STATS 240: Design and Analysis of Surveys and Experiments - Assignment 4: ANOVA
STATS 240: Design and Analysis of Surveys and Experiments
Assignment 4 Semester 2, 2022
NOTES:
. It is assumed that, wherever possible, you will use inzight Lite for analyses and calculations.
. Answer all questions with respect to the context of the relevant experiment. I.e., questions should be answered with speci city by making reference to the details of the speci c experiment, as appropriate, and not in generalities.
. Clearly label your answers so that it is clear to the marker which assignment question you are anwering. Unlabelled assignments will not be marked.
. You may either copy and paste inzight Lite output into your assignment as text or as a screen grab. If you choose to use text, please ensure that you use a mono-spaced font. Output which is not mono-spaced will be ignored and receive zero marks.
. Where tables are requested, these should have a clear and tidy presentation.
1. [20 marks] An experiment was conducted to compare the effectiveness of five different diet preparations on weight gain. A random sample of 50 males was randomly divided into five equal groups, with preparation A assigned to the first group, B to the second group and so on. Each male in the experiment was given a pre-study physical and told how many kilograms underweight he was. A comparison of the mean number of kilograms underweight before the experiment showed no significant differences among the groups. The study program was then begun, with each group taking the prescribed preparation for a fixed period of time. At the end of the study period, weight gain was recorded (in kg). The data are in the weightGain.csv file available on Canvas.
(a) List the response and the treatment factor used in the experiment. Give an example of a
treatment. 3 marks
(b) Describe an experimental unit for the experiment. 2 marks
(c) What is the replication of each treatment? 1 mark
(d) Generate a dotplot above a boxplot of the weight gain data by diet, superimposing the mean weight gain on each. Present your plot. Brie y describe any similarities and/or differences in weight gain between diets. Hint: Consider features such as the centre, spread and outliers
(if any). 3 marks
(e) An essential assumption of a completely randomised design is that no pair of experimental units is any more similar than any other pair. Brie y explain why using multiple males from the same family would violate this assumption. 1 mark
(f) Briefly explain how the data model for this experiment relates the response to both the
treatments and the experimental units. 2 marks
(g) Fit an ANOVA model to the data to assess whether there is evidence of an effect of diet on weight gain. Present the ANOVA table. What broad conclusion(s) can you draw from the
results in this table? 2 marks
(h) Briefly explain why this experiment has a balanced design and why this fact tells us that,
for this experiment, the margin of error is the same for all treatment means. Calculate the
margin of error for this dataset. 3 marks
(i) Calculate the LSD (Least Significant Difference) and TSR (Tukey's Studentised Range) for comparing pairs of treatment means at the α = 0.01 level of significance. Present your
results, rounding to three decimal places. What conclusions can you draw about the effects
of diets A E on weight gain? 3 marks
2. [20 marks] Japanese beetles ate the Roma beans in my neighbour's garden a couple of years ago. When she visited the garden centre to purchase a suitable pesticide, she found that there were three brands, namely A, B and C, claiming to control Japanese beetles. Not knowing which she should buy, she bought a bottle of each. She then proceeded to run an experiment to learn which of the three pesticides was most effective in keeping the beetles off her beans. My neighbour had six garden beds with beans. Since spray drifts in the wind, very small areas cannot be sprayed.
She therefore divided each garden bed into two plots and sprayed a different pesticide brand on each plot. Below are the numbers of beetles per plot.
Bed
1 2 3 4 5 6
19 A 9 A 25 B 9 A 26 A 13 B
21 B 16 C 30 C 11 B 33 C 18 C
(a) What are the experimental units in this experiment? 1 marks
(b) What are the blocks in this experiment and how many are there? 2 marks
(c) List the treatments in this experiment. 1 marks
(d) How often does each pair of treatments occur together in blocks in this experiment? 1 marks
(e) Name the design which best describes the experiment my neighbour ran? Justify your
answer. 3 marks
(f) Rearrange the above data into a table layout suitable for tting an ANOVA model to it
in inzight Lite, storing it in a CSV le named beetles.csv. Present a copy of your data
table. 2 marks
(g) Generate a dotplot above a boxplot of the beetle Counts by garden Bed. Present your plot.
What do these plots tell you about the six garden beds? 3 marks
(h) Find the appropriate ANOVA for this experiment and explain what you learn from this
table. 3 marks
(i) Explain why the use of blocking was very e ective in this experiment. 2 marks
(j) Calculate the efficiency of this design. What does it tell us regarding the information about
differences between treatment means? 2 marks
