Krzysztof Cipora, Loughborough University, Loughborough, England, UK

Not Approved

https://doi.org/10.5256/f1000research.156364.r258012

In the paper, the authors aim at investigating relations between mathematics anxiety, mathematics self-concept, mathematics self-efficacy, and mathematics performance in 12th graders in Kafa zone in Ethiopia. They show that both self-efficacy and self-concept are related to mathematics performance ... Continue reading

In the paper, the authors aim at investigating relations between mathematics anxiety, mathematics self-concept, mathematics self-efficacy, and mathematics performance in 12th graders in Kafa zone in Ethiopia. They show that both self-efficacy and self-concept are related to mathematics performance while mathematics anxiety is not linked to mathematics performance.

It is great that the study has been conducted in a population, which has been understudied, and this is a great value. In that sense it can make a valuable contribution to our understanding of mathematics anxiety and attitudes and its relations to mathematics performance. It needs a bit more thorough theoretical background, some clarifications about the context and methods. Discussion needs substantial improvements as well.

I tried to be as constructive as possible in my comments below. They are ordered according to the order of appearance of the issues in the paper.

Specific comments:

Abstract:

method section, please name the country, not only the region
results section: maybe mention also relationships between predictors (associations between math anxiety, math-self efficacy and self-concept).
No effect of math anxiety on performance - not at all, or not after controlling for other predictors?

Keywords: I assume it should be “math anxiety” rather than “anxiety”, same holds true for self-concept and self-efficacy.

Introduction:
Somewhat fails to provide distinction between self-concept / self-efficacy and those constructs when referred to mathematics (I.e., math self-concept, math self-efficacy). There is quite a lot of literature on that, and it would be good to introduce this distinction.

It would be also good to say something about interrelations between math anxiety, math self-concept and math self-efficacy. The paper by Lee (2009) analysing PISA data with respect to these constructs would be a good starting point here (I am not related to that paper).

When discussing the role mathematics anxiety, self-concept and self-efficacy play for math achievement, the authors may consider reporting typical effect sizes associated with these effects.

In the “Problem statement” section the authors discuss how important it is to look at these problems is Kafa zone. It left me wondering whether there is something specific to this region which makes it different from the rest of Ethiopia? Or it is representative to the entire country. It may be interesting to some of the readers too.

“Research hypothesis” section - I think it would make more sense to state the research hypotheses rather than null hypotheses. This is the more typical way of doing it and it may be more convenient to the readers.

“Methods” section
I am wondering how much the information about neighbours of Ethiopia helps here. What would be somewhat more informative would be giving some information about the population / educational system / cultural values / stereotypes about mathematics etc.

Last sentence of the first paragraph of the “Research design” section and the entire second paragraph of this section does not contain much useful information as it essentially states that authors carefully conducted the study:
“High focus was given to a survey method so as to portray the extent of association between pupils’ self-concept, self- efficacy, and anxiety related to mathematics and their academic performance.

Considerable effort was exerted to prevent the effect of extraneous variables to bias the results of this study. In this regard, the researcher employed proper design, suitable tools of data collection, appropriate methods of data analysis, proper sample size and sample selection techniques so as to prevent the confounding variables to alter the results of the study.”

In my view this section may be skipped.

“Measurement of variables” section - each of the paragraphs (bullet points) says one sentence abut the instrument, which is also not very informative e.g., “self-developed scales based on self-efficacy theory”. I think this section could be combined with the “Research instruments” section.

“Sampling” section - the second paragraph is just a duplication of the ending of the first paragraph just above. Please remove the duplicated statement. The third paragraph could be streamlined a bit.
6-th paragraph of this section says that sampling considered “students’ sections”. However, these are not explained anywhere. Please give some details.

The schools being recruited are named several times. Naming them once would be enough.

Table 1 - Firstly, I am not sure whether it is needed here. It would be enough to state that this method was used. I am also unsure whether the authors considered the population size (and the size of the population is not provided). To be fair, I am not familiar with this method of sample size estimation. How does it relate to power analysis which is probably the more adequate technique as it looks into probability of detecting effects of specified size.

As a measure of reliability the authors are using Cohen’s kappa, which they define as “inter-scorer reliability”. I am not sure how this method is suited for this type of analysis. Were there different scorers evaluating anxiety / self-concept of each student?

“All items pass all psychometric properties of item analysis” - please be more specific.

Age of participants - they were all grade 12 students but the age range is 18-25. Was this range of 7 years due to some outliers who repeated the class many times / specificities of local educational system / some other factors. Relatedly, the row “Age” in Table 2 is not very informative.

“Demographic Data” section: What does “profession in science” mean? It seems that more than 1/3 of participants came from families where at least one parent had a “profession in science”. Does it mean they were children of academics? If yes, I am somewhat surprised and doubt whether the sample was representative of the population (in any country, I can think of).

“Evaluation by experts” section - please specify who the experts were (i.e., what was their expertise?)

“Item difficulty and discrimination index” - Make the last section more concise - there is no need to name all the items that were retained twice in two adjacent sentences.

Work a bit more on streamlining. For instance text in the section “Measurement level model estimates” is a set of single-sentence paragraphs. Similar problem in the last paragraph of p.14, where single sentences are referring to different papers, but would benefit from streamlining.

I also find it hard to follow how the authors come from 25 items of self-concept, 25 items of self-efficacy, and 26 items of Math anxiety (as reported on p.6) to 19 items overall in the CFA. Maybe I am missing something, but I guess a statistician should have a look into this. Responses to only 19 items are also present in shared datafile, while the number of items shared in the OSF is different than what was reported in the paper and what we have in the shared data. Potentially some SPSS / STATA syntax would help, as well as sharing data in more raw format.

P.13 “predicator” -> “predictor”.

Statistics and reporting - p-value is never 0. It can be negligibly small and then should be denoted < 0.001.

Figures 5 and 6: What do A, C, and E mean in item names? Does it mean that items originally designed as anxiety (my suspicion what A may stand for) turned out to load self-concept? Same holds for other letters and loadings.

Discussion (section “Conclusion” is quite weak and would need substantial rewriting. As for now, in my view it only paraphrases the results, and there is not much attempt at discussing the implications of the findings etc.

Style:
First sentence of paragraph 4 of the introduction could be somewhat streamlined. Now it goes “many studies in Ethiopia have focused on (…) achievement in Ethiopia.”

“Problem statement” section: this may be streamlined too: “The result pointed out that least mathematics self-concept and least mathematics self-efficacy frequently exhibit elevated mathematics anxiety”

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

I cannot comment. A qualified statistician is required.
Are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Numerical cognition, Cognitive psychology, mathematics anxiety

I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above.

