Question

he following is the results if three measures of language capacity following brain damage to the area of the brain associated with receptive language

Person	Speech	Conceptual	Syntax
1	8	7	6
2	6	8	6
3	9	5	3
4	5	4	5
5	6	6	3
6	8	7	4

Perform a RM ANOVA with any post-hoc tests. You do not have to make corrections to a violation of sphericity

Answer 1

n=	6
k=	3
N=	18
G=	106
ΣX²=	676

correction factor,cf=G²/N=           624.2222222
SSTreatment=1/nΣT²-cf=           19.44444444
df=k-1=       2  
          
total SS=ΣX²-cf=           51.77777778
df=N-1=       17  
          
error SS=total SS-treatment SS=           32.33333333
df error=N-k=       15  
          
PSS=1/kΣP²-cf=       13.11111111  
df=n-1=       5  
          
SS error=ESS-PSS=       19.22222222  

Table
Source	SS	df	MSS	F	F-critic	P-Value
B/w groups	19.4444	2	9.7222	5.0578	4.10	0.0304
Within Group	32.3333	15	2.1556
i) B/w Subject	13.1111	5	2.6222
ii) Error	19.2222	10	1.9222
Total:	51.7778	17			α=	0.05

   Decision:   p-value<α , reject null hypothesis    
          
conclusion :    there is enough evidence of significant mean difference among three treatments