## KEY CONCEPTS

KEY CONCEPTS

• Research questions about two independent groups ask whether the means are different or the proportions are different.

• Confidence intervals using the t distribution determine the confidence with which we can assume differences between two means will vary in future studies.

• A pooled standard deviation is used to form the standard error of the differences.

• An “eye-ball” test is helpful when reports present graphs of the mean with 95% confidence intervals.

• Using the t distribution requires the two groups to be independent from each other as well as the assumptions of normality and equal variances in the two groups.

• Tests of hypothesis are another way to test the difference between two means.

• The assumption of equal variances can be tested with several procedures.

• The nonparametric Wilcoxon rank sum test is an excellent alternative to the t test when the assumptions of normality or equal variances are not met.

• Both confidence intervals and statistical tests can be used to compare two proportions using the z test, again using a pooled standard deviation to form the standard error.

• The chi-square test is a very versatile statistical procedure used to test for differences in proportions as well as an association between two variables.

• Fisher’s exact test is preferred to chi-square when two characteristics are being compared, each at two levels (i.e., 2 × 2 tables) because it provides the exact probability.

• The relative risk, or odds ratio, is appropriate if the purpose is to estimate the strength of a relationship between two nominal measures.

• When two groups are compared on a numerical variable, the numerical variable should not be turned into categories to use the chi-square test; it is better to use the t test.

• It is possible to estimate sample sizes needed to compare the means or proportions in two groups, but it is much more efficient to use one of the statistical power packages, such as G*Power.

## PRESENTING PROBLEMS

### Presenting Problem 1

See Chapter 3, Presenting Problem 1 (Davids et al, 2014)

### Presenting Problem 2

Ström and colleagues (2013) studied the effectiveness of an Internet-delivered therapist-guided physical activity to treat mild to moderate depression. They used a randomized design to assign 48 participants to the Internet-delivered therapy and standard care.

The article may be accessed at this link:

Ström M, Uckelstam C, Andersson G, Hassmén P, Umefjord G, Carlbring P: Internet-delivered therapist-guided physical activity for mild to moderate depression: a randomized controlled trial.