11.10 Thirty pea seeds were randomly assigned to 3 groups of 10. One group was g
ID: 3054031 • Letter: 1
Question
11.10 Thirty pea seeds were randomly assigned to 3 groups of 10. One group was germinated in the presence of chemical A, a second group with chemical B, and the third group served as a control. After five days, the length (in millimeters) of the primary root was mea sured. We wish to know if either or both of these chemicals affects root growth, and if so, if one is more effective than the other. Chemical A Chemical B Control 120 125 122 100 82 97 105 115 103 121 130 107 106 120 100 125 102 128 121 115 130 120 105 89 100 90Explanation / Answer
>data1=read.csv(file.choose(),header=T) #importing csv file into R
> attach(data1)
> data1
Chemical.A Chemical.B Control
1 115 120 82
2 103 125 97
3 98 122 105
4 121 100 90
5 130 90 102
6 107 128 98
7 106 121 105
8 120 115 89
9 100 130 100
10 125 120 90
> chemical=c(Chemical.A,Chemical.B,Control)
> type=c(rep(1,10),rep(2,10),rep(3,10))
> type=as.factor(type)
> df=data.frame(chemical,type)
> df
chemical type
1 115 1
2 103 1
3 98 1
4 121 1
5 130 1
6 107 1
7 106 1
8 120 1
9 100 1
10 125 1
11 120 2
12 125 2
13 122 2
14 100 2
15 90 2
16 128 2
17 121 2
18 115 2
19 130 2
20 120 2
21 82 3
22 97 3
23 105 3
24 90 3
25 102 3
26 98 3
27 105 3
28 89 3
29 100 3
30 90 3
> model=aov(chemical~type,data=df)#Fitting one-way ANOVA
> summary(model)
Df Sum Sq Mean Sq F value Pr(>F)
type 2 2512 1256.2 10.95 0.000329 ***
Residuals 27 3097 114.7
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Since p-value is very small, we reject the null hypothesis of no difference and conclude that there is significant difference in the root growth among different treatments.
> TukeyHSD(model) #Tukey HSD test
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = chemical ~ type, data = df)
$type
diff lwr upr p adj
2-1 4.6 -7.275541 16.475541 0.6076159
3-1 -16.7 -28.575541 -4.824459 0.0046602
3-2 -21.3 -33.175541 -9.424459 0.0003840
Since p-values for (1,3) and (2,3) are < 0.05, we can say that the difference in root growth for control and chemical A and that for control and chemical B are significant but the difference in root growth for chemical A and B are not significant since p-value>0.05.
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