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Reviewer Report 25 Mar 2024

Cristian Rojas-Barahona, Faculty of Psychology, Universidad de Talca, Talca, Maule Region, Chile

Anabel Fernández, Faculty of Psychology, University of Talca, Talca, Chile

Not Approved

https://doi.org/10.5256/f1000research.156364.r250563

Revision:
The article investigates the influence of self-efficacy, self-concept, and anxiety on mathematics achievement among students in the Kafa Zone, Ethiopia. Utilizing varied techniques including confirmatory factor analysis and structural equation modeling, the study finds that self-efficacy and self-concept ... Continue reading

Revision:
The article investigates the influence of self-efficacy, self-concept, and anxiety on mathematics achievement among students in the Kafa Zone, Ethiopia. Utilizing varied techniques including confirmatory factor analysis and structural equation modeling, the study finds that self-efficacy and self-concept positively influence mathematics achievement, while anxiety shows a negative relationship, albeit not statistically significant. The findings underscore the importance of addressing self-efficacy and self-concept to enhance mathematics performance in this context. Recommendations are made for various stakeholders to pay special attention to these variables. The study highlights the significance of psychological factors in mathematics achievement and provides valuable insights for educators, policymakers, and researchers interested in improving mathematics education outcomes in similar settings.
Specific comments per section:
Section
Comment

Abstract
The abstract highlights the use of Confirmatory Factor Analysis along with structural equation modeling to analyze the data, offering initial insight into the methodology employed. However, the abstract could benefit from further clarity by explicitly stating the purpose of each technique utilized, including Item Response Theory and Exploratory Factor Analysis. Providing this clarification would enhance the abstract's clarity and ensure a clear understanding of the analytical approach taken in the study.

Introduction
(page 3, paragraphs 1-2)
If self-efficacy and self-concept are explained in independent paragraphs, it would be reasonable to expect that math anxiety, being another variable under study, would also receive a comparable level of explanation. Therefore, it's advisable to revisit the section and consider whether each variable is receiving the attention it deserves based on its significance to the research question and the overall aim of the study.

Introduction
(page 3, paragraph 3, last sentence)
While it is acknowledged that math self-concept, self-efficacy, and math anxiety play significant roles in mathematics achievement, it is important to recognize that there may be other factors beyond the scope of this study that also contribute to student performance in mathematics. Therefore, rather than stating definitively that these variables are the main factors influencing math achievement, it may be more appropriate to acknowledge them as important factors among others, the full extent of which may require further investigation.

Introduction
(page 3, paragraph 4, first sentence)
Revise the sentence:
“In Ethiopia, as pupils’ low academic-achievement and low pass rates as well as high dropouts were serious problems
(Tamire, 1997; Adem, 2005; Tesfaye, 2007) many studies in Ethiopia have focused on factors affecting students’
academic achievement in Ethiopia.”
Edit and avoid repetition of "in Ethiopia".

Introduction
(page 3, paragraph 5, first sentence)
While it is asserted that mathematics plays a crucial role in daily life and national development, and that the achievement of math is significantly influenced by factors such as math anxiety, math self-concept, and math self-efficacy, it is important to ensure that these claims are proved by empirical evidence. Therefore, providing citations and references supporting the results that justify the influence of math anxiety, math self-concept, and math self-efficacy on math achievement would enhance the validity of the assertion.

Introduction
Problem statement
(page 3, first paragraph)
It is suggested that acronyms be used for the main variables (math anxiety (MA), mathematics self-efficacy (MSE)), such as it is happening in this section, from its first appearance in the text and throughout the entire document. This practice will enhance readability and streamline the presentation of the variables in the study.

Introduction
Problem statement
(page 4, first paragraph)
Based on the complex relationships among variables such as self-efficacy, self-concept, and math anxiety, it may be advisable to avoid using the term “linear combination”. Since the relationship between these variables could be nonlinear, it might be more appropriate to describe their interplay without implying a specific mathematical model.

Introduction
Research hypotheses
(page 4)
While stating the hypotheses as null hypotheses can be appropriate in certain contexts, it's important to ensure that it aligns with the research aims and questions. Consider whether stating the hypotheses as research hypotheses would better suit the goals of your study and provide a clearer framework for your analysis and interpretation.
Make sure to use the plural form “hypotheses” instead of “hypothesis” when referring to multiple hypotheses in the article.

Introduction
Objectives
(page 4)
The objectives effectively outline the scope of the study and what the researchers intend to accomplish. However, it may be helpful to consider ensuring that the objectives are phrased consistently (e.g., using “to identify” or “to examine” for all specific objectives). If the variables are treated the same way in the study, the corresponding objectives should be phrased consistently.

Methods
Research design
(page 4, paragraph 2)
It may be beneficial to explicitly state that actions taken to ensure proper design will be detailed in upcoming sections.

Methods
Measurement of variables
Sampling
(page 5, first paragraph)
Overall, the paragraph provides a detailed description of the sampling procedure and data collection process used in the study. However, there is some repetition in the paragraph, particularly in the description of how students were selected from each school. Try to avoid repeating similar information multiple times to streamline the text and avoid redundancy. While the paragraph describes the sampling and data collection procedures, it lacks explanation or rationale for why these specific methods were chosen. Providing a brief explanation of why purposive sampling and random selection were used, as well as the importance of stratification, would add context and clarity to the paragraph.

Methods
Measurement of variables
Sampling
(page 5, paragraph 2)
The information provided in the second paragraph repeats details already mentioned in the first paragraph. It would be beneficial to synthesize these details into a single paragraph to avoid repetition and ensure clarity.

Methods
Figure 1
(page 6)
The inclusion of Figure 1 in the manuscript is noted; however, it appears that the figure is not referenced or discussed in the text. It's important to refer to the figure in the relevant sections of the text where its content is discussed.

Methods
Data collection
Research instruments
(page 6, paragraph 1)
The section appropriately attributes the sources from which the questionnaire items were adapted, including Butler (2016), Al Mutawah (2015), and Woldemichael (2023). This attribution allows researchers to trace the origins of the questionnaire items.
While the section describes the adaptation and validation process briefly, it lacks explanation or rationale for why these specific instruments were chosen or how they were adapted to fit the context of Ethiopia. Providing a brief explanation of the rationale behind selecting these instruments and the adaptation process would add context and clarity to the section.
There are some awkward phrasings that could be revised for clarity and readability. For example, "in which the students were asked to rate" could be clarified to specify what the students were asked to rate and the corresponding categories. While the text effectively outlines the research instruments used in the study, it lacks prior clarification about what the acronym “MAT” refers to.

Methods
Data collection
Research instruments
(page 6, paragraph 2)
It's advisable to ensure clarity when introducing acronyms or abbreviations for the first time in the text. For instance, when first mentioning Item Response Theory (IRT), it's helpful to provide the full term followed by the acronym in parentheses (e.g., Item Response Theory (IRT)).
The information regarding the duration for participants to complete the instruments, approximately 1 hour, has been reiterated. Additionally, details about the absence of breaks and the completion within a class period have been included. To streamline the text and avoid redundancy, it's recommended to consolidate all pertinent details regarding the data collection process into one section (“Data Collection”section rather than the “Sampling” section), eliminating the need for repeated mentions throughout the manuscript.

