Department of Statistics
STATS 240: Design and Analysis of Surveys and Experiments
Assignment 4 Semester 2, 2022
Value: 40 marks total (6% of the total grade)
Due date: 11:00am Tuesday, 27 September, 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 eectiveness of ve dierent diet
preparations on weight gain. A random sample of 50 males was randomly divided into ve equal
groups, with preparation A assigned to the rst 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 signi cant dierences among the groups. The study program was then begun, with each group
taking the prescribed preparation for a xed period of time. At the end of the study period,
weight gain was recorded (in kg). The data are in the weightGain.csv le 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 dierences
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) Brie y 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 eect 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) Brie y 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 Signi cant Dierence) and TSR (Tukey's Studentised Range) for
comparing pairs of treatment means at the α = 0.01 level of signi cance. Present your
results, rounding to three decimal places. What conclusions can you draw about the eects
of diets AE 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 eective in keeping the beetles o 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 dierent 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 eective in this experiment. 2 marks
(j) Calculate the e ciency of this design. What does it tell us regarding the information about
dierences between treatment means? 2 marks