A psychologist is interested in whether or not handedness is related to gender. Specifically she wants to know if the percentage left-handed men in the population is different from the percentage of left-handed women. She collected data on handedness for 200 men and 200 women. What type of statistical test would be appropriate?

#### t-test for independent samples

Incorrect.

A t-test can be used to compare the means of two groups. We do not have means; instead we have frequency data.

#### t-test for paired data

Incorrect.

A t-test for paired data is used to compare the means of two samples where observations are paired across samples. We do not have means; instead we have frequency data.

#### Chi-square goodness of fit test

Incorrect.

The chi-square goodness of fit test can be used to compare frequency data from a sample to expected frequencies based on a hypothesized distribution. In this example we have two samples to be compared rather than one sample to be compared to a population.

#### Chi-square test of independence

Correct.

We have the frequencies of left- and right-handed men and women. The null hypothesis is that the proportions are the same for men and women. This can be expressed as hypothesizing that handedness is independent of gender. The chi-square test for independence can applied to frequency data to test whether whether the distributions of frequencies differ for two groups.

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#### The Expert says…

The null hypothesis is that the proportions of left-handedness are the same for men and women. This can be expressed as hypothesizing that handedness is independent of gender. The observed data are the frequencies of left- and right-handed men and women.

The data can be summarized in a 2×2 table with gender (male, female) on one axis and handedness (left, right) on the other. The chi-square test for independence can applied to this table of frequency data to test whether whether the relative frequencies of handedness differ for men and women.