SIMPSON'S  PARADOX  COMPARISONS  OF  IMMIGRANTS  AND NATIVES

        Jeffrey S. Passel and Julian L. Simon


             Simpson's paradox is one of the most of the most counter-

        intuitive of all analyses of statistical data.  The best-known

        example is that of admission data for male and female graduate

        students at Berkeley, wherein the aggregate probability of

        acceptance was lower for women, but the probabilities in most

        departments were higher for women.  Two more neat examples of the

        paradox should be welcome.

        1. Data on Welfare Usage of Immigrants and Natives

        Consider the data in Table 1, originally drawn from the Urban

        Institute (Passell and Fix, 1994). The aggregate proportion of

        immigrants aged 15 and over receiving welfare (defined as food

        stamps, Supplemental Security Income, Aid to Families with

        Dependent Children, and General Assistance) declined from 1979 to

        1989.  But the proportions in the two sub-groups increased. These

        results seem inconsistent on their face, and caused confusion

        among critics.1

                                     Table 1

             Despite the apparent internal contradiction, however, the

        data are not at all implausible, and are explained by Simpson's

        Paradox.

             Given that the ratio of over-65 persons to 15-65s was 23 to

        77 in 1979, and was 15 to 85 in 1989, the observed data are per-

        fectly consistent with each other, as Figure 1 shows.

                                     Figure 1

        2.  Population Aged 65 and Over in Nursing Homes

             Table 2 shows data for natives, and for immigrants who

        entered the U. S. before 1960, who are aged 65 or over and are in

        "nursing homes" (institutionalized group quarters).  The

        aggregate percentage for immigrants is higher, the the

        percentages for each age sub-group are lower, for immigrants than

        for natives,  The explanation is that the 85+ age group

        constitutes 21 percent of the total for immigrants but only 9

        percent for natives.

                                     Table 2


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                                     ENDNOTE

             1.  In a pamphlet Behind the Curtain: Julian Simon's Manipu-

        lation of Immigration Studies (Washington:  Federation for

        American Immigration Reform, 1996), John L. Martin and C. Scipio

        Garling wrote that the table is necessarily in error and

        "obviously wrong" (their p. 14), something that "Simon [and

        presumably the Urban Institute] should have recognized" (pp. 13-

        14).  They say that "the data belie that conclusion" (p. 13) that

        the Urban Institute and I arrived at, and that "he disproves his

        own claims" because of a supposed internal contradiction.



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