Methods
Data analysis
(page 6, paragraph 1)
The sentence outlines the procedures involved in adapting and validating the scales for the Ethiopian context. However, to provide a more comprehensive understanding of the analytical techniques applied, it's advisable to include specific details regarding the procedures used in both explanatory factor analysis (EFA) and confirmatory factor analysis (CFA). For EFA, consider elaborating on the rotation method (e.g., varimax, promax, oblimin) and factor extraction methods (e.g., maximum likelihood estimation, principal axes factor). Additionally, provide information on the criteria used to determine the number of factors extracted (e.g., parallel analysis, eigenvalues, scree plot). Similarly, for CFA, detail the indices utilized for model fit assessment (e.g., Comparative Fit Index (CFI), Root Mean Square Error of Approximation (RMSEA)) and any adjustments made to improve model fit. Incorporating these technical details will offer a deeper insight into the analytical methods of the study.

Methods
Data analysis
(page 6, paragraph 2)
There is no prior context on why Cohen’s kappa coefficient was calculated to test inter-scorer reliability.
Instead of stating that "all the items pass all psychometric properties of item analysis," consider providing more specific information about which psychometric properties were assessed and how they were evaluated.
While it's mentioned that Item Response Theory (IRT) was employed for item analysis, it would be beneficial to provide a brief explanation of IRT and its relevance to the analysis.

Methods
Data analysis
(page 6, paragraph 3)
While it's mentioned that structural equation modeling (SEM) was employed as the main data analysis tool, consider providing more detail about the specific SEM used. Mentioning the types of models (e.g., confirmatory factor analysis, path analysis) and any unique features of the analysis can enhance understanding.
The mention of construct validity, convergent and discriminant validity, and internal consistency reliability is valuable. However, providing a brief explanation of these concepts and detailing how they were assessed (e.g., through factor loadings, correlation matrices, McDonald’s omega) would offer a clearer understanding of the validation procedures.
While it’s noted that goodness of fit was investigated, specifying the indices or criteria used to assess model fit (e.g., Comparative Fit Index, Root Mean Square Error of Approximation) as well as reference values, would provide a more precise understanding of the analysis conducted.

Results
Demographic data
(pages 7-8)
It's important to provide a rationale for why specific demographic variables (parental education, parental employment status, and parental profession in science) were included in relation to the study variables (self-efficacy, self-concept, math anxiety, and math achievement). Anticipating this rationale in the introduction and reflecting on it in the discussion ensures consistency throughout the manuscript. If these demographic variables are not used as part of the results or discussion, it should be considered whether reporting them is pertinent.

Results
Item analysis for MAT
Evaluation by experts
(page 8)
The extensive discussion on the procedures and techniques used to assess face validity and content validity, as well as the explanation of the calculations for content-validity indices, appears more suited for the Data Analysis section rather than the Results section. These details provide valuable insights into the methodology employed but do not directly contribute to the presentation of study findings. However, the final sentence, which reports the acceptance of 31 items based on content validity assessment, appropriately belongs in the Results section as it directly pertains to the outcomes of the analysis.

Results
Item analysis for MAT
Cognitive interview
(page 8)

While the cognitive interview results provide valuable insights into the clarity and comprehensibility of the math test items, it's noteworthy that there was no prior mention in the document about conducting interviews to assess item clarity. It's advisable to include a brief explanation in the methods section outlining the planned cognitive interview process and its objectives.

Results
Item difficulty and discrimination index
(pages 8-10)

The detailed explanation provided regarding the test characteristic curve, test-information-function curve, and the application of the two-parameter IRT model to determine item difficulty and discrimination indices offers valuable insights into the methodology employed. However, it appears that some sections of this information may be more appropriately categorized under the Methods section, particularly the description of the test characteristic curve and the test-information-function curve. These aspects outline the procedures and techniques utilized in the analysis rather than presenting the actual results of the study. Conversely, the outcomes of the analysis, including the identification of items retained for the final data collection based on acceptable difficulty and discrimination indices, are more aligned with the presentation of results. To enhance clarity and organization, it’s recommended to discern which sections of the given information correspond to methods and which pertain to results, ensuring consistency in reporting throughout the manuscript.

Results
Scale Validation
Confirmatory Factor Analysis
Table 4
(pages 10-11)
The inclusion of Table 4 is appreciated, as it offers insights into the allocation of items to different factors. However, to enhance clarity and interpretation, it's advisable to edit the table in a way that clearly presents the content of the items and identifies factors 1, 2, and 3 as self-efficacy, self-concept, and math anxiety, respectively. The title of the table should accurately reflect its content, such as “Allocation of Items to Self-Efficacy, Self-Concept, and Math Anxiety Factors”.
Additionally, while principal component analysis (PCA) is a commonly used method for factor extraction, it's important to note that it may not always be the best choice for determining the underlying structure of an instrument. Unlike other methods such as maximum likelihood estimation, PCA accounts for all variance in the data rather than solely focusing on shared variance among items, which could lead to a less accurate representation of the underlying constructs. Therefore, considering alternative factor extraction methods that prioritize shared variance may provide a more robust analysis of the instrument's structure.
While varimax rotation is a widely used method for orthogonal rotation and offers easily interpretable results, it's essential to consider the nature of the underlying factors, particularly in psychological constructs such as self-efficacy, self-concept, and math anxiety. Orthogonality may not always be the most appropriate assumption for factors in psychological sciences, where correlations among factors are expected due to the interrelated nature of human behavior. Therefore, it is advisable to reconsider the choice of rotation method and explore oblique rotation techniques, which allow factors to correlate and may provide a more accurate representation of the underlying structure.

Results
Scale Validation
Confirmatory Factor Analysis
(page 11, last paragraph)
It's recommended to present the interpretation of the scree plot and determination of the number of factors before displaying the table with items allocation to the extracted factors. This sequence ensures that information with the rationale behind the decision to retain three factors based on the scree plot analysis is first provided.

Results
Structural equation modeling
(page 11, paragraphs 1-3)
It would improve the clarity and focus of the results section to integrate the observations from Tables 5, 6, and 7 into a single paragraph.

Results
Structural equation modeling
(Tables 5, 6, and 7, pages 11-12)
To enhance clarity and interpretation, it is recommended to include a brief description of the items' content within the tables. Additionally, consider adding a footnote specifying the acronyms used to indicate the content of each column. As it is generally better to focus on reporting the model path coefficients rather than detailed regression-like statistics for individual observed variables, revise the decision on reporting these detailed tables.

