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.
