STAT 5817, Final Exam.Name:

About the Final Exam (Read this before you do the exam problems.)

Turn in the electronic copy (through WebCT and name your file as Final_your-last-name.doc) of your final examby Monday of the Final Exam week.

For each of the hypothesis testing questions, you must state the null and the alternative hypotheses.

When writing the conclusion about a testing a hypothesis, just saying reject null hypothesis is not good enough. You must indicate whether the evidence support the alternative hypothesis or not and explain in a way so that readers do not have background in statistical hypothesis testing can understand the conclusion.

  • If SPSS is used for the analysis, you must attach table(s) that contains information you used for drawing conclusion.
  • If you do the problems by hand, you must show all the works that lead to your conclusions.

I. Evaluation of Dosage Forms for a Drug

Five subjects agreed to participate in a study examine the concentration of drug in the bloodstream for three different dosage forms (A, B, and C) of the same product following a single dose. Subjects fasted for eight hours from 10:00 p.m. from the night prior to the study and then took the assigned dose form. The blood samples (15 ml) were obtained after 1 hour after dosing, and were analyzed for the concentration of the drug product in the bloodstream. The same procedure was used on the same five subjects with all three different dosage forms one on each Monday starting with form A and then form B, and the form C was used on the third week. Researchers believe that six days is a long enough washout period. The data in ng/ml were recorded and presented in the following table.

Dosage Forms
Subject / Form A / Form B / Form C
1 / 35 / 85 / 110
2 / 43 / 73 / 120
3 / 44 / 68 / 131
4 / 60 / 89 / 152
5 / 58 / 98 / 142
  1. Make a profile line chart to show the pattern of the responses from various dosage forms versus subjects. Each line represents the outcome from each dosage form. Does the use of different dosage forms seem to have different outcomes?
  1. Run a repeated measure analysis of variance to see if there is any significant difference in responses to the different dosage forms at 5% level of significance?
  1. If there is difference, indicate where the difference lies by post hoc analysis.

II. Study of Antidepressants

An investigator studied the effects of three different antidepressants (A, B, and C) on patient ratings of depression. Patients were all male and were stratified into three age groups. The results in depression scale ratings were recorded and listed in the following table. There are three patients in each treatment and age group combination. The experimenter randomly allocated the treatment and assigned to random sample of three patients from each age group.

Antidepressants

Age Group

/ A / B / C
Less than 20 / 47, 45, 48 / 38, 37, 38 / 29, 33, 32
20 to 40 / 43, 35, 42 / 34, 31, 30 / 22, 27, 25
Above 40 / 45, 46, 48 / 36, 38, 41 / 26, 29, 28
  1. Make a profile line chart for examining the pattern of the average responses from various antidepressants. Each line represents the outcome from each antidepressant. Is there significant difference between the three antidepressants?
  1. At 5% level of significance, test to see if there is significant interaction effect.
  1. At 5% level of significance, test to see if there is significant main effect due to antidepressant.
  1. If there is significant main effect due to antidepressant, identify where the difference lie by performing the post hoc multiple comparisons.

III. Study of Fertilizers

There are four different sites selected for the investigation of four different brands of fertilizers. Four different plots each with different type of soil were used at each experimental site. Latin square design was used to investigate the performance of the four types of fertilizers. Each type of fertilizer is randomly assigned to different site and soil combination with the following Latin Square Design layout. The data listed below were collected from this experiment, and values in parenthesis are the yields of apple (in 100 lb).

  1. State the statistical hypotheses and perform the ANOVA to test whether there is significant effect due to site, soil or fertilizer.
  1. If there is/are significant main effect(s), perform multiple comparisons and identify the homogeneous subsets. Make Profile Plots if necessary to examine the main effect pattern.

IV. Breast Cancer Survival Analysis

Data: BreastCancerSurvival.sav

Download the data above and perform the survival analysis on this breast cancer survival data.

In this data file,

time  Survival time or time till death. (in months)

b_lypos Number of lymph nodes detected cancer cells (0: 1 or less; 1: 2 or more)

status Censor variable (0: Censored; 1: Died)

It is believed that number of infected lymph nodes is strongly related to the survival of breast cancer patients. Researchers create this data to understand the risk factors in breast cancer survival.

  1. Use the data to perform Kaplan-Meier survival function estimation and produce the survival curves for patients with “2 or more infected lymph nodes” and for those with “1 or less” and also interpret the graph. Also, use the Log-rank test to evaluate the significance of the “Lymph Node (b_lypos)” variable.
  1. Use the Cox regression technique to assess the risk of having “2 or more infected lymph nodes” versus “1 or less” to see if the number of infected lymph nodes is a significant predictor for the survival of breast cancer patients. Present you result in terms of the relative risk and the p-value of the test. (Use a 5% level of significance for the test.)