12. Crosstabulations and Simpson's Paradox Suppose an educational researcher analyzes graduation data for the senior classes of two high schools. The data are summarized in the following crosstabulation. Table 1 Graduated School Yes No Total A 810 492 1,302 B 185 53 238 Total 995 545 1,540 for School A is The graduation rate of School B. than the graduation rate of for The researcher decides to take a closer look at the characteristics of the classes from each of the two schools. She obtains data on the income status of the students' families and classifies the students according to whether they came from a low-income family or a middle- or high-income family. The additional data are summarized in the following two crosstabulations. Table 2: School A Graduated Income Yes Middle- or high-income 320 Low-income 490 Total 810 No Total 31 351 461 951 492 1,302 Table 3: School B Graduated Income Yes No Middle- or high-income 162 28 Low-income 23 25 Total 185 53 Total 190 48 238 Among students coming from middle- or high-income families, the graduation rate of for School A is than the graduation rate of for School B. Among students coming from low-income families, the graduation rate of for School A is than the graduation rate of for School B. Your conclusions from comparing the schools' graduation rates based on the collected data in Table 1 are your conclusions from comparing the schools' graduation rates based on the unaggregated data in Tables 2 and 3. The researcher notices that in both schools, students from middle- or high-income families have a likelihood of graduating than students from low-income families. School A has a overall graduation rate because its senior class has a lower proportion of students from families