# ANOVA tests

Please, help me with my “SPSS research methods” class. Explain me the difference between a one-way ANOVA and a two-way ANOVA test and when they should be used. Thanks!

### 1 comment to ANOVA tests

• Analytic

The Analysis Of Variance (ANOVA) is a powerful and common statistical procedure in the social sciences. It can handle a variety of situations. The ANOVA is very useful techniques which can compare parameters within different groups. One way ANOVA is a technique used to compare means of two or more samples by using the F distribution.

This technique can be used only for numerical data. The ANOVA tests the null hypothesis that samples in two or more groups are drawn from the same population. For this, two estimates are made of the population variance. Then, these estimates rely on various assumptions. The ANOVA produces an F statistic, the ratio of the variance calculated among the means to the variance within the samples. If the group means are drawn from the same population, the variance between the group means should be lower than the variance of the samples, following central limit theorem. A higher ratio therefore implies that the samples were drawn from different populations. From SPSS it can easily done by clicking compare mean options and then selecting K sample mean comparison and then put the name of variables and grouping variables.

For two-way ANOVA population should come from normal or approximately normal distribution. Again, samples must be independent and the variances of the population must be equal. And the groups also have same sample size. The two-way ANOVA used for comparing two factors. Here, the two independent variables in a two-way ANOVA are called factors. The idea is that there are two variables/factors, which affect the dependent variable. Each factor will have two or more levels within it, and the degrees of freedom for each factor is one less than the number of levels. Like one way ANOVA F test is also used here. So it’s an extension of one way ANOVA which gives additional information on interaction between two factors.