Do Ultra-Orthodox Israeli Jews Suffer more than Secular Israeli Jews from Obesity? Gender, Cohort Effect and the Yule-Simpson Paradox.

The Yule-Simpson paradox indicates contradicting statistical outcomes for the pooled sample and for each stratified group separately. The objective of the current study is to demonstrate this paradox. The sample is based on a 2015-2016 longitudinal survey carried out by the Israeli Central Bureau of Statistics. The sample includes 1194 individuals, where the responses of 1140 individuals were assessed twice (in 2015 and 2016) and the responses of 54 individuals were recorded only once. This gives a total sample of 2334 observations × years. The sample includes 609 females and 585 males. We use the limited dependent binary probit regression model. The dependent variable is a dummy variable that equals 1 if the individual is obese (BMI ≥ 30, where BMI = WEIGHT ÷ (HEIGHT2), WEIGHT is measured in kilograms and HEIGHT is measured in meters) and zero otherwise. The independent variables are the denomination (secular vs. ultra-Orthodox) and age in years. Findings suggest that on the one hand, for the pooled sample of 21-50-year-old females and males, results clearly support the conclusion that compared with secular Israeli Jews, projected probability of obesity (BMI ≥ 30) among ultra-Orthodox Israeli Jews is higher (p = 0.0128). On the other hand, when stratified by gender, one cannot reject the opposite conclusion, according to which projected probability of obesity is equal for all cohorts among ultra-Orthodox and secular Israeli Jews. Research findings thus stress the importance of cautious and rigorous statistical analysis and robustness tests prior to statistical inference.