Results
Structural equation modeling
Modification indices
(page 12, paragraphs 1-2)
While modifications were mentioned, the specific changes made based on the modification indices are not detailed. Providing insights into the adjustments made would enhance transparency and understanding of the model.
The interpretation of goodness-of-fit statistics should be more nuanced. While the values provided indicate some fit indices, a comprehensive assessment considering multiple fit indices and their thresholds would offer a more robust evaluation of model fit (there are more indices reported in Table 9). For thresholds consider revising:
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal, 6(1), 1-55. (Ref [1])
The reported goodness-of-fit statistics (relative Chi-Square = 655.147; CFI = .817, RMSEA = .089, SRMR = .072, p = .000) indicate a model fit that may not meet the criteria for good fit according to Hu and Bentler's guidelines. Beyond considering Hu and Bentler's guidelines for model fit evaluation, it is crucial to find references that support the alignment between the obtained goodness-of-fit statistics and the conclusion of a good model fit. This will help ensure that the interpretation of the fit indices is substantiated by established literature and standards in the field, enhancing the credibility and validity of the model assessment.
Tables 8 and 9, which detail the goodness of fit for the original and modified models, may not be necessary if the goodness of fit statistics are thoroughly explained in the text. Providing a comprehensive explanation of the goodness of fit statistics within the text can effectively convey the model's fit without the need for additional tables

Results
Structural equation modeling
(Figures 5 and 6, page 13)
Consider editing the final model figure to achieve a more organized and visually engaging presentation that effectively communicates the model findings rather than provide model figures directly as they result from Stata. The model prior to modification does not require a figure.
The model path figure with coefficients in a clear and comprehensive manner becomes unnecessary to include an additional table (Table 10) summarizing the structural level estimates. The clear presentation of the model path figure with coefficients can effectively convey the structural relationships and estimates, making a separate table redundant. The text should accurately reference the coefficients presented in the figure depicting the final model.

Results
Structural equation modeling
(page 13 last paragraph – page 15)
This text appears to be part of the discussion section rather than the results section. In the discussion section, authors typically interpret their findings in the context of existing literature and provide explanations for the observed results. The text discusses the results of the study in relation to findings from other studies, synthesizing the information to draw conclusions and implications.

Conclusion
(page 15)
The conclusions accurately summarize the main findings regarding the relationships between self-efficacy, self-concept, anxiety, and math achievement. However, it's important to provide a nuanced interpretation of the results, acknowledging any limitations or potential confounding factors that may have influenced the findings.

General comments
Given the suggestion to remove several tables, take the opportunity to delve deeper into the background, interpretation of the data obtained, and its implications. Review the organization of the document to ensure that the methodological information is presented prior to the results and that they are clearly understood in relation to the preceding methodology. Review the headings and subheadings to ensure that they all correspond to the accompanying text.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

References

1. Hu, L. T., & Bentler, P. M.: Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal. 1999.

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Psychology

We confirm that we have read this submission and believe that we have an appropriate level of expertise to state that we do not consider it to be of an acceptable scientific standard, for reasons outlined above.

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Cristian Rojas-Barahona, Universidad de Talca, Talca, Chile

Anabel Fernández, University of Talca, Talca, Chile
Krzysztof Cipora, Loughborough University, Loughborough, UK
Jones Apawu, University of Education Winneba, Winneba, Ghana

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Reviewer Report

5 Views

13 May 2024 | for Version 1

Jones Apawu, University of Education Winneba, Winneba, Central, Ghana

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Approved With Reservations

I have thoroughly read through the manuscript have fashioned my report under the following headings:

Abstract:
The research design and population are missing in the abstract.

Introduction:

Once you have a direct quotation, the page number(s) must be provided and vice versa. On page 3, line 3 from the top, no page number was provided for this quotation “Self-efficacy can be understood as the individual’s conviction that he or she is capable of successfully performing a specific given task” (Bandura, 1997).
On page 3, line 14 from the top, page number was provided without any quotes on any text (see Richardson and Suinn, 1972, p. 551).
On page 3, line 27 from the top, the parenthetical citations should be arranged in alphabetical order (i.e. Tamire, 1997; Adem, 2005; Tesfaye, 2007 should be Adem, 2005; Tamire, 1997; Tesfaye, 2007). There are others in the manuscript.
On page 4, the subheading should be "Research hypotheses" not "Research hypothesis" since there were three (3) hypotheses that were formulated. H01, H02 and H03 should be H₀₁, H₀₂, H₀₃.
The "Objectives" subheading should come before the "Research hypotheses".

Methods:

On page 4, the subheading "Research design" should be deleted since the writings are not only about research design.
On page 4, line 10 from the bottom, "…the researcher..." should be "…the researchers..." since the manuscript has three (3) authors.
On page 4, line 17, the "quantitative methods" in my opinion should be reconciled with interviews under the subheading "Data sources".
Sampling heading on page 5 should be "Population and sampling".
On page 5 the population should be stated explicitly. For instance, the population of Ethiopia is 128,911,361 but not a description of e.g., all the people in Ethiopia. On page 5, how did the authors arrive at 122, 131, and 131 grade 12 students?
The following sentences, i.e. "Once these students were selected randomly, the questionnaire together with the mathematics achievement test was distributed in hard copy to each respondent personally by the researcher. It took about one hour for students to complete the questionnaire as well as to take the math achievement test. The questionnaire and the math achievement were provided to students in hard copy, both attached together. Students first completed the questionnaire including their demographic characteristics and then performed on the mathematics achievements test. It took about one hour for students to complete the questionnaire as well as to take the math achievement test. The questionnaire and the math achievement were provided to students in hard copy, both attached together. Students first completed the questionnaire including their demographic characteristics and then performed on the mathematics achievements test." should not be under "Population and sampling". This sentence, "This was so that grade 12 students were purposively selected to perform on a mathematics achievement test which includes all chapters of mathematics contents from grade 9 to grade 12." is not clear. The subheading "Population and sampling" must be written again making sure that things not relating to population and sampling are not included.
The authors should avoid vague pointers such as below, above, s/he, etc. For instance, on page 5, line 6 from the bottom, below after Table 1 should be deleted.
On page 5, line 1 from the bottom, the sentence "The stratification was also balanced based on the gender of students" is not clear. From Table 1, does it mean the population of the three (3) schools is 500,000 or more?
On page 6, there is a conceptual framework which I think the authors should have a brief write-up on it and it must come after the "Research hypotheses" subheading.
On page 6, lines 6 and 7 under "Research instruments", "... questionnaire and MAT file was ..." should be "... questionnaire and MAT file were ...". The sentence "The factor analysis along with the structural equation modeling was employed to validate the adapted questionnaire" under "Research instruments" seems inappropriate since factor analysis and SEM are not research instruments.
On page 6, line 10 under "Research instruments", IRT should be in full and abbreviated in parentheses since it is the first usage.
On page 6, line 7 from the bottom, for the sentence, “The data was entered into SPSS 23, and Stata 13 was used for analysis” should be made clearer. One software is used for data entering the other one without data is used for data analysis. SPSS 23 should be IBMSPSS 23.
On page 6, line 1 from the bottom, … “SPSS data” is not clear.
To make write-ups fit well, the authors should have paragraphs under the heading Methods since there were instances write-ups do not fit under some subheadings.
Pilot testing of the instruments was conspicuously missing.

