Question

Imagine you are testing for the effects of two experimental drugs (data sets B and C)relative to a control group (Data set A) on a physiological variable.

Data set A: 105.51,111.46,104.35,115.27,113.98,119.18,116.45,119.98

Data set B: 93.63,88.90,95.03,86.08,85.86,98.22,105.46,96.50

Data set C: 95.12,97.12,94.08,99.78,101.44,101.27,104.70,103.70

a) Conduct an ANOVA on the data set. Show all calculations, table of results, and state your conclusion.

Please show the calculations.

Answer 1

One Way Analysis of Variance (ANOVA)              

treatment	A	B	C
count, ni =	8	8	8
mean , x̅ i =	113.273	93.71	99.651
std. dev., si =	5.826	6.665	3.886
sample variances, si^2 =	33.947	44.416	15.100
grand mean , x̅̅ =	Σni*x̅i/Σni =	102.21
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	122.351	72.271	6.554
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	978.810	578.170	52.429		1609.408825
SS(within ) = SSW = Σ(n-1)s² =	237.629	310.911	105.697		654.2368

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   24
df within = N-k =   21
  
mean square between groups , MSB = SSB/k-1 =    804.7044
  
mean square within groups , MSW = SSW/N-k =    31.1541
  
F-stat = MSB/MSW =    25.8298

anova table
	SS	df	MS	F	p-value	F-critical
Between:	1609.409	2	804.704	25.830	0.0000	3.467
Within:	654.237	21	31.154
Total:	2263.646	23
					α =	0.05

value of test stat=   25.83
p value is    0.0000

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