e-Statistics > 4480-5480 Probability and Statistics II

## Comparison of Two Means

Data are collected from two groups, say Group 1'' and Group 2,'' concerning with how Group 1 and Group 2 differ in terms of their respective population means and . Then the hypothesis test can be stated with the alternative hypothesis

The test statistic is calculated from the sample means and and the sample standard deviations and from Group 1 and Group 2 with the respective sample sizes and

In general procedure the variance estimate of is given by with the sample variances and of Group 1 and 2. Then the test statistic is likely observed around zero, positive, or negative, under the respective null hypothesis  ,''  ,'' or  .'' The opposite of such an observation is expressed by the p-value smaller than , and it suggests an evidence against the null hypothesis .

When it is reasonable to assume that the two population variances and of Group 1 and 2 are equal, the variance estimate is given by via pooled sample variance .

If the null hypothesis is rejected, it would be preferable to construct the confidence interval for the population mean difference .

( , )

Here the choices of confidence level are 90%, 95%, or 99%.