Question

An experiment is conducted to determine whether there is a difference 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.

	A	B	C	D	E
Plant 1	1313	2222	2525	1414	1111
Plant 2	1717	2323	2020	1010	99
Plant 3	1010	1515	2424	1919	88
Plant 4	1313	3030	2020	1818	1313
Mean	13.2513.25	22.522.5	22.2522.25	15.2515.25	10.2510.25
Standard Dev.	2.87232.8723	6.13736.1373	2.63002.6300	4.11304.1130	2.21742.2174

It is also given that the overall mean = 16.7.

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

Answer 1

Reorganise the data in the format given below and import in R.

Run the following code:

summary(aov(dat$`Weight Increase`~dat$Strains+dat$Plants))

Output:

Df SS MS F value Pr(>F)

dat$Strains(TR) 4 7360137 1840034 8.703 0.00155 **

dat$Plants 3 868871 289624 1.370 0.29904

Residuals(Error) 12 2537193 211433

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Reorganised Data:

Plants	Strains	Weight Increase
Plant 1	A	1313
Plant 1	B	2222
Plant 1	C	2525
Plant 1	D	1414
Plant 1	E	1111
Plant 2	A	1717
Plant 2	B	2323
Plant 2	C	2020
Plant 2	D	1010
Plant 2	E	99
Plant 3	A	1010
Plant 3	B	1515
Plant 3	C	2424
Plant 3	D	1919
Plant 3	E	88
Plant 4	A	1313
Plant 4	B	3030
Plant 4	C	2020
Plant 4	D	1818
Plant 4	E	1313