Results:

On page 7, line 9 from the top, above should be deleted after Table 2.
What was the motivation for demographic data. In my opinion, demographic data is not necessary because there was no research question and/or research hypothesis that needed demographic results. Consequently, Tables 2 and 3 are not necessary.
There should be a preamble under “Item analysis for Mathematics achievement Test (MAT)”.
Write-ups under “Item analysis for Mathematics achievement Test (MAT)” up to before scale validation fit under Methods.
On page 10, the sentence “That is, the above 25 items, namely item-2, item-4, item-6, item-8, item-9, item-10, item-11, item-12, item-13, item-14, item-15, item-16, item-17, item-18, item-20, item-21, item-22, item-24, item-25, item-26, item-27, item-28, item-29, item-30, and item-31” should be deleted because it is a repetition.
On page 10, line 2 from the top, “because they met the acceptable level of discriminating and difficulty indices” should come after collection.
On page 10, line 1 on top of Table 4 do not reconcile with “In this regard, 25 items of self-concept and 25 items of self-efficacy scales were adapted from Butler (2016) whereas 26-items of the anxiety scale were adapted from Al Mutawah (2015).” On page 6, lines 4 and 5 under “Research instruments”.
The authors should have a preamble under “Structural equation modeling”.
On page 11, line 1 under “Measurement level model estimates”, (α=00<.05) should be relooked at and corrected.

Conclusion:

The conclusion heading should be “Conclusions and recommendations”.
On page 15, line 11 under “Conclusion”, hypothesis should be hypotheses.
Consent of participants write-ups should be part of Methods.

In-text citations and references list:

The authors should situate in-text citations and the references list in known style of referencing. The style used in the manuscript seems to have the lens of APA referencing which was not followed judiciously.
The references list should be reformatted with the lens of APA style of referencing.
The authors should arrange the references list in alphabetical order. For instance, “Hodges CB: Self-efficacy in the context of online learning environments: A review of the literature and directions for research. Perform. Improv. Q. 2008; 20(3-4): 7–25” should come before “Kiamanesh AR, Hejazi E, Esfahani ZN: The role of math self-efficacy, math self-concept, perceived usefulness of mathematics and math anxiety in math achievement. Proceedings of the 3rd International Biennial SELF Research Conference, Self-Concept, Motivation and Identity: Where to from here. 2004.”
The authors can peruse the basics of APA style of referencing from https://libguides.csudh.edu/ld.php?content_id=52097964

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Yes
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Mathematics Education in general, ICT integration into the teaching and learning of mathematics, differentiated instruction, TPACK

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

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Reviewer Report

7 Views

17 Apr 2024 | for Version 1

Krzysztof Cipora, Loughborough University, Loughborough, England, UK

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Not Approved

In the paper, the authors aim at investigating relations between mathematics anxiety, mathematics self-concept, mathematics self-efficacy, and mathematics performance in 12th graders in Kafa zone in Ethiopia. They show that both self-efficacy and self-concept are related to mathematics performance while mathematics anxiety is not linked to mathematics performance.

It is great that the study has been conducted in a population, which has been understudied, and this is a great value. In that sense it can make a valuable contribution to our understanding of mathematics anxiety and attitudes and its relations to mathematics performance. It needs a bit more thorough theoretical background, some clarifications about the context and methods. Discussion needs substantial improvements as well.

I tried to be as constructive as possible in my comments below. They are ordered according to the order of appearance of the issues in the paper.

Specific comments:

Abstract:

method section, please name the country, not only the region
results section: maybe mention also relationships between predictors (associations between math anxiety, math-self efficacy and self-concept).
No effect of math anxiety on performance - not at all, or not after controlling for other predictors?

Keywords: I assume it should be “math anxiety” rather than “anxiety”, same holds true for self-concept and self-efficacy.

Introduction:
Somewhat fails to provide distinction between self-concept / self-efficacy and those constructs when referred to mathematics (I.e., math self-concept, math self-efficacy). There is quite a lot of literature on that, and it would be good to introduce this distinction.

It would be also good to say something about interrelations between math anxiety, math self-concept and math self-efficacy. The paper by Lee (2009) analysing PISA data with respect to these constructs would be a good starting point here (I am not related to that paper).

When discussing the role mathematics anxiety, self-concept and self-efficacy play for math achievement, the authors may consider reporting typical effect sizes associated with these effects.

In the “Problem statement” section the authors discuss how important it is to look at these problems is Kafa zone. It left me wondering whether there is something specific to this region which makes it different from the rest of Ethiopia? Or it is representative to the entire country. It may be interesting to some of the readers too.

“Research hypothesis” section - I think it would make more sense to state the research hypotheses rather than null hypotheses. This is the more typical way of doing it and it may be more convenient to the readers.

“Methods” section
I am wondering how much the information about neighbours of Ethiopia helps here. What would be somewhat more informative would be giving some information about the population / educational system / cultural values / stereotypes about mathematics etc.

Last sentence of the first paragraph of the “Research design” section and the entire second paragraph of this section does not contain much useful information as it essentially states that authors carefully conducted the study:
“High focus was given to a survey method so as to portray the extent of association between pupils’ self-concept, self- efficacy, and anxiety related to mathematics and their academic performance.

Considerable effort was exerted to prevent the effect of extraneous variables to bias the results of this study. In this regard, the researcher employed proper design, suitable tools of data collection, appropriate methods of data analysis, proper sample size and sample selection techniques so as to prevent the confounding variables to alter the results of the study.”

In my view this section may be skipped.

“Measurement of variables” section - each of the paragraphs (bullet points) says one sentence abut the instrument, which is also not very informative e.g., “self-developed scales based on self-efficacy theory”. I think this section could be combined with the “Research instruments” section.

“Sampling” section - the second paragraph is just a duplication of the ending of the first paragraph just above. Please remove the duplicated statement. The third paragraph could be streamlined a bit.
6-th paragraph of this section says that sampling considered “students’ sections”. However, these are not explained anywhere. Please give some details.

The schools being recruited are named several times. Naming them once would be enough.

Table 1 - Firstly, I am not sure whether it is needed here. It would be enough to state that this method was used. I am also unsure whether the authors considered the population size (and the size of the population is not provided). To be fair, I am not familiar with this method of sample size estimation. How does it relate to power analysis which is probably the more adequate technique as it looks into probability of detecting effects of specified size.

