Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your name and your lab time. Show all work for full credit.
Round all answers to at least 3 decimal places and assume, unless otherwise noted, that α=0.05
1. A research study compared the effect of three different treatments in reducing blood pressure in hypertensive individuals. A total of 72 subjects were randomly assigned to one of three groups. One group was given an experimental drug. Another group was given the drug and put on an exercise regimen. The third group was a control and received a placebo. At the end of the study, they measured the change in blood pressure (initial measurement – measurement at the end of the study period, in mmHg) for each participant. The gender of the participant was also recorded.
a. The mean change in blood pressure for each treatment group and gender is displayed in the table below. Sketch an interaction plot to show this data. Put the treatment variable on the horizontal axis and plot gender with two separate lines. (3pt)
Mean Change in Blood Pressure (mmHg)
Male
Female
Drug only
10.47
7.84
Drug and Exercise
13.93
11.04
Control
5.36
4.89
b. Does your plot give any indication that there is an interaction effect between treatment and gender on the change in blood pressure? Why/why not? (2pt)
c. Below is a partial ANOVA table of the results. Fill in the rest of the table, and put either p<0.05 or p>0.05 in the last column for each main effect and interaction term. (4pts)
df
SS
MS
F
p-value
Treatment
939.80
Gender
95.89
Treatment*Gender
Error
1032.19
TOTAL
2085.64
d. Assuming all relevant assumptions were confirmed, write a full conclusion to this analysis? (3pt)
e. What percent of the variation in blood pressure change is accounted for by the effects of treatment, gender, and their interaction? (1pt)
2. A botanist wanted to know if the average stem length of daffodils differed depending on which side of a building they grew on. So she collected 20 daffodils each from the north, east, south, and west sides of the building and calculated their stem lengths (cm).
a. Write the null and alternative hypotheses for this analysis. (1pt)
b. If she calculated a test statistic of 𝐹=4.01, what would be her conclusion, in the context of the data? (2pt)
c. If she runs a post-hoc analysis using the Bonferroni correction, what will her cut-off be for finding a significant difference between each pair of means? (2pt)
d. Below is a grouped boxplot of the stem lengths across all four building sides. Which assumption appears to be violated? What should she do to confirm? (2pts)
Distributions of Daffodil Stem Lengths North East South West
Stem Length (cm)