## The Difference between Two Means

This section covers how to test for differences between means from two separate groups of subjects and gives an example of opinions on animal research. The detailed testing procedure is carried out using the standard steps in hypothesis testing.

1. The distributions are skewed and therefore violate the assumption of normality.

2. Population 1 is skewed and therefore violates the assumption of normality. Population 2 has a larger variance.

3. Population 2 has a larger variance.

4. The statistic is the value you are interested in testing. Here you are interested in the difference between means.

5. The hypothesized value is the population parameter you are comparing your statistic to. Here you are interested in the difference between population means.

6. If the population means are equal, then the hypothesized value of the difference between means is 0.

7. Since the statistic in question is the difference between means, the denominator is the estimated standard error of the difference between means.

8. The $df$ is $4+4-2=6 .$ The $\mathrm{p}$ value is $0.0578$

9. Compute the $t$ for an independent-groups $t$ test. If you are using a program, make sure to recode the data as described. $t = 2.9594$