As a measure of reliability the authors are using Cohen’s kappa, which they define as “inter-scorer reliability”. I am not sure how this method is suited for this type of analysis. Were there different scorers evaluating anxiety / self-concept of each student?

“All items pass all psychometric properties of item analysis” - please be more specific.

Age of participants - they were all grade 12 students but the age range is 18-25. Was this range of 7 years due to some outliers who repeated the class many times / specificities of local educational system / some other factors. Relatedly, the row “Age” in Table 2 is not very informative.

“Demographic Data” section: What does “profession in science” mean? It seems that more than 1/3 of participants came from families where at least one parent had a “profession in science”. Does it mean they were children of academics? If yes, I am somewhat surprised and doubt whether the sample was representative of the population (in any country, I can think of).

“Evaluation by experts” section - please specify who the experts were (i.e., what was their expertise?)

“Item difficulty and discrimination index” - Make the last section more concise - there is no need to name all the items that were retained twice in two adjacent sentences.

Work a bit more on streamlining. For instance text in the section “Measurement level model estimates” is a set of single-sentence paragraphs. Similar problem in the last paragraph of p.14, where single sentences are referring to different papers, but would benefit from streamlining.

I also find it hard to follow how the authors come from 25 items of self-concept, 25 items of self-efficacy, and 26 items of Math anxiety (as reported on p.6) to 19 items overall in the CFA. Maybe I am missing something, but I guess a statistician should have a look into this. Responses to only 19 items are also present in shared datafile, while the number of items shared in the OSF is different than what was reported in the paper and what we have in the shared data. Potentially some SPSS / STATA syntax would help, as well as sharing data in more raw format.

P.13 “predicator” -> “predictor”.

Statistics and reporting - p-value is never 0. It can be negligibly small and then should be denoted < 0.001.

Figures 5 and 6: What do A, C, and E mean in item names? Does it mean that items originally designed as anxiety (my suspicion what A may stand for) turned out to load self-concept? Same holds for other letters and loadings.

Discussion (section “Conclusion” is quite weak and would need substantial rewriting. As for now, in my view it only paraphrases the results, and there is not much attempt at discussing the implications of the findings etc.

Style:
First sentence of paragraph 4 of the introduction could be somewhat streamlined. Now it goes “many studies in Ethiopia have focused on (…) achievement in Ethiopia.”

“Problem statement” section: this may be streamlined too: “The result pointed out that least mathematics self-concept and least mathematics self-efficacy frequently exhibit elevated mathematics anxiety”

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

I cannot comment. A qualified statistician is required.
Are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Numerical cognition, Cognitive psychology, mathematics anxiety

I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above.

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Reviewer Report

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25 Mar 2024 | for Version 1

Cristian Rojas-Barahona, Faculty of Psychology, Universidad de Talca, Talca, Maule Region, Chile

Anabel Fernández, Faculty of Psychology, University of Talca, Talca, Chile

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Revision:
The article investigates the influence of self-efficacy, self-concept, and anxiety on mathematics achievement among students in the Kafa Zone, Ethiopia. Utilizing varied techniques including confirmatory factor analysis and structural equation modeling, the study finds that self-efficacy and self-concept positively influence mathematics achievement, while anxiety shows a negative relationship, albeit not statistically significant. The findings underscore the importance of addressing self-efficacy and self-concept to enhance mathematics performance in this context. Recommendations are made for various stakeholders to pay special attention to these variables. The study highlights the significance of psychological factors in mathematics achievement and provides valuable insights for educators, policymakers, and researchers interested in improving mathematics education outcomes in similar settings.
Specific comments per section:
Section
Comment

Abstract
The abstract highlights the use of Confirmatory Factor Analysis along with structural equation modeling to analyze the data, offering initial insight into the methodology employed. However, the abstract could benefit from further clarity by explicitly stating the purpose of each technique utilized, including Item Response Theory and Exploratory Factor Analysis. Providing this clarification would enhance the abstract's clarity and ensure a clear understanding of the analytical approach taken in the study.

Introduction
(page 3, paragraphs 1-2)
If self-efficacy and self-concept are explained in independent paragraphs, it would be reasonable to expect that math anxiety, being another variable under study, would also receive a comparable level of explanation. Therefore, it's advisable to revisit the section and consider whether each variable is receiving the attention it deserves based on its significance to the research question and the overall aim of the study.

Introduction
(page 3, paragraph 3, last sentence)
While it is acknowledged that math self-concept, self-efficacy, and math anxiety play significant roles in mathematics achievement, it is important to recognize that there may be other factors beyond the scope of this study that also contribute to student performance in mathematics. Therefore, rather than stating definitively that these variables are the main factors influencing math achievement, it may be more appropriate to acknowledge them as important factors among others, the full extent of which may require further investigation.

Introduction
(page 3, paragraph 4, first sentence)
Revise the sentence:
“In Ethiopia, as pupils’ low academic-achievement and low pass rates as well as high dropouts were serious problems
(Tamire, 1997; Adem, 2005; Tesfaye, 2007) many studies in Ethiopia have focused on factors affecting students’
academic achievement in Ethiopia.”
Edit and avoid repetition of "in Ethiopia".

Introduction
(page 3, paragraph 5, first sentence)
While it is asserted that mathematics plays a crucial role in daily life and national development, and that the achievement of math is significantly influenced by factors such as math anxiety, math self-concept, and math self-efficacy, it is important to ensure that these claims are proved by empirical evidence. Therefore, providing citations and references supporting the results that justify the influence of math anxiety, math self-concept, and math self-efficacy on math achievement would enhance the validity of the assertion.

Introduction
Problem statement
(page 3, first paragraph)
It is suggested that acronyms be used for the main variables (math anxiety (MA), mathematics self-efficacy (MSE)), such as it is happening in this section, from its first appearance in the text and throughout the entire document. This practice will enhance readability and streamline the presentation of the variables in the study.

Introduction
Problem statement
(page 4, first paragraph)
Based on the complex relationships among variables such as self-efficacy, self-concept, and math anxiety, it may be advisable to avoid using the term “linear combination”. Since the relationship between these variables could be nonlinear, it might be more appropriate to describe their interplay without implying a specific mathematical model.

Introduction
Research hypotheses
(page 4)
While stating the hypotheses as null hypotheses can be appropriate in certain contexts, it's important to ensure that it aligns with the research aims and questions. Consider whether stating the hypotheses as research hypotheses would better suit the goals of your study and provide a clearer framework for your analysis and interpretation.
Make sure to use the plural form “hypotheses” instead of “hypothesis” when referring to multiple hypotheses in the article.

Introduction
Objectives
(page 4)
The objectives effectively outline the scope of the study and what the researchers intend to accomplish. However, it may be helpful to consider ensuring that the objectives are phrased consistently (e.g., using “to identify” or “to examine” for all specific objectives). If the variables are treated the same way in the study, the corresponding objectives should be phrased consistently.

