Statistics II: General Description

Correlation and Analysis of Variance (ANOVA) are among the most powerful of the parametric statistics. Both test for the presence of a relationship between two characteristics, and are based on an assumption that is called the “general linear model.” This assumption states that the relationship between characteristics (or “variables”), in its ideal form, can be described as a straight line. In other words, a change in one variable always produces a change in other variables and that change is always in a certain direction (greater or less) and at the same strength. For many relationships, this makes sense. The harder you swing a hammer, the bigger the dent you make in the wood. The harder you push on the gas pedal, the faster you go. The harder you work in school, the better the grades you get. And so on. As long as you can reasonably make this assumption (that there is a relationship, and that it is “linear”), then you can apply the linear model. Correlation requires the additional assumption that both variables are “normally” distributed; ANOVA only requires that one of the variables be normally distributed.

The advantage of correlation and ANOVA over, for example, c-square, is that they can tell you not only whether there is a relationship but also what the relationship looks like and how strong it is. This is a direct result of the linear assumption: The shape of the relationship can be described by the line that best fits it (that is, by the direction and the slope of the line). The strength can be described by how closely the data fit the ideal line which describes the relationship.

Next Section

Back to Syllabus

609