Conduct a oneway ANOVA to test for differences between means

Conduct a one-way ANOVA to test for differences between means. Show all your work to calculate the F-ratio and state your conclusions. To obtain the p-value you can use the following online calculator:

http://www.danielsoper.com/statcalc3/calc.aspx?id=7

Group A   Group B   Group C
60.34   62.49   65.37
60.54   62.86   65.5
61.28   65.93   65.24
61.29   63.79   65.54
61.47   65.34   65.99
61.6   65.19   66.26
61.65   66   67.41
61.5   65.42   68.15

Solution

GroupA  

GroupB  

GroupC

Total

60.34

62.49

65.37

60.54

62.86

65.5

61.28

65.93

65.24

61.29

63.79

65.54

61.47

65.34

65.99

61.6

65.19

66.26

61.65

66

67.41

61.5

65.42

68.15

sum

489.67

517.02

529.46

1536.15

sum of squares

29973.8

33427.14

35048.83

98449.77

Corrction factor CF=1536.15² /24 = 98323.20

SST =98449.77- 98223.20 = 226.57

SSGroup = (489.67² +517.02²+529.46²)/8 - 98223.20 =103.58

SSE = 126.57-103.58 =22.99

DF for treatment = 3-1=2

DF for total = 24-1=23

DF for error = 23-2=21

MSGroup=103.58/2 =51.79

MSE = 22.99/21 = 1.09

F= 51.79 /1.09 =47.51

ANOVA table

Source

SS

   df

MS

F

Treatment

103.58

2

51.79

47.51

Error

22.99

21

1.09

Total

126.57

23

Table value of F( 2,21) at 0.05 level =3.47

Calculated F=47.51 > 3.47 the table value

Calculated P= 0.0000   < 0.05 level of significance.

The null hypothesis is rejected

We conclude that the three group means are different.

	GroupA	GroupB	GroupC	Total
	60.34	62.49	65.37
	60.54	62.86	65.5
	61.28	65.93	65.24
	61.29	63.79	65.54
	61.47	65.34	65.99
	61.6	65.19	66.26
	61.65	66	67.41
	61.5	65.42	68.15
sum	489.67	517.02	529.46	1536.15
sum of squares	29973.8	33427.14	35048.83	98449.77