Question

Following are the details of sales ( in Lakhs) done by A,B and C. Test for the significant difference in their performance.

Sales Men	Monthly Sales
A	48	49	50	49
B	47	49	48	48
C	49	51	50	50

Answer 1

one way Anova-

treatment	A	B	C
count, ni =	4	4	4
mean , x̅ i =	49.000	48.00	50.000
std. dev., si =	0.816	0.816	0.816
sample variances, si^2 =	0.667	0.667	0.667
total sum	196	192	200		588	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				49.00
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	0.000	1.000	1.000
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	0.000	4.000	4.000		8
SS(within ) = SSW = Σ(n-1)s² =	2.000	2.000	2.000		6.000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   12
df within = N-k =   9
  
mean square between groups , MSB = SSB/k-1 =    4.0000
  
mean square within groups , MSW = SSW/N-k =    0.6667
  
F-stat = MSB/MSW =    6.0000

anova table
	SS	df	MS	F	p-value	F-critical
Between:	8.00	2	4.00	6.00	0.0221	4.256
Within:	6.00	9	0.667
Total:	14.00	11
					α =	0.05

Ho: µ1=µ2=µ3
H1: not all means are equal

F stat = 6.00

Decision:   p-value<α , reject null hypothesis    

conclusion :    there is enough evidence of significance difference among three treatments