Occupational structure of bearers of Jewish rabbinical, occupational and generic surnames

Participants

Our data was acquired over four years (November 2015 – February 2020) from individuals who were part of an educational family history program that was implemented by the Am haZikaron Institute for Science and Heritage of the Jewish People in Tel Aviv, Israel. Our program was obligatory for participants of a larger, very inclusive program so that to the best of our knowledge the only bias in the sample was some degree of affiliation with the Jewish people.

The individuals were Russian-speaking Jewish family members residing in the Former Soviet Union (FSU). They voluntarily provided genealogical data for the program via online forms that were sent to them before their arrival in Tel Aviv (see section Data collection). The forms were presented in the native language of the individual (Russian) and informed the individuals that their data could be used for future academic purposes. Completion of the form was taken as consent to allow their data to be used for this academic study (some participants chose not to complete the form). This study did not seek ethical approval as it was deemed low risk, none of the participants were considered vulnerable, the participants consented for their data to be used in future academic research, and all participants were over 18 years of age.

Data from an individual was not selected for inclusion in this study if it was intentionally distorted. Data verification was accomplished during a meeting in Tel Aviv between the authors. Upon the completion of the educational program, the participants returned to their home countries.

Data collection

Information was obtained on professions of a participant’s family members for the last four generations. This resulted in a collection of data on individuals who were born throughout the 20th century. The educational programs at Am haZikaron are open to all, and so there was no known statistical bias toward any particular professions. Similarly, there is no known correlation between the starting letter of the name and the profession. Hence, to the best of our judgement, the obtained data, arranged alphabetically, is a random list of Jewish individuals and their professions. The randomness holds up to small clusters of individuals who belong to the same family and have some correlations. These correlations are yet to be studied and are not the focus of our study. It will be seen later that randomness is consistent with the statistics.

In the research by Clark et al. (Clark, 2015; Clark, 2012; Clark et al., 2015), the major source of information were professional directories that list all individuals in a particular professional area. In contrast, our data is a random pool of the population that necessitates a different methodology for analysis. We partitioned the population into the three groups of surnames (rabbinical, occupational, generic), which could be biased with respect to their occupational distribution due to the bias in their ancestry. We checked if the bias persists through time and found that there is a statistically significant difference in the professional preferences of the three groups.

Dataset description and considerations

We collected the data over four years until the pool included a statistically significant amount of surnames where the confidence interval allowed to reasonably fix the share of each profession in the total population. We obtained data on 858 (57.8.% men) bearers of rabbinical and 1057 (59.7% men) bearers of occupational surnames. The other 7471 (57.6% men) individuals had a generic surname, which was neither rabbinical not occupational. Men are slightly overrepresented since the maiden names of the female family members were sometimes unknown to the participants. This slight difference in gender composition of the groups may cause some professional bias; however, this is negligible compared with the magnitude of the groups’ differences (shown below).

The studied population included different birth cohorts. The earliest birth date for an individual in the data was 1858 and the latest 2001. We did not perform separate study of different cohorts since the data available for them would not be statistically significant. For adequate comparison of the groups, we must have roughly the same share of each group born in each of the considered generations. Therefore, we divided the historical period spanned by our data into four periods (1858–1894, 1895–1930, 1931–1966, 1967–2001; Table 1).

From Table 1, it is seen that the birth date distributions of the groups are very similar so that the comparison of occupations is reasonable. The difference of shares of different generations holds for many reasons: each participant was asked to fill the data for two parents, four grandparents and eight great grandparents, where the data on the older generations was often forgotten, while the younger generation could still be studying or have no profession yet. However, the precise form of the birth date distribution is irrelevant for our comparative study, for only birth date distributions of different groups are similar.

The birthplaces were scattered all over the territory of the FSU. Jewish families have a long tradition of studying and those who would want to acquire education would typically receive such an opportunity. In other words, with a good approximation, an individual born into a Jewish family of the FSU would have an equal opportunity for getting that or another profession irrespective of birthplace. Therefore, we disregarded the geographical factor in our study.

No detectable bias toward some profession due to a different number of reported family members was observed. This number was never too large, and rarely reached five individuals (other ancestors were not Jewish and not considered by our study).

The data on professions was self-reported in the native (Russian) language of the participant and was not standardized. We processed the data to a standard of occupations according to the methodology below.

