- An institutional researcher at a large university wants to compare the mathematical abilities of its male and female students. A researcher selects 100 men and 100 women at random from each of the four classes, and administers a standardized mathematics test. The men average 500 on the test, with a standard deviation of 120. The women average 450 on the test, with a standard deviation of 110. What test would be appropriate to determine whether the difference between men and women is real or due to chance variation?
#### Pearson Correlation (r)

Possibly correct but there is a better answer.

Here we are interested in comparing the means for two groups. Correlation is most often used to assess a linear relationship between two continuous variables. With special coding, it can be used to measure a relationship between a dichotomous variable and a continuous variable, regression generally is not the preferred analysis in this situation.

#### Regression analysis

Possibly correct, but there is a better answer.

Regression analysis can be used to derive an equation from which we can predict scores on one variable based on scores on one or more other variables. In this example, we wish to compare the means of two groups on a continuous measure. Although this can be done with regression analysis, there is a test that is designed for the situation we have here.

#### t-test for independent samples

Correct!

The t-test for independent groups is used when comparing means derived from two different and unrelated groups. We have a continuous measure (mathematics test score) from two independent groups in this example, men and women.

#### t-test for paired data (dependent t)

Incorrect.

A paired samples t-test is appropriate for data which are paired or matched, as with before/after measures. In this case we have two groups which we have no reason to believe constitute pairs. Because the cases in our two groups are not paired across groups, they are termed independent.

Need some help? Ask the Expert!

#### The Expert says…

The null hypothesis is that there is no gender difference in average scores on the mathematics test in the population.

We have a continuous measure (mathematics score) from two groups (men and women). The scores from the two groups are independent in that students are not paired. This is a good place for an independent groups t-test.

Of course, we should check whether we have met the assumptions of the statistical test before we apply it. In particular, we assume that the distributions of mathematics scores are reasonably normal within each gender group and that the variances are the same. We should include measures of precision, such as confidence intervals, along with the test of significance.

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