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 = 16.75.

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

A B C D E Plant 1 9 21 25 16 7 Plant 2 14 24 21 17 12 Plant 3 13 17 20 11 15 Plant 4 18 27 24 17 7 Mean 13.5 22.25 22.5 15.25 10.25 Standard Dev. 3.6968 4.2720 2.3805 2.8723 3.9476

Explanation / Answer

From Excel

a) SSTR=473.5

SSE=184.25

MSTR=118.375

MSE=12.28

F =MSTR /MSE =9.6370

Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 4 54 13.5 13.66667 B 4 89 22.25 18.25 C 4 90 22.5 5.666667 D 4 61 15.25 8.25 E 4 41 10.25 15.58333 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 473.5 4 118.375 9.637042 0.000458 3.055568 Within Groups 184.25 15 12.28333 Total 657.75 19

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