Data analysis

Grouping the data by profession. We separated the data into the three groups described (rabbinical, occupational, generic). We then grouped the professions into 23 narrower professional activities. These were defined either by their significant presence in the data, e.g. bookkeepers who constituted about 5% of all individuals, or by a unique character of the profession, for example interpreter/linguist. The groupings of professions, when performed, did not contradict the International Standard Classification of Occupations. The 23 categories of professions were as follows:

We calculated the number of individuals having each one of the above professions for each of the three studied groups of surnames. The main target of our study is the share of each profession (P_i) in each of the considered three groups of surnames. Thus, if N is the total number of members of Russian-speaking Jewish families with a generic surname then P_i*N is the total number of members of these families with the i-th profession. For instance, P₂₁*N would be the total number of librarians. The data on the full group consisting of millions of people (as defined by the fraction of Russian-speaking Jews whose names are neither rabbinical nor occupational where we count not only our contemporaries but all those who lived in the twentieth century) are unavailable. Thus, we have the standard problem of constraining P_i from the incomplete information on the studied groups that is at our disposal. This is done by the statistical analysis relying on the observation that with good approximation our data constitute a random pool of the considered population groups.

A typical result of counting the professions is presented in Table 2 where the example of generic surnames is used. The total pool of data consisted of 7471 individuals. Due to presence of correlated clusters of individuals in the data, we found it instructive to use coarse-grained variables X_i(k) for the statistical calculations. These variables separate the data into blocks of hundreds. In contrast with individual data which is not randomly sampled, the blocks can be be considered as a result of random sampling where a hundred was taken from the population and then, independently, another hundred and so forth, see below. Moreover separation into blocks demonstrates what we can anticipate to see if we pick 100 members from the considered population: for the pool size of 100, the statistical properties are seen already. Frequencies of different professions in each block of 100 are similar with some fluctuations. The usage of the variables X_i(k) is necessary for the statistical considerations as explained in detail below, otherwise they give an idea how the described laws apply in practice when the sample sizes are moderate. The statistics of X_i(k) answers the question – if we took a pool of 100 representatives of one of the groups what would be the typical occurrences of each profession?

Thus we took out of our pool the first 100 individuals and determined the numbers X_i(100) of individuals with the i-th profession. Then we took 100 more individuals and determined the numbers X_i(200) of individuals with the i-th profession in the range of 101–200. Continuing in this way, we determined X_i(k) determined by the columns in Table 2. We used the pool size up to 1000 because this size allows comparison with the groups of rabbinical and occupational surnames where the total pool was about 1000. Thus, we used the pool of 7471 as the control size that allows to test how well the pool of 1000 individuals represents the whole considered group. Average over a limited pool size k gives an approximation p_i(k) for P_i defined above. Up to fluctuations p_i(k) monotonously approach P_i on increasing k and we can hope that a reasonable approximation to P_i can be obtained already from the largest k available from our data. Indeed, we demonstrate quantitatively that distributions derived from the pools of 1000 and 7471 individuals are rather similar. Thus, making the reasonable assumption that pool size of 7471 represents the full group accurately, which is proved by the calculation of confidence intervals, we conclude that the occupational distribution of the generic surnames can be derived quite accurately (quantified below) from the distribution of 1000 individuals. Assuming that the groups of bearers of rabbinical and occupational surnames are similar statistically we can then conclude that the distributions for these groups, derived from the study of about 1000 individuals, provide a good characterization of the full groups. Despite that, we rely in our conclusions on the rigorously defined confidence intervals; qualitatively it is probable that the means obtained from studies of 858 rabbinical and 1057 occupational surnames provide accurate idea of the full groups.

Distance between the distributions. There was a need for quantitative comparison of distributions P_i of the three considered groups (Figure 1). Thus, considering the finite pool sizes’ approximations to P_i in Figure 1 (in %), it is seen that they are different; however how different? To make the comparison, we calculated the distance between the distributions. There is no unique conventional definition of the distance between probability distributions. We used the Hellinger distance (see for example. Yang & Le Cam, 2000), whose definition can be understood by observing that since the distributions are normalized, ${\displaystyle {\sum }_{i=1}^{23}}{\text{P}}_i=1,$ then what needs the comparison are the shapes of the distributions. For instance, for all three distributions in Figure 1, the heights of all bars sum to 100 and only the shapes distinguish the distributions. The shapes can be compared by considering the overlap, which is conveniently defined by the Bhattacharyya coefficient (Bhattacharyya, 1943):

