Question 2

We aim to test pesticides' impact on the survival time for bugs. In the experiment, the researchers consider three dose levels (low, medium, high) are applied with the same type of pesticides produced by four different companies.

a. In the first study, only the factor of dose level is the main factor of interest. A scientist suspects the different companies introduce variances into pesticides. Due to the limited budget in experiment, the experimenter can only have 12 bugs available for testing.In this study, demonstrate how to apply Randomised Complete Block Design (RCBD) in this study and state its advantage over CRD.

b. The researcher is going to use R to conduct the ANOVA test for Randomised Complete Block Design (RCBD). The data is summarised in Table Q2(b), where the columns denote 'dose level' and rows denote the pesticide produced by different companies, and the number in each box records the survival time for each treatment. Show your codes to conduct ANOVA test and construct the ANOVA table in R for RCBD.

		Dose Level
Pesticide company	Low	Med	High
A	0.4	0.3	0.2
B	0.8	0.8	0.3
C	0.5	0.3	0.2
D	0.6	0.6	0.3

Table Q2(b)

c. Explain the results in Question 2(c) and draw your conclusions.

d. In the second study, the researcher wants to conduct a completely randomised design with two-factor design. So the experimenter increase the sample size from 12 bugs to 24 bugs for testing. Implement such a completely randomised design (CRD) in steps.

e. Based on the implementation of CRD with two factors in Question 2(d), the data is summarised in Table Q2(e). Construct the ANOVA table in R on this data. Explain the results and draw your conclusions.

		Dose Level
Pesticide company	Low	Med	High
A	0.4, 0.2	0.3, 0.2	0.3, 0.1
B	0.8, 0.7	0.5, 0.6	0.4, 0.5
C	0.8, 0.6	0.3, 0.7	0.5, 0.7
D	0.7,0.8	0.5, 0.5	0.3, 0.4

Table Q2(e)