HSCI 6263 Biostat Assignment 2: Interpreting Confidence Intervals & Paired T-Test
HSCI 6263 Biostat Assignment 2: Interpreting Confidence Intervals & Paired T-Test
Biostat Assignments provide opportunities for you to develop hypotheses, to calculate statistics, and to interpret output and summary tables. Each assignment focuses on one or two of the statistical concepts discussed in the weekly readings. Week 3 assignment focuses on the interpretation of confidence intervals and the Paired t-Test. There are 10 questions below; each question is worth 1 point.
NAME: _______________________
Part One: Confidence Intervals
Suppose that we were to conduct a study in which 20 volunteers adopt a low-cholesterol diet for 3 months. We measure the cholesterol level of subjects at baseline and after 3-months. Suppose that we observe a mean difference in cholesterol level was equal to 20 mg/dL and a standard deviation of differences equal to 35 mg/dL. [Note: Don’t round too soon in the calculation. Report four decimal places in questions 1 and 2; round to two decimals for your final answer to question 3.]
1) Before calculating the 95% confidence interval, it is always a good plan to first identify the values of the elements in the formula in order to complete the calculation. From Dawson and Trapp, we know that the formula for a 95% confidence interval for a mean difference is: Difference± Confidence factor of the differencex Standard error.
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[see Chapter 5, “Means When the Same Group Is Measured Twice” section]
Based on the information provided in the Part One scenario, what are the values for the difference, the confidence factor of the difference, and standard error?[Note: You will need to refer to Table A-3 in the textbook to help select the confidence factor. Also, you will need to calculate standard error using the values provided in the Part One scenario. Finally, always use a “0.05 area in two tails” in this class unless otherwise told.]
2) Now that you have those values, calculate the 95% confidence interval (CI). What is the lower and upper bounds of that interval? [Show your work.]
3) Interpret this 95% CI.
4) As an added bonus, CIs can also be used to test a null hypothesis. In this scenario, we are told that the cholesterol level was measured before and after patients adopting a low-cholesterol diet. Let’s assume that the null hypothesis states that the mean difference incholesterol level will be zero. Consider the 95% CI that you calculated in question 2 above. Does the null value fall inside or outside of that 95% CI? Based on that, would you Reject or Fail to Reject the null hypothesis?
5) Dawson and Trapp discuss the similarities between hypothesis testing and confidence intervals and highlight one noticeable benefit of reporting confidence intervals. According to the authors of our textbook, what is the additional insight that CIs provide that hypothesis testing does not?
Reflect on what you have seen reported within the literature in your own field. Discuss when CIs are appropriate and useful in interpreting results and when they are not. [Cite accordingly]
Part Two: Paired t-Test
A pharmaceutical company is developing a new appetite suppressing compound for use in weight reduction. A preliminary study of 30 obese patients were conducted on patients’ body weights (in pounds) before and after 10 weeks of treatment with the new compound.We want to examine whether the new treatment is promising or not. Suppose that we observe the results in Table 1 (see the last page) from SAS when we analyzed our data using the UNIVARIATE procedure.
1) What is the purpose of a Paired t-Test and why is it the appropriate statistical test to conduct in this situation?
2) State the Null and Alternative hypotheses.
3) We can use information from the SAS output to calculate a 95% CI for the estimate of the mean difference. Towards the top of the table, we find the N of 30 and the mean difference of 4.23333 (pounds). SAS has also calculated the standard deviation (6.14022 pounds) for us. We do need to determine the confidence factor of the difference or t(n-1) by going to Table A-3 in the textbook. Calculate and report the 95% CI. [Show your work.]
4) We can also use that information to calculate the test statistic (i.e. the t-score). Dawson and Trapp note the t-score formula as:
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Note that the denominator in that equation is standard error (which SAS has already calculated for us). Calculate the t-score using the values provided by SAS. Use Table A-3 and determine the critical value for a 0.05 area in two tails. [Don’t forget to determine the degrees of freedom (i.e. n-1) for this study in order to select the correct critical value.]
5) Based on what you calculated in question 4 above, what conclusion would you make about the null hypothesis (i.e. would you Reject or Fail to Reject the null hypothesis)? What is your interpretation of the test statistic?
[Side Note: The following comments and questions are not part of this graded assignment. They are given to help highlight some of the added insights from the SAS output table.
Statistical programs such as SAS do all the work for us. In question 4, you calculated the t-score test statistic. Take another look at the SAS output table – do you see that same test statistic value listed somewhere in the table?If so, notice the reported P-value for that test statistic. Consider the supplemental video about using P-values to test hypotheses. Based on the P-value approach, would you come to the same conclusion as you did in question 5? ]
Table 1: Output for Part Two
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