An experiment is conducted to determine whether there is a differnce among the m

Question

An experiment is conducted to determine whether there is a differnce among the mean increases in growth produced by five strains (A, B, C, D and E) of growth hormones for plants. The experimental material consists of 20 cuttings of a shrub (all of equal weight), with four cuttings randomly assigned to each of the five different strains. The increases in weight for each cutting along with the sample mean and sample standard deviation of each group are given in the table below.

It is also given that the overall mean = 17.35.

Compute the following:
(a) SSTR=  
(b) SSE =  
(c) MSTR =  
(d) MSE =  
(e) F =

A B C D E Plant 1 18 23 24 16 10 Plant 2 12 24 21 10 14 Plant 3 17 22 21 13 8 Plant 4 16 30 23 13 12 Mean 15.75 24.75 22.25 13 11 Standard Dev. 2.6300 3.5940 1.5000 2.4495 2.5820

Explanation / Answer

An experiment is conducted to determine whether there is a differnce among the mean increases in growth produced by five strains (A, B, C, D and E) of growth hormones for plants. The experimental material consists of 20 cuttings of a shrub (all of equal weight), with four cuttings randomly assigned to each of the five different strains. The increases in weight for each cutting along with the sample mean and sample standard deviation of each group are given in the table below.

Compute the following:
(a) SSTR=  562.3
(b) SSE =  104.25
(c) MSTR = 140.575
(d) MSE =  6.95
(e) F = 20.2266

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

A

4

63

15.75

6.9167

B

4

99

24.75

12.9167

C

4

89

22.25

2.2500

D

4

52

13

6.0000

E

4

44

11

6.6667

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

562.3000

4

140.5750

20.2266

0.0000

3.0556

Within Groups

104.2500

15

6.9500

Total

666.5500

19

Level of significance

0.05

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

A

4

63

15.75

6.9167

B

4

99

24.75

12.9167

C

4

89

22.25

2.2500

D

4

52

13

6.0000

E

4

44

11

6.6667

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

562.3000

4

140.5750

20.2266

0.0000

3.0556

Within Groups

104.2500

15

6.9500

Total

666.5500

19

Level of significance

0.05

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