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.
[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:
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
