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The expected worth for each cell requirements to be at least 5 in order for you to usage this test.

You are watching: Why does the test for homogeneity follow the same procedures as the test for independence?


Hypotheses

(H_0): The distributions of the two populaces are the very same. (H_a): The distributions of the two populaces are not the same.

Test Statistic

Use a (chi^2) test statistic. It is computed in the very same way as the test for freedom.

Degrees of Freedom ((df))

(df = extvariety of columns - 1)

Requirements

All worths in the table must be greater than or equal to five.

Common Uses

Comparing 2 populaces. For example: men vs. women, prior to vs. after, eastern vs. west. The variable is categorical through even more than two possible response values.




Example 11.5.2

Both before and after a recent earthquake, surveys were performed asking voters which of the 3 candidates they planned on voting for in the upcoming city council election. Has there been a adjust given that the earthquake? Use a level of definition of 0.05. Table reflects the outcomes of the survey. Has tright here been a change in the distribution of voter choices since the earthquake?

Perez Chung Stevens
Before 167 128 135
After 214 197 225

Answer

(H_0): The circulation of voter choices was the same before and also after the earthquake.

(H_a): The distribution of voter preferences was not the exact same before and after the earthquake.

Degrees of Freedom (df):

(df = extvariety of columns - 1 = 3 - 1 = 2)

Distribution for the test: (chi^2_2)

Calculate the test statistic: (chi^2 = 3.2603) (calculator or computer)

Probability statement: (p ext-value = P(chi^2 > 3.2603) = 0.1959)

Press the MATRX key and arrowhead over to EDIT. Press 1:. Press 2 ENTER 3 ENTER. Go into the table values by row. Press ENTER after each. Press second QUIT. Press STAT and also arrowhead over to TESTS. Arrow down to C:χ2-TEST. Press ENTER. You have to view Observed: and Expected:. Arrow down to Calculate. Press ENTER. The test statistic is 3.2603 and also the p-worth = 0.1959. Do the procedure a 2nd time however arrow dvery own to Draw instead of calculate.

Compare (alpha) and the (p ext-value): (alpha = 0.05) and also the (p ext-value = 0.1959). (alpha Exercise (PageIndex2)

Ivy League schools get many type of applications, however just some have the right to be welcomed. At the schools noted in Table, 2 kinds of applications are accepted: regular and early on decision.

Application Type Accepted Brown Columbia Cornell Dartmouth Penn Yale
Regular 2,115 1,792 5,306 1,734 2,685 1,245
Early Decision 577 627 1,228 444 1,195 761

We want to know if the variety of consistent applications welcomed adheres to the same distribution as the number of early applications embraced. State the null and also alternate hypotheses, the levels of freedom and the test statistic, sketch the graph of the p-worth, and also draw a conclusion around the test of homogeneity.

Answer

(H_0): The distribution of consistent applications accepted is the exact same as the circulation of at an early stage applications welcomed.

(H_a): The circulation of regular applications accepted is not the same as the distribution of early applications embraced.

(df = 5)

(chi^2 exttest statistic = 430.06)

*
Figure (PageIndex1).

Press the MATRX essential and arrowhead over to EDIT. Press 1:. Press 3 ENTER 3 ENTER. Go into the table worths by row. Press ENTER after each. Press second QUIT. Press STAT and also arrow over to TESTS. Arrow down toC:χ2-TEST. Press ENTER. You have to see Observed: and also Expected:. Arrow dvery own to Calculate. Press ENTER. The test statistic is 430.06 and the (p ext-value = 9.80E-91). Do the procedure a 2nd time but arrowhead dvery own to Draw instead of calculate.

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Exercise (PageIndex3)

A math teacher wants to view if two of her classes have the very same circulation of test scores. What test must she use?

Answer

test for homogeneity





Use the following indevelopment to answer the next five exercises: Do private practice physicians and hospital medical professionals have the same distribution of working hours? Suppose that a sample of 100 exclusive exercise physicians and 150 hospital medical professionals are schosen at random and also asked about the variety of hours a week they job-related. The results are displayed in Table.

20–3030–4040–5050–60
Private Practice 16 40 38 6
Hospital 8 44 59 39

Exercise (PageIndex8)