This chapter has covered the t test for independent means. Now that you have read this chapter, you should understand the following concepts and techniques:
- Like the t test for dependent means, the t test for independent means is used to compare two groups of scores when you do not know the population variance. Unlike the t test for dependent means, which is used to compare two groups of scores from a single group of people, the t test for independent means is used to compare two groups of scores from two entirely separate groups of people.
- Because the focus of the t test for independent means is the difference between the means of two groups, the appropriate comparison distribution is a distribution of differences between means. If the null hypothesis is true (i.e., if the two populations have the same mean), the distribution of differences between means will have a mean of 0.
- One assumes that the two populations represented in a t test for independent means have the same variance. When estimating the population variance from the scores in the samples, then, one obtains two separate estimates of what should be the same numbers. The two estimates are thus pooled, weighting each one according to its degrees of freedom. The pooled estimate of the population variance is the best estimate for both populations.
- If the samples are not of the same size, the distribution of means taken from each one will have different variances and different standard deviations. The variance of each distribution of means is computed by dividing the pooled estimate of the population variance by each sample's N; the standard deviation is computed by taking the square root of the variance. The variance of the distribution of differences between means is the sum of the variance each population's distribution of means, and the standard deviation of the distribution of differences between means is the square root of that.
- Because it is based on estimated population variances, the distribution of differences between means is a t distribution. The degrees of freedom is equal to the sum of the degrees of freedom of each sample (i.e., the total number of participants minus 2).
- To compute a t score for a t test for independent means, divide the mean difference by the standard deviation of the comparison distribution, the distribution of differences between means. Then, determine whether your computed t score surpasses the cutoff score on the comparison distribution for your chosen level of significance; if it does, reject the null hypothesis.
- The t test for independent means has two assumptions: The two populations are both assumed to follow a normal curve and the two populations are assumed to have the same variance. In practice, the t test gives a fairly accurate result in most cases even when these assumptions are violated.
- The effect size for the t test for independent means is the difference between the population means divided by the pooled estimate of the population standard deviation (the square root of the variance of the population of individuals). The power associated with small, medium, and large effect sizes can be determined from a table. Power is greatest when the participants are divided into two equal groups.
