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Suppose we want to compare three teaching methods based on the mean test scores for each method. The competing theories would be:H0: There is no difference between the three teaching methods with respect to mean test scoreH1: There is a difference between the three teaching methods with respect to the mean test score
Notice that there are two types of variation we are looking at, the between variability and the within variability. The test statistic we’ll use to judge if at least one of the means is significantly different is based on these measures.
1. The F-distribution is not symmetric; it is skewed to the right.
2. The values of F can be 0 or positive, they cannot be negative.
3. There is a different F-distribution for each pair of degrees of freedom for the numerator and denominator. Let I be the number of means (populations drawn from) and n = total sample size across all populations sampled.