Statistics - Factorial Anova Projects

Calculate a two-way ANOVA for the following situation. Suppose you are a school psychologist in a classroom

Problem: Calculate a two-way ANOVA for the following situation. Suppose you are a school psychologist in a classroom setting and you want to find the effect that five teaching styles have on three types of learning activities with respect to knowledge gained. Answer the following questions:

What are the independent variables, and what are the dependent variables?
What would be an appropriate null hypothesis?
What is the research design?
What is the measurement instrument?
What is the confidence level?

What are the f values using the following data?
The data that actually appears in the table are samples; two samples from each treatment group were taken. (Do not be concerned with the specific meaning of the data, as this is used as an example so that you concentrate on the process of using this version of ANOVA.)

	Teaching Style 1	Teaching Style 2	Teaching Style 3	Teaching Style 4	Teaching Style 5
Learning Activity A	106, 110	95, 100	94, 107	103, 104	100, 102
Learning Activity B	110, 112	98, 99	100, 101	108, 112	105, 107
Learning Activity C	94, 97	86, 87	98, 99	99, 101	94, 98

There is an f test for each of the hypotheses, and the f test is the mean square for each main effect and the interaction effect divided by the within variance. The numerator degrees of freedom come from each effect, and the denominator degrees of freedom is the degrees of freedom for the within variance in each case.
It is assumed that main effect A has "a" levels (and A = a – 1 df), main effect B has "b" levels (and B = b – 1 df), n is the sample size of each treatment, and N = abn is the total sample size. Notice the overall degrees of freedom are once again one less than the total sample size.