Figure 1. Occupational distributions of the three groups of surnames according to the 23 professional activities (%).

where k and p are indices of the considered two groups (in this equation and below); when there is a need to indicate to which group P_i refers, we use the notation ${\text{P}}_{\text{i}}^{\text{r}},$ ${\text{P}}_{\text{i}}^{\text{o}},$ ${\text{P}}_{\text{i}}^{\text{g}},$ for the P_i of rabbinical, occupational and generic surnames, respectively. The Bhattacharyya coefficient is the scalar product (type of overlap) of two vectors in 23-dimensional space with components $\sqrt{{\text{P}}_{\text{i}}^{\text{k}}}$ and $\sqrt{{\text{P}}_{\text{i}}^{\text{p}}}$. The square root is introduced in the definition because $\sqrt{{\text{P}}_{\text{i}}^{\text{k}}}$ are unit vectors in the 23-dimensional space, which allows definition of “the shape of the distribution” as the direction of these unit vectors. The coefficient changes between zero, holding for non-overlapping distributions, and one, holding for identical distributions. The Hellinger distance between the distributions is then defined as:

Thus, H(k, p) is proportional to the Euclidean distance between two vectors $\sqrt{{\text{P}}_{\text{i}}^{\text{k}}}$ and $\sqrt{{\text{P}}_{\text{i}}^{\text{p}}}$ in the 23 dimensional spaces. It provides a good definition of the distance because the Euclidean distance does. We will see below that on their own the distances do not allow the distributions’ comparison, however in conjunction with statistical analysis they become useful.

Confidence interval under the random sampling assumption. Our sample consists of 858 bearers of rabbinical surnames, 1057 bearers of occupational surnames and 7471 bearers of generic surnames (we often use in the calculations the rounded number of 7400). These samples are quite large; however, the population means that can be derived from them still contain quite a large uncertainty. Here we describe the derivation of the confidence interval, i.e. the interval within which the population means are contained with high probability (95% probability in our study). The derivation in this section is done assuming that our list of individuals is a random sample of the studied population groups. This is a good assumption up to the presence of sequences of 3–5 individuals with the same surname who belong to the same close family. These individuals can be assumed to have a certain correlation of professions, which violates the assumption of random sampling. The consistency of the assumption of random sampling despite these correlations will be demonstrated in the next section.

The material in the rest of this section is mostly well-known. We consider a total population of X individuals, of whom X_i have a property “i”. In the application of interest in this work, this property is a certain profession; however, the nature of this property is irrelevant for general considerations. We make a random sampling of the population, i.e. we pick an individual at random. Then, by definition of random sampling, the individual with property “i” is picked with probability p_i = X_i/X. If we continue the random sampling, then the probability distribution of the number X_i(N) of individuals with the property “i” in randomly picked N individuals is given by the binomial distribution with the success probability p_i. Here we assume that N is much smaller than both X_i and X so that the random sampling occurs in approximately identical conditions. The average and variance of X_i(N) are given by the well-known formulas of binomial distribution

where here and below the angular brackets stand for averaging. Large N binomial distribution can be approximated by Gaussian, implying that the distribution of X_i(N) is Gaussian and is determined uniquely by the mean and the variance above. We find that the distribution of x≡(X_i(N)- p_i N)/[p_i N(1- p_i)]^1/2 is the standard normal distribution with zero mean and unit variance. For this distribution, it is well-known that the probability that x will fall between -1.96 and 1.96 is approximately 0.95. This probability equals the probability that X_i(N)/N falls between p_i-[p_i(1- p_i)/N]^1/2 *1.96 and p_i+[p_i(1- p_i)/N]^1/2 *1.96 that is designated by $\text{P}({\text{p}}_{\text{i}}-1.96*\sqrt{{\text{p}}_{\text{i}}(1-{\text{p}}_{\text{i}})/\text{N}}\le {\text{X}}_{\text{i}}(\text{N})/\text{N}\le {\text{p}}_{\text{i}}+1.96*\sqrt{{\text{p}}_{\text{i}}(1-{\text{p}}_{\text{i}})/\text{N}})$ and obeys

Our data provides X_i(N)/N, from which we want to find the confidence interval of p_i that is the interval to which p_i belongs with 95% certainty. If the observation provides the value X_obs for X_i(N) then, with 95% probability, the unknown quantity p_i obeys

This inequality is equivalent to (X_obs - p_i N)² ≤1.96² p_i N(1- p_i), which gives

We find

where we defined

We have neglected terms of order 1/N and introducing (pi)_obs≡ X_obs/N that

with 95% probability. This has the same form as Equation (2) above because p_i and (p_i)_obs coincide in the leading order in N>>1. For not so large sample, however, there is a difference, the property which is often not mentioned in the discussions.

