Chi-Square Tests Question

Question

a. A chi-square goodness of fit test, a chi-square independence test, or a chi-square homogeneity test is always right-tailed. Why?

b. Suppose you are conducting chi-square goodness of fit test. If the sum of the expected frequencies does not equal the sample size, what do you conclude?

Answer 1

a) Chi-square goodness of fit test, chi-square independence test, or chi-square homogeneity test is only one direction of testing. Chi-square is a single number and that number is representing the difference between observed counts and expected counts -- test statistic is squared

Recall that in other testing, say the mean, you are testing whether the test value is higher or lower (directions) from the mean which would imply a one tail testing for two different directions.

b) The sum of the expected frequencies should be the same as the sum of the observed frequencies, both are the sample size. There might be a difference in how the counts are distributed but the frequencies of both are the same, see table below There is a data entry error if they are not the same.

This is data from an experiment where rats are sent down a ramp, n = 90. And the observed count is for how many rats entered respective doors in the experiment.*

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Door

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1 2 3

Observed Cell Frequencies n1 = 23 n2 = 36 n3=31

Expected Cell Frequencies (30) (30) (30)

1. Mathematical Statistics with Applications, Mendenhall, Wackerly, and Scheaffer, p. 645