Methods
Research design
(page 4, paragraph 2)
It may be beneficial to explicitly state that actions taken to ensure proper design will be detailed in upcoming sections.

Methods
Measurement of variables
Sampling
(page 5, first paragraph)
Overall, the paragraph provides a detailed description of the sampling procedure and data collection process used in the study. However, there is some repetition in the paragraph, particularly in the description of how students were selected from each school. Try to avoid repeating similar information multiple times to streamline the text and avoid redundancy. While the paragraph describes the sampling and data collection procedures, it lacks explanation or rationale for why these specific methods were chosen. Providing a brief explanation of why purposive sampling and random selection were used, as well as the importance of stratification, would add context and clarity to the paragraph.

Methods
Measurement of variables
Sampling
(page 5, paragraph 2)
The information provided in the second paragraph repeats details already mentioned in the first paragraph. It would be beneficial to synthesize these details into a single paragraph to avoid repetition and ensure clarity.

Methods
Figure 1
(page 6)
The inclusion of Figure 1 in the manuscript is noted; however, it appears that the figure is not referenced or discussed in the text. It's important to refer to the figure in the relevant sections of the text where its content is discussed.

Methods
Data collection
Research instruments
(page 6, paragraph 1)
The section appropriately attributes the sources from which the questionnaire items were adapted, including Butler (2016), Al Mutawah (2015), and Woldemichael (2023). This attribution allows researchers to trace the origins of the questionnaire items.
While the section describes the adaptation and validation process briefly, it lacks explanation or rationale for why these specific instruments were chosen or how they were adapted to fit the context of Ethiopia. Providing a brief explanation of the rationale behind selecting these instruments and the adaptation process would add context and clarity to the section.
There are some awkward phrasings that could be revised for clarity and readability. For example, "in which the students were asked to rate" could be clarified to specify what the students were asked to rate and the corresponding categories. While the text effectively outlines the research instruments used in the study, it lacks prior clarification about what the acronym “MAT” refers to.

Methods
Data collection
Research instruments
(page 6, paragraph 2)
It's advisable to ensure clarity when introducing acronyms or abbreviations for the first time in the text. For instance, when first mentioning Item Response Theory (IRT), it's helpful to provide the full term followed by the acronym in parentheses (e.g., Item Response Theory (IRT)).
The information regarding the duration for participants to complete the instruments, approximately 1 hour, has been reiterated. Additionally, details about the absence of breaks and the completion within a class period have been included. To streamline the text and avoid redundancy, it's recommended to consolidate all pertinent details regarding the data collection process into one section (“Data Collection”section rather than the “Sampling” section), eliminating the need for repeated mentions throughout the manuscript.

Methods
Data analysis
(page 6, paragraph 1)
The sentence outlines the procedures involved in adapting and validating the scales for the Ethiopian context. However, to provide a more comprehensive understanding of the analytical techniques applied, it's advisable to include specific details regarding the procedures used in both explanatory factor analysis (EFA) and confirmatory factor analysis (CFA). For EFA, consider elaborating on the rotation method (e.g., varimax, promax, oblimin) and factor extraction methods (e.g., maximum likelihood estimation, principal axes factor). Additionally, provide information on the criteria used to determine the number of factors extracted (e.g., parallel analysis, eigenvalues, scree plot). Similarly, for CFA, detail the indices utilized for model fit assessment (e.g., Comparative Fit Index (CFI), Root Mean Square Error of Approximation (RMSEA)) and any adjustments made to improve model fit. Incorporating these technical details will offer a deeper insight into the analytical methods of the study.

Methods
Data analysis
(page 6, paragraph 2)
There is no prior context on why Cohen’s kappa coefficient was calculated to test inter-scorer reliability.
Instead of stating that "all the items pass all psychometric properties of item analysis," consider providing more specific information about which psychometric properties were assessed and how they were evaluated.
While it's mentioned that Item Response Theory (IRT) was employed for item analysis, it would be beneficial to provide a brief explanation of IRT and its relevance to the analysis.

Methods
Data analysis
(page 6, paragraph 3)
While it's mentioned that structural equation modeling (SEM) was employed as the main data analysis tool, consider providing more detail about the specific SEM used. Mentioning the types of models (e.g., confirmatory factor analysis, path analysis) and any unique features of the analysis can enhance understanding.
The mention of construct validity, convergent and discriminant validity, and internal consistency reliability is valuable. However, providing a brief explanation of these concepts and detailing how they were assessed (e.g., through factor loadings, correlation matrices, McDonald’s omega) would offer a clearer understanding of the validation procedures.
While it’s noted that goodness of fit was investigated, specifying the indices or criteria used to assess model fit (e.g., Comparative Fit Index, Root Mean Square Error of Approximation) as well as reference values, would provide a more precise understanding of the analysis conducted.

Results
Demographic data
(pages 7-8)
It's important to provide a rationale for why specific demographic variables (parental education, parental employment status, and parental profession in science) were included in relation to the study variables (self-efficacy, self-concept, math anxiety, and math achievement). Anticipating this rationale in the introduction and reflecting on it in the discussion ensures consistency throughout the manuscript. If these demographic variables are not used as part of the results or discussion, it should be considered whether reporting them is pertinent.

Results
Item analysis for MAT
Evaluation by experts
(page 8)
The extensive discussion on the procedures and techniques used to assess face validity and content validity, as well as the explanation of the calculations for content-validity indices, appears more suited for the Data Analysis section rather than the Results section. These details provide valuable insights into the methodology employed but do not directly contribute to the presentation of study findings. However, the final sentence, which reports the acceptance of 31 items based on content validity assessment, appropriately belongs in the Results section as it directly pertains to the outcomes of the analysis.

Results
Item analysis for MAT
Cognitive interview
(page 8)

While the cognitive interview results provide valuable insights into the clarity and comprehensibility of the math test items, it's noteworthy that there was no prior mention in the document about conducting interviews to assess item clarity. It's advisable to include a brief explanation in the methods section outlining the planned cognitive interview process and its objectives.

Results
Item difficulty and discrimination index
(pages 8-10)

The detailed explanation provided regarding the test characteristic curve, test-information-function curve, and the application of the two-parameter IRT model to determine item difficulty and discrimination indices offers valuable insights into the methodology employed. However, it appears that some sections of this information may be more appropriately categorized under the Methods section, particularly the description of the test characteristic curve and the test-information-function curve. These aspects outline the procedures and techniques utilized in the analysis rather than presenting the actual results of the study. Conversely, the outcomes of the analysis, including the identification of items retained for the final data collection based on acceptable difficulty and discrimination indices, are more aligned with the presentation of results. To enhance clarity and organization, it’s recommended to discern which sections of the given information correspond to methods and which pertain to results, ensuring consistency in reporting throughout the manuscript.

