Question

A child development specialist is studying the effect of teaching method on standardized test scores of 5th graders. Two teaching methods (method A and B) are being evaluated. Eight primary schools are randomly selected from all the primary schools in the state which have at least three fifth grade classes. Four of the eight schools are randomly chosen to use teaching method A while the remaining four schools use method B. At the end of the school year, two fifth grade classes are randomly chosen from each school and two students from each class are randomly chosen to take a standardized test. Test scores are determined for each student. This experiment gives rise to 32 test score observations.

Develop a 'skeleton' ANOVA table (sources and degrees of freedom). Identify the appropriate ratio of mean squares (F ratio) to test that the true mean of Method A test scores of fifth graders equals the true mean Method B test scores. Explain why you know this is the proper F-test.  

Answer 1

Degress of Freedom:

Df_School(A) = a-1 = 4-1 = 3

Df_Methond (B) = b-1 = 2-1 = 1

df _Interaction (A*B) = (a-1) * (b-1) = 3*1 = 3

df _error = N – ab = 32 – 4*2 = 24

df _total= N – 1 = 32 – 1 = 31

	Df	SS	MS	F
School	3
Method	1
Interaction	3
Error	24
Total	31

F_School = MS _School/MS _Error

_­F_Method = MS _Method/MS _Error

F_Interaction = MS _Interaction/MS _Error

This is a proper case of Factorial ANOVA with Two Independent Factors being School and Method.