Question

13a. Jessica thinks that college major and year of study affect performance on a standardized math test. To determine if she is right, Jessica recruits a sample of 80 students for her experiment. Of her 80 students, Jessica recruits 20 students who are freshmen, 20 who are sophomores, 20 who are juniors and 20 who are seniors. Ten students from each year of study are Psychology majors and the other 10 students from each year of study are Math majors. Fill in the table below Df MS Between College Major Year of Study CollMaj x YrStudy 20 5 144 Within 234 Total 13b. Is there a significant main effect of college major? 13c. Is there a significant main effect of year of study? 13d. Is there a significant interaction between college major and year of study?

Answer 1

Calculate the blank cells using the following formulae

There are 4 years of study      
Hence df-Yrstudy = 4 - 1 = 3      
There are 2 college majors (Psychology and Math)      
Hence df-CollgMaj = 2 - 1 = 1      
df-CollMaj x YrStudy = df-Yrstudy * df-collgmaj      
                       = 3 * 1 = 3      
       
df-Total = Total sample size (N) - 1      
         = 80 - 1      
         = 79      
df-within = df-total - sum(all other dfs)      
          = 79 - 7      
          = 72      
       
MS = SS/Df      
MS-YrStudy = 20,   Df-YrStudy = 3      
Hence, SS-YrStudy = 20 * 3 = 60      
       
MS-within = SS-within / df-within      
             = 144/72      
             = 2      
       
F-collg x Yrstudy = MS-collgxYrstudy / MS-within      
MS-collgxYrstudy = 5 * 2 = 10      
SS-collgxYrstudy = MS-collgyrstudy * df-collgYrstudy      
                                  = 10 * 3      
                                  = 30      
       
SS-collgmajor = SS-total - sum(all other SS)      
              = 234 - (60 + 30 + 144)      
              = 0      
MS-collg major = SS/df = 0/1 = 0      
F-collg major = MS/MS-within = 0/2 = 0      
       
F-yrstudy = MS/MS-within = 20/2 = 10      
The filled up ANOVA table is given below

MS Source df Main Effect A A, SS/df MS(A) /MS(W) given SS/df Main Effect B MS(B) MS(W) given b-1 Interaction Effect MS(A*B) MS(W) A B SS/df given (a-1)(b-1) Within N-ab SS/df gven ab n-1) sum of others Total abn -1

	SS	Df	MS	F
Between
College Major	0	1	0.00	0.00
Year of Study	60	3	20	10
CollgMajxYrStudy	30	3	10.00	5.00
Within	144	72	2
Total	234	79

Green are the filled in cells

Let α = 0.05  Level of Significance    
We find the p-value for each F-value using Excel function F.DIST      
13b p-collgmaj = F.DIST.RT(0, 1, 72)      
                 = 1      
p-collgmaj > 0.05      
Hence, there does not exist a significant effect of college major      
       
13c p-yrstudy = F.DIST.RT(10, 3, 72)      
                   = 0.000014      
p-yrstudy < 0.05      
Hence, there is a significant effect of Year of Study      
       
13d p-collgmajxyrstudy = F.DIST.RT(5,3, 72)      
                    = 0.00332      
p-collgmajxyrstudy < 0.05      
Hence, there is a significant interaction between college major and year of study