### Chapter Four The Statistical Significance of F and Effect Strength

We continue here with our discussion of the elements of the summary table provided in Table 3.2. We have discussed the sources of variance, the sum of squares, the degrees of freedom, and the mean squares in Chapter 3; we are now ready to deal with the F ratio, the probability of the F value occurring by chance based on its sampling distribution (so that we can determine whether or not it is statistically significant), and the eta squared value (η^{2}) representing the strength of the effect of the independent variable. We begin with the F ratio.

#### 4.1 The F ratio

##### 4.1.1 The F ratio and the null hypothesis

As Snedecor (1946) stated so well, ANOVA tests the null hypothesis, which states ...