In the rest of this work we keep using the definition of the confidence interval by 95% certainty. This and the factor of 1.96 above are somewhat arbitrary. If we used 90% confidence interval instead, then 1.645 would be present in the formula above instead of 1.96. This would result in more differences between the studied groups; however, we prefer to stick to the more conservative estimate of the differences.

Data consistency with random sampling. We have already reported that the assumption of perfectly random sampling is not accurate. However, our data is still composed of independent information units where the unit is defined by the information provided by one participant. This unit is the information on the close family of the participant. Hence for a large number of participants, considering with very good approximation the information that they provide as independent, the data is still the sum of independent identically distributed random variables. The variable is the number of people with profession “i” in one reported family. Therefore, by the central limit theorem (see e.g. Gnedenko & Kolmogorov, 1968), the distribution of the number of representatives of each profession is still Gaussian, as in the case of random sampling. Having the Gaussian distribution, we can then evaluate the confidence interval and obtain the appropriate generalization of the results of the previous section. Below we quantify these considerations and provide the changes that are in order.

Table 3 provides a typical excerpt from our list of individuals and their professions. It is seen that some surnames are included multiple times. In Table 3, individuals with the same surname do not necessarily belong to the same family, as seen from the places of origin. In some cases (not shown), the bearers of the same names did belong to the same family and had similar professions. For instance in the list of 858 individuals with rabbinical surnames, we found two Berlins who were architects, two Wahls who were salesmen, two Halperins who were accountants, two Hellers who were teachers, three Hellers who were engineers, four Hellers who were economists, two Ginzburgs who were accountants and two who worked in delivery, two Gordovers who were engineers, two Gordons who were workers, and nine Horowitzs who were engineers. These correlations might cause the statistics to behave differently from the situation where each individual is picked at random from the studied group. This issue must be considered quantitatively. We observed previously that the number of reported people from the same family rarely exceeded five and typically was much less. For quantitative treatment of the effect of these correlations of limited range (below five), we consider the statistics of X_i(N) – the number of individuals with profession “i” in the list with total number of individuals N. We introduce the random variable x_i(p). This variable equals 1 if the individual in place “p” of the list has profession “i” and 0 otherwise. Then

We assume that the list is ordered so that individuals with possible correlations of professions are grouped together; the list can be thought of as obtained in this way. We pick at random individuals from the considered group (bearers of rabbinical or occupational or generic surname) and then we pick their close family of random size as determined by the statistics of family sizes (which is of no interest here). This implies that x_i(p) in the equation above have finite correlation range so that the variance < x_i(p) x_i(p+k)>- < x_i(p) > < x_i(p+k)> is non-zero for some positive integer k. k is bounded from above by k_max, which is formally given by the maximal family size, which is fifteen (individual, parents, great and great great-parents); however, this is five in reality as we have already explained. For large N>>k_max the distribution of X_i(N) is still Gaussian as in the case of random sampling. This can be seen as the result of application of the central limit theorem to the sum of independent random variables where each variable is the sum of x_i(p) over one family, i.e.

Here we introduced the random variable (y_family)_l , which counts the number of representatives of profession “i” in the l-th family where l is the index of the family. Thus the statistics of (y_family)_l could be obtained by partitioning the considered group of population (rabbinical, occupational or generic) into families, where the family is defined as information unit in our data and not otherwise, with the unit’s definition given in the beginning of this section. Considering (y_family)_l with different l as independent, we conclude from the central limit theorem that X_i(N) is approximately Gaussian random variable, which is uniquely characterized by its mean and variance (a finer consideration can be done using the version of the central limit theorem for random variables with fast decaying correlations, see Gnedenko and Kolmogorov). These are given by

