Question 1.
The file “folate.txt” contains data on red cell folate levels (folate) in patients receiving three different methods of ventilation (ventilation) during anesthesia. The three different methods are coded as follows:
1 = 35-50% oxygen given continuously for 24 hours
2 = 50% nitrous oxide and 50% oxygen given continuously for 24 hours.
3 = 50% nitrous oxide and 50% oxygen given only during the operation.
a. Plot the data, and summarise the information available from the plot.
b. Fit a model to compare the folate for different ventilation methods. Produce and inter-pret the summary table of coefficients.
c. There is one pairwise comparison that cannot be tested explicitly by referring to thetable of coefficients. Create a contrast that allows for that comparison. You should also create a second contrast to complete an orthogonal set.
(i) State the null hypothesis corresponding to each of these contrasts, in words andusing statistical notation.
(ii) Verify that the two contrasts form an orthogonal set.
(iii) Rerun the model by partitioning the SS for ventilation using the two
contrasts. Produce and interpret relevant output.
Question 2.
A factorial experiment was conducted to investigate the yield (BYIELD) of barley. Thirty-six plots were divided into four blocks (BBLOCK). Three varieties (BVARIETY) were compared at three different row spacings (BSPACE). The data are stored in Data File: Barley.txt
(a) Produce two exploratory data plots. With reference to the plots, describe how the meansmay vary with variety and spacing. What statistical model is suggested?
(b) Fit a model that includes all main effects and the interaction between variety and spacing.Produce relevant outputs and assess whether the interaction is significant. Write an informative summary that relates to the context of the question
