BUS 3059: Two Sample Hypothesis Testing

Hypothesis testing based on the comparison of two samples is similar to the testing of a single sample

against a benchmark. A statistic is calculated from both samples and the two statistics are compared.

The statistics, which are often the two means of the samples, but that can be other statistics, like the

two variances of the samples or two proportions of the samples, are often assumed to be equal. Thus, the null hypothesis is stated in terms of some expression suggesting this equality of the two samples.

The alternative hypothesis is that the two statistics are in some way unequal. As with single sample

hypothesis testing, left-tailed tests, right-tailed tests, and two-tailed tests can be conducted.

In left-tailed tests involving two samples, the null hypothesis is that the statistic calculated from one

sample is greater than or equal to the statistic calculated from the other sample. The alternative

hypothesis for these tests states that the statistic calculated from the ?rst sample is less than the statistic calculated from the second sample.

In right-tailed tests involving two samples, the null hypothesis is that the statistic calculated from one

sample is less than or equal to the statistic calculated from the other sample. The alternative

hypothesis for these tests states that the statistic calculated from the ?rst sample is greater than the

statistic calculated from the second sample.

In two-tailed tests involving two samples, the null hypothesis is that the two statistics calculated the

samples are equal. The alternative hypothesis for these tests states that the statistics calculated from the two samples are not equal.

The supplemental material entitled “Two Sample Hypothesis Tests” provides more information about

the comparison of two sample test statistics to critical values in statistics tables. This can guide you

into the appropriate ways of handling each of these types of two sample tests.