where we used directly the definition X_i(N)= ∑^N_p=1 x_i(p). Here <x_i(p)>= p_i, where p_i were defined in the previous section. We can consider the last sum as sum of diagonal and off-diagonal elements. The sum over the diagonal elements is readily found by using that x_i(p)=1 with probability p_i and x_i(p)=0 with probability 1-p_i. Thus <x²_i(p)>=p_i and

which is the same answer as for the random sampling. It is the sum of the off-diagonal terms ∑_p≠k (<x_i(p) x_i(k)>- <x_i(p) > <x_i(k)>), a non-trivial quantity, which characterizes the correlations of professions within one family. Thus <x_i(p) x_i(p+1)> is the probability that two consecutive individuals from the list have identical profession “i”. This probability is larger than <x_i(p)> <x_i(p+1)>, which would hold if professions of the individuals were independent. The finite difference <x_i(p) x_i(p+1)>- <x_i(p)> <x_i(p+1)> is caused by the finite probability that individuals p and p+1 belong to the same family and thus have positively correlated professions. It seems inevitable that within-family correlations are positive so that

The left-hand side of the above equation is identically zero for k> k_max (see above). It is then readily seen from the definition in Equation (3) above that the variance obeys

where the constant c_i is independent of N. The question is how different c_i is from the random sampling value p_i(1-p_i) because of the described correlations.

We face the problem of estimating the normalized dispersion c_i for our unknown sampling statistics. This can be done quite accurately in the case of bearers of generic surnames where we have data on more than 7400 individuals. This is accomplished by partitioning the list into 74 hundreds and considering the corresponding 74 numbers [X_i(100)]^k with k running from 1 to 74 as independent realizations of X_i(100). Here the independence of [X_i(100)]^k with different k holds due to 100>>k_max, which implies that the number of correlated professions in different hundreds is negligibly small in comparison with the total numbers. Indeed, we have

where <x_i(p)(x_i(k)> differs from <x_i(p)><x_i(k)> only for indices p and k in narrow vicinity of p=k=100, which can be neglected. We find the independent variables law <[X_i(100)]^k[X_i(100)]^k+1>=<[X_i(100)]^k><[X_i(100)]^k+1> (similar consideration can be done for higher order correlations). This independence is the reason why we group the data in blocks of 100 (of course the block size is not defined uniquely). We observe that Y_i≡(1/74) ∑⁷⁴_k=1([X_i(100)] ^k)² is a sum of independent Gaussian variables and hence it is Gaussian itself. The average of Y_i is <(X_i(100))²> and its dispersion is

where we used independence of [X_i(100)] ^k with different k and that Gaussianity of [X_i(100)] ^k implies <([X_i(100)] ^k)⁴>=3 <([X_i(100)] ^k)²>²=3 <(X_i(100)])²>². Thus the distribution of (Y_i/<(X_i(100))²>-1) √37 is the standard normal distribution with zero mean and unit variance. We find that the value of Y_i obtained from our data limits <(X_i(100))²> within the interval given by

with the confidence level of 95% (see above). The random sampling would give <(X_i(N))²>= p_i N+N(N-1) p_i² with N=100 as seen readily from the properties of the binomial distribution. The comparison between the dispersion determined from our data and the dispersion predicted by the random sampling assumption is provided in Table 4.

We find that the observed dispersion agrees with the prediction of the random sampling assumption with accuracy which is well beyond what could be hoped for, as is clear from the confidence interval. Here we used for p_i the values obtained from averaging over the sample of more than 7400 individuals, where we neglect the error using the large sample size. The observed agreement over as many as 23 categories is completely consistent with the assumption that the data are equivalent to random sampling of the group of bearers of generic surnames. In other words, the correlations between the profession of different individuals, which are present in the data, are negligible. Since these correlations do not seem to be different for other groups (bearers of rabbinical and artisanal surnames) then we will assume in the Results below that our data provides the random sampling of all the considered population groups. We have also derived dispersion for other groups and saw that the assumption works well (these comparisons are not provided since for these groups the sample of about 1000 individuals is too small for reaching rigorous conclusions).

Underlying data

The dataset described here cannot be shared openly due to the identifiable nature of the data (surnames, occupations, birth dates, birthplaces). Any researchers wishing to access the underlying data can contact the corresponding author (itzhak8@gmail.com). Data will be shared under the following conditions: researchers will need to declare that they are currently undertaking similar research, that the data will not be shared with anyone other than the researcher who requested it, and it will be exclusively used for academic purposes.