Question

Suppose you are interested in testing whether mean time spent in the library is different for different classifications of students (freshmen, sophomores, juniors, and seniors). If you conduct an ANOVA to test your hypothesis, you would expect that ____________.

	a.	SSA is greater than SSW when the null hypothesis is not true
	b.	An answer cannot be deterined from the information provided.
	c.	SSA is about the same as SSW when the null hypothesis is true
	d.	SSW is greater than SSA when the null hypothesis is true

Answer 1

The Null hypothesis in ANOVA is valid when all the sample means are equal, or they don’t have any significant difference.

Total variation can be split into two parts:
SST=SSA + SSW

SST = Total Sum of Squares (Total variation)
SSA = Sum of Squares Among Groups (Among-group variation)
SSW = Sum of Squares Within Groups (Within-group variation)

SSA is a measure of how much the means differ from one another. Its conceptualized a little differently, because it is thought of as the variation of each mean from the mean of the total sample.

SSW - If we calculated the SSW from scratch, it would be the deviation of the scores in each group from its group mean, then added together. Represents variation within groups

Hence correct option is (c) SSA is about the same as SSW when the null hypothesis is true