Illuminating Statistical Analysis Using Scenarios and Simulations

32Two-Way Proportions: Independence

Statistical Scenarios—College Majors

You have a random sample of local college student records that indicate student's sex and academic major. You want to know whether, in the campus population, certain majors are equally appealing to both sexes and whether certain majors appeal to one sex more than the other.

Tables 32.1a and b have count breakdowns by sex and major. Which of the two tables seem to indicate that students' relative preference for the two majors is independent of their sex, and which of the two tables seem to indicate that students' relative preference for the two majors depends on their sex?

These two tables¹ portray scenarios that can be made obvious to the naked eye. Let's fill in some totals and percentages to make the relative proportions for males and for females easier to see—Tables 32.2a and b.

Table 32.1 a&b

Major1	Major2	Major3	Major4
Male	40	60	Male	90	10
Female	18	32	Female	10	40

In Table 32.2a, we can see that similar proportions of males and females are enrolled in the two majors. Relative preference for each of the two majors seems independent of students' sex. To analyze this, we can use the Chi-squared (X²) test for independence. (The arithmetic involved is the same as the test for homogeneity!) This scenario yields a low value and thus a high -value: is 0.22 giving a -value of 0.64. Verdict: ...