Results
Scale Validation
Confirmatory Factor Analysis
Table 4
(pages 10-11)
The inclusion of Table 4 is appreciated, as it offers insights into the allocation of items to different factors. However, to enhance clarity and interpretation, it's advisable to edit the table in a way that clearly presents the content of the items and identifies factors 1, 2, and 3 as self-efficacy, self-concept, and math anxiety, respectively. The title of the table should accurately reflect its content, such as “Allocation of Items to Self-Efficacy, Self-Concept, and Math Anxiety Factors”.
Additionally, while principal component analysis (PCA) is a commonly used method for factor extraction, it's important to note that it may not always be the best choice for determining the underlying structure of an instrument. Unlike other methods such as maximum likelihood estimation, PCA accounts for all variance in the data rather than solely focusing on shared variance among items, which could lead to a less accurate representation of the underlying constructs. Therefore, considering alternative factor extraction methods that prioritize shared variance may provide a more robust analysis of the instrument's structure.
While varimax rotation is a widely used method for orthogonal rotation and offers easily interpretable results, it's essential to consider the nature of the underlying factors, particularly in psychological constructs such as self-efficacy, self-concept, and math anxiety. Orthogonality may not always be the most appropriate assumption for factors in psychological sciences, where correlations among factors are expected due to the interrelated nature of human behavior. Therefore, it is advisable to reconsider the choice of rotation method and explore oblique rotation techniques, which allow factors to correlate and may provide a more accurate representation of the underlying structure.

Results
Scale Validation
Confirmatory Factor Analysis
(page 11, last paragraph)
It's recommended to present the interpretation of the scree plot and determination of the number of factors before displaying the table with items allocation to the extracted factors. This sequence ensures that information with the rationale behind the decision to retain three factors based on the scree plot analysis is first provided.

Results
Structural equation modeling
(page 11, paragraphs 1-3)
It would improve the clarity and focus of the results section to integrate the observations from Tables 5, 6, and 7 into a single paragraph.

Results
Structural equation modeling
(Tables 5, 6, and 7, pages 11-12)
To enhance clarity and interpretation, it is recommended to include a brief description of the items' content within the tables. Additionally, consider adding a footnote specifying the acronyms used to indicate the content of each column. As it is generally better to focus on reporting the model path coefficients rather than detailed regression-like statistics for individual observed variables, revise the decision on reporting these detailed tables.

Results
Structural equation modeling
Modification indices
(page 12, paragraphs 1-2)
While modifications were mentioned, the specific changes made based on the modification indices are not detailed. Providing insights into the adjustments made would enhance transparency and understanding of the model.
The interpretation of goodness-of-fit statistics should be more nuanced. While the values provided indicate some fit indices, a comprehensive assessment considering multiple fit indices and their thresholds would offer a more robust evaluation of model fit (there are more indices reported in Table 9). For thresholds consider revising:
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal, 6(1), 1-55. (Ref [1])
The reported goodness-of-fit statistics (relative Chi-Square = 655.147; CFI = .817, RMSEA = .089, SRMR = .072, p = .000) indicate a model fit that may not meet the criteria for good fit according to Hu and Bentler's guidelines. Beyond considering Hu and Bentler's guidelines for model fit evaluation, it is crucial to find references that support the alignment between the obtained goodness-of-fit statistics and the conclusion of a good model fit. This will help ensure that the interpretation of the fit indices is substantiated by established literature and standards in the field, enhancing the credibility and validity of the model assessment.
Tables 8 and 9, which detail the goodness of fit for the original and modified models, may not be necessary if the goodness of fit statistics are thoroughly explained in the text. Providing a comprehensive explanation of the goodness of fit statistics within the text can effectively convey the model's fit without the need for additional tables

Results
Structural equation modeling
(Figures 5 and 6, page 13)
Consider editing the final model figure to achieve a more organized and visually engaging presentation that effectively communicates the model findings rather than provide model figures directly as they result from Stata. The model prior to modification does not require a figure.
The model path figure with coefficients in a clear and comprehensive manner becomes unnecessary to include an additional table (Table 10) summarizing the structural level estimates. The clear presentation of the model path figure with coefficients can effectively convey the structural relationships and estimates, making a separate table redundant. The text should accurately reference the coefficients presented in the figure depicting the final model.

Results
Structural equation modeling
(page 13 last paragraph – page 15)
This text appears to be part of the discussion section rather than the results section. In the discussion section, authors typically interpret their findings in the context of existing literature and provide explanations for the observed results. The text discusses the results of the study in relation to findings from other studies, synthesizing the information to draw conclusions and implications.

Conclusion
(page 15)
The conclusions accurately summarize the main findings regarding the relationships between self-efficacy, self-concept, anxiety, and math achievement. However, it's important to provide a nuanced interpretation of the results, acknowledging any limitations or potential confounding factors that may have influenced the findings.

General comments
Given the suggestion to remove several tables, take the opportunity to delve deeper into the background, interpretation of the data obtained, and its implications. Review the organization of the document to ensure that the methodological information is presented prior to the results and that they are clearly understood in relation to the preceding methodology. Review the headings and subheadings to ensure that they all correspond to the accompanying text.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

References

1. Hu, L. T., & Bentler, P. M.: Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal. 1999.

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Psychology

We confirm that we have read this submission and believe that we have an appropriate level of expertise to state that we do not consider it to be of an acceptable scientific standard, for reasons outlined above.

Respond to this report

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Mathematics self-efficacy, self-concept and anxiety in relation to Mathematics achievement: The case of Kafa Zone School adolescents, Ethiopia

Abstract

Background

Methods

Results

Conclusions

Keywords

Introduction

Problem statement

Research hypothesis

Objectives

Methods

Research design

Data sources

Measurement of variables

Table 1. Population range and sample size approximation.

Figure 1. The hypothesized model and the association between the constructs based on theories of self-efficacy, anxiety, and self-concept.

Data collection

Data analysis

Results

Response rate

Demographic data

Table 2. Gender, age, school and grade level.

Table 3. Parental education, parental employment status, and parental profession in science.

Figure 2. The Test Characteristic Curve (TCC).

Figure 3. The Test Information Curve (TIC).

Figure 4. The scree plot.

Table 4. Rotated component matrixa.

Table 5. Measurement model estimates anxiety items.

Table 6. Measurement model self-efficacy estimates.

Table 7. Measurement model estimate of self-concept.

Figure 5. Fully fledged model.

Figure 6. The modified model.

Table 8. Overall goodness of fit.

Modification indices

Table 9. The modified model goodness of fit.

Table 10. Structural level estimates.

Conclusion

Consent of participants

Data availability

Underlying data

Extended data

References

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Table 4. Rotated component matrix^a.