ii. The plan in the figure below and on page 73 of Rosemary's book is the field layout of an experiment conducted in 1935 at Rothamsted Experimental Station (an agricultural research station founded in 1843). Each plot had a notice on it showing the block number and the plot number. These are the top two numbers given in each plot in the plan. The purpose of the experiment was to compare various types of fumigant, in single and double doses, for their ability to control eelworms in the soil where oats were being grown. A "control treatment (i.e. no fumigant) was included. In the plan, each plot shows, in order below the plot number, the level of a factor called Fumigant, then the dose, then the type of chemical. In the spring, 400 gm of soil were sampled from each plot, and the number of eelworm cysts in each sample counted and recorded. The oats were sown, fumigated, grown and harvested. After harvest the plots were sampled again in the same way, and the number of cysts recorded. The variable logcount was calculated as logcount log(number of eelworm cysts at harvest) -log(number of eelworm cysts in spring before treatment) where the logarithms are to base e. This variable is shown at the bottom of each plot in the plan. (a) How many treatments were there? (b) How were the plots divided into blocks? (c) After sampling soil from plot 4 of block III, which plot should the scientist sample next? (d) Devise a better way of numbering the plots. (e) Why do you think logarithms were used to present the data in the form logcount? 73 Questions for discussion 1 1 1 1 1 1 1 2 3 4 5 6 1 2 2 2 2 1 0 2 1 1 1 0 Z K N M S Z 0.549 -0.0110.457 0.599 0.341 0.784 1 I 1 1 1 1 7 9 10 11 12 1 2 2 2 1 2 0 2 2 1 0 2 Z M $ K Z M 0.799 0.365 0.277 0.107 1.187 0.740 IV IV TV 37 38 2 2 2 2 2 2 M S 0.7390M 0.574 11 DI II 14 15 16 25 26 27 28 2 1 2 2 2 1 2 2 1 0 1 2 2 0 1 1 K 2 S K K Z K M 0.771 0.873 0.801 06090.414 0.5210.191 1.088 TV IV TV 40 41 42 1 2 2 1 1 Z V 1.482 0.791 1316 II 17 18 19 20 29 30 31 32 2 2 2 1 2 2 1 0 2 2 1 0 2 2 0 N S N Z N S Z 1.269 1.067 0.888 1665 2.170 2.325 0.499 1.719 E-ONS IV IV TV 43 45 2 1 1 1 0 M Z Z 1.457 0.616 1.398 IV TV IV 46 47 1 2 2 2 N S 2.138 1.992 1.271 II II 21 22 231 24 33 34 35 36 2 1 2 1 2 2 1 2 2 1 0 0 0 1 1 2 M Z M Z S N Z 0812 1.081 1.355 1.6181.347 1.792 1.807 1.836 -ON type of fumigant Z no fumigant Nchloroinitrobenzene N Cymag' S carbon disulphide jelly K Seckay dose of fumigant O no fumigant 1 single dose 2 double dose Fig. 48. Field layout for the experiment in Question 43 ii. The plan in the figure below and on page 73 of Rosemary's book is the field layout of an experiment conducted in 1935 at Rothamsted Experimental Station (an agricultural research station founded in 1843). Each plot had a notice on it showing the block number and the plot number. These are the top two numbers given in each plot in the plan. The purpose of the experiment was to compare various types of fumigant, in single and double doses, for their ability to control eelworms in the soil where oats were being grown. A "control treatment (i.e. no fumigant) was included. In the plan, each plot shows, in order below the plot number, the level of a factor called Fumigant, then the dose, then the type of chemical. In the spring, 400 gm of soil were sampled from each plot, and the number of eelworm cysts in each sample counted and recorded. The oats were sown, fumigated, grown and harvested. After harvest the plots were sampled again in the same way, and the number of cysts recorded. The variable logcount was calculated as logcount log(number of eelworm cysts at harvest) -log(number of eelworm cysts in spring before treatment) where the logarithms are to base e. This variable is shown at the bottom of each plot in the plan. (a) How many treatments were there? (b) How were the plots divided into blocks? (c) After sampling soil from plot 4 of block III, which plot should the scientist sample next? (d) Devise a better way of numbering the plots. (e) Why do you think logarithms were used to present the data in the form logcount? 73 Questions for discussion 1 1 1 1 1 1 1 2 3 4 5 6 1 2 2 2 2 1 0 2 1 1 1 0 Z K N M S Z 0.549 -0.0110.457 0.599 0.341 0.784 1 I 1 1 1 1 7 9 10 11 12 1 2 2 2 1 2 0 2 2 1 0 2 Z M $ K Z M 0.799 0.365 0.277 0.107 1.187 0.740 IV IV TV 37 38 2 2 2 2 2 2 M S 0.7390M 0.574 11 DI II 14 15 16 25 26 27 28 2 1 2 2 2 1 2 2 1 0 1 2 2 0 1 1 K 2 S K K Z K M 0.771 0.873 0.801 06090.414 0.5210.191 1.088 TV IV TV 40 41 42 1 2 2 1 1 Z V 1.482 0.791 1316 II 17 18 19 20 29 30 31 32 2 2 2 1 2 2 1 0 2 2 1 0 2 2 0 N S N Z N S Z 1.269 1.067 0.888 1665 2.170 2.325 0.499 1.719 E-ONS IV IV TV 43 45 2 1 1 1 0 M Z Z 1.457 0.616 1.398 IV TV IV 46 47 1 2 2 2 N S 2.138 1.992 1.271 II II 21 22 231 24 33 34 35 36 2 1 2 1 2 2 1 2 2 1 0 0 0 1 1 2 M Z M Z S N Z 0812 1.081 1.355 1.6181.347 1.792 1.807 1.836 -ON type of fumigant Z no fumigant Nchloroinitrobenzene N Cymag' S carbon disulphide jelly K Seckay dose of fumigant O no fumigant 1 single dose 2 double dose Fig. 48. Field layout for the experiment in Question 43