Design and Analysis of Experiments Assignment #2, due Saturday, 12th Feb 2022, 23h59

1. An experiment was conducted in 1935 at Rothamsted Experimental Station to study the effectiveness of four soil fumigants in reducing the numbers of eelworms in the soil. The fumigants were Chlorodinitroben- zene (CN), Carbon disulphide jelly (CS), Cymag (CM) and Seekay (CK). Each fumigant was tested both in a single and a double dose. The doses and types of fumigants result in 8 distinct treatments. There is a control treatment as well which is no fumigant. The experimental units were divided into four groups with each group having 12 experi- mental units. The combinations of types and doses (8 treatments) were randomly applied to 8 plots in each group. The control treatment is applied to four plots in each group. Therefore, each non-control treat- ment was replicated four times. Whereas, the control was repeated 16 times. The data are arranged in eelworm.csv file according to the groups.

A sample of 400 grams of soil was taken from each plot and the number of eelworm cysts were counted for each sample before and after fumigant treatments.

Upload the eelworm.csv file and respond to the following.

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(a) Use R coommand factor() to make factors from the columns Block, dose and type. Give the list of factors in R. Example: bfac ¡- factor(Block) bfac (this command will give (print) the list of fac- tors)

(b) Find logcount = log(after) – log(before)

(c) Find all the treatment combinations using

Tmnt < − dfac:tfac dfac= dose factors, tfac=type factors Tmnt gives all eight treatments +control
(d) Fit the model logcount ∼Tmnt + bfac. Perform data analysis by using aov() function.
(e) Give analysis of variance table.
(f) Whatdothep-valuescorrespondingtothevariabletmnt(treatments) and bfac (block factors) indicate?
(g) Find table of means using print(model.tables(model name,”means”))
(h) Find the standard error for the pairs of the contrasts.
(i) Make a two level factor by Make a two-level factor fumigant which contrasts control with fumigants by using
> f < −c(0,1,1)
> fumigant < −factor(f[dfac])
> fumigant

(j) Analyse the data fitting the model logcount ∼fumigant + bfac

(k) Find table of means using

print(model.tables(model name,”means”))

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