Previous Problem List Next (4 points) An experiment is conducted to determine wh
ID: 3042470 • Letter: P
Question
Previous Problem List Next (4 points) An experiment is conducted to determine whether there ls 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 A BC DE Plant 19 17 22 16 14 Plant 2 | 16 27-2 | 13 7 Plant 3 12 21 2015 11 Plant 4 14 21 22 18 10 Mean 12.75 21.5 21.5 15.5 10.5 Standard Dev.2.9861 4.1231 1.0000 2.0817 2.8868 It is also given that the overall mean = 16.35. Compute the following quantities. Hint: Instead of computing these by hand, use R to find the complete table and find the requested quantities. A sample data set can be found in a .csv file in Blackboard (under Assignment #4 data in Assessments). You can write your own numbers in that file to have the correct format, then save it as a.csv file. You will learn how to do ANOVA using R this week during workshop. (a) Sum of Squares of Treatments SSTR= (b) Sum of Squares of Error-SSE (c) Mean Square of Treatment-MSTR = (d) Mean Square Error. MSE = (e) F statisticExplanation / Answer
Answer:
R code:
x=c(9,16,12,14,17,27,21,21,22,22,20,22,16,13,15,18,14,7,11,10)
group=factor(c(1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5))
a1 = aov(x ~ group); a1
summary(a1); a1
R output:
Call:
aov(formula = x ~ group)
Terms:
group Residuals
Sum of Squares 403.80 118.75
Deg. of Freedom 4 15
Residual standard error: 2.813657
Estimated effects may be unbalanced
> summary(a1)
Df Sum Sq Mean Sq F value Pr(>F)
group 4 403.8 100.95 12.75 0.000101 ***
Residuals 15 118.8 7.92
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> a1
Call:
aov(formula = x ~ group)
Terms:
group Residuals
Sum of Squares 403.80 118.75
Deg. of Freedom 4 15
Residual standard error: 2.813657
Estimated effects may be unbalanced
a): SSTR=403.80
b): SSE =118.8
c): MSTR=100.95
d):MSE =7.92
e): F=12.75
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