Statistics for People Who (Think They) Hate Statistics

by Neil J. Salkind

one factor or one independent variable (such as group membership) is being explored and this factor has more than two levels. Simple ANOVA is also called one-way analysis of variance because there is only one grouping factor. The technique is called analysis of variance because the variance due to differences in performance is separated into (a) variance that’s due to differences between individuals between groups and (b) variance due to differences within groups. The between-groups variance is assumed to be due to treatment differences, while the within-group variance is due to differences between individuals within each group. This information is used to figure out how much the groups would be expected to differ just by chance. Then, the observed difference between groups is compared to the difference that would be expected by chance, and a statistical conclusion is reached. ANOVA is, in many ways, similar to a t test. (An ANOVA with two groups is, in effect, a t test. In fact, the t computed in an independent t test is the square root of the F computed in a one-way analysis of variance!) In both ANOVA and t tests, differences between means are computed. But with ANOVA, there are more than two means, and you are interested in the average difference between means. For example, let’s say we were investigating the effects on language development of being in preschool for 5, 10, or 20 hours per week. The group to which the children belong is the independent variable (or the ...