Question

Complete the following ANOVA summary table for a model, where there are four levels of factor A selected at random and three levels of factor B selected at random. Each cell of the design includes 20 students (α = .05).

Also, in statistical language (symbols) what is the most appropriate null and alternative hypothesis for each factor (effect) for the model?

Source	SS	DF	MS	F	CriticalValue	Decision	η2	ω2
A	12
B	22
AB
Within	114
Total	172

Answer 1

SOLUTION

ource	SS	DF	MS	F	CriticalValue	Decision	η2	ω2
A	12	3	4	0.2807	4.0662	Not significant
B	22	2	11	0.7719	4.4590	Not significant
AB	24	6	4	0.2807	3.5806	Not significant
Within	114	8	14.25
Total	172	19

There are three sets of hypothesis with the two-way ANOVA.

The null hypotheses for each of the sets are given below.

1. The population means of the first factor are equal. HA0=
2. The population means of the second factor are equal. HB0=  
3. There is no interaction between the two factors.