quiz

FSU Math 924 Spring 2021 Midterm Exam Name: Click here to enter text.

Note: The exam has 2 tasks. For Task II, you will first need to do the homework from class 8.

Task I: Determine whether Aspirin prevents the formation of new polyps in colon cancer patient.

When colon cancer advances to a more severe state it forms more so-called polyps in the gut. Here are some data from a clinical trial that tested whether taking Aspirin would prevent or reduce new polyp formation in colon cancer patients.

The researchers enrolled 635 colon cancer patients in the trial and randomly assigned half of them (317) to receive the drug (Aspirin) for 6 months and the other half (318) to receive a placebo. After 6 months they examined whether new polyps had formed in the guts of the patients during that time.

Here are the results of the study in summary form:

Clinical Trial Format: Prospective study
# of patients enrolled in the study			635
# of patients receiving aspirin				317
# of patients receiving placebo				318
RESULTS
# of patients who received aspiring developing polyps	54
# of patients who received aspiring not developing polyps	263
# of patients who received placebo developing polyps	86
# of patients who received placebo not developing polyps	232

Questions and Tasks:

1. How many variables does the study have?

2. List the variables and the possible values / outcomes / for each variable

Variable 1: outcomes/values:

Variable 2: outcomes/values:

(If you think there are more variables, add more lines)

3. Classify the kind of data produced by the study. (Click on a box to add a check mark)

Are these:

☐ Categorical data?

☐ Continuous, numerical data?

4. What kind of summary statistics do these data produce?

☐ A table with counts, row proportions, column proportions and joint proportions

☐ Mean, median, standard deviations, range and percentiles

5. Determine what kind of statistical analysis can be done to answer the question posed in Task II.

(Check all that apply)

Test whether the difference between two means is significant Test whether two proportions are significantly different Determine whether the variables are associated Determine whether the variables are correlated

6. List the hypothesis test(s) you will perform for the statistical analysis you picked in Q5.

7. State the null hypothesis and the alternative hypothesis for the test(s).

H0:

HAlt:

8. Select the significance level for your test.

Significance level α=

9. Perform the test, using Minitab, Excel or a website of your choice.

10. Provide the summary statistics for the data (paste here from Minitab or Excel).

11. Provide the results of the statistical analysis test that are relevant for your answer. Paste them below.

12. Draw your conclusion about the outcome of the hypothesis test.

13. Draw your conclusion about the research questions asked in the title. State the relevant statistical parameters that support your conclusion.

14. If you determined that Aspirin does indeed prevent polyp formation in colon cancer patients, state the risk ratio (by how many fold the risk of polyp formation is reduced when taking Aspirin as compared to not taking Aspirin).

15. Extra Credit: If you do obtain a risk ratio in question 14, include the 95% confidence intervals for that number.

Task II

Using Minitab, provide the summary statistics and create a box plot for each of these two data sets:

· The systolic blood pressures (y data) from the class 8 homework

· The y residuals from the regression analysis from that homework

Then answer the two questions and possibly the extra credit question on the next page.

(Reminder: as described in the homework instructions, Excel outputs the y residuals by default. In Minitab you needed to select “y residuals” as one of the “Storage” items.)

1. Enter the two columns (blood pressure, residuals) into a Minitab worksheet.

2. Obtain the summary statistics for each column.

3. Create two box plots within the same graph (same scale of the y axis, for easier comparison).

Minitab provides an option to put both boxplots in the same graph. It’s called “Multiple Y’s”.

Here is where to find it: And here is how it looks like:

4. Copy the results from Minitab (the table with the summary statistics and the graph with the two box plots) in the space below here.

Then, answer the following questions:

Q 1.) Compare the interquartile range (IQR) for the y variable (blood pressure) and the y residuals. By about how much is the IQR from the y residuals smaller than the IQR from the blood pressure?

Q 2.) List the mean of the y residuals here:

Q 3.) EXTRA CREDIT: You will notice that the mean of the y residuals is essentially zero. Explain why that is the case.

Additional Information:

Comparing spread of the y values with the spread of the y residuals illustrates by how much the regression analysis improved the variability of the blood pressure data. In other words: if we assume that there is no correlation with body weight, the prediction of the actual blood pressure value of a person (NOT the blood pressure that doctors recommend!) would be based on the mean and standard deviation of the y values from the data set. Adding the body weight as a correlated variable or predictor variable reduces that prediction interval to a much narrower range, essentially to the box plot of the residuals. So your predictive powers become a lot better if you have a variable that has a correlation with the variable you are interested in and you run a linear regression.