The subjects are eleven people diagnosed as being dependent on caffeine.  During one time period, these people were barred from coffee, colas, and other substances containing caffeine and instead took capsules containing their normal caffeine intake.  During a different time period, they took placebo capsules with no caffeine.  The order of the time periods in which the subjects took caffeine and placebos was randomized.   The subjects, pill administrators, and testers did not know when they got each pill.

Subjects were assessed on the Beck Depression Inventory, which is a psychological test that measures depression.  Higher scores on the test mean the subject shows more symptoms of depression.   Additionally, subjects were asked to press a button 200 times as quickly as possible, and their number of presses per minute was measured.   The researchers are interested in whether being deprived of caffeine affects either of these outcomes.

This is a matched pairs study, because comparisons of the treatments are made on the same person.  The data are in the file caffeine (click here).

Questions

Make new columns for the differences in depression scores and in beats.  For both differences, take (caffeine score - placebo score) as the ordering.   To input the differences, you'll have to edit the columns and use a Formula.  Call over a TA if you have trouble doing this.  

1a) (not handed in) Examine the distribution of depression score differences (caffeine - placebo).  Does a normal curve seem like a reasonable description of the differences?  You don't have to turn anything in for this part, just make the plots to check assumptions.  If the normal curve seems like a reasonable fit, you can use the t-test approach.  Otherwise, because the sample size is small, you have to use other methods that we have not covered in this course.

1b) (handed in)  Test the null hypothesis that caffeine addicts deprived of caffeine have the same population average depression score as caffeine addicts not deprived of caffeine.  Write on your lab report your hypotheses, the value of the test statistic (show the numerator and denominator that go into the test statistic), the p-value, and your conclusions.  Use a two-sided alternative hypothesis, since we don't know whether caffeine deprivation will make people more or less depressed.

To do a t-test in JMP for a single mean, first run Analyze - Distribution on the variable of interest.  Then, click on the arrow next to the variable name, and select Test Mean.  Enter the hypothesized value of the mean in the first box.  Leave the second box empty.  Click OK.   JMP reports three p-values at the bottom of the output:  1) Prob > |t|, which is the p-value when the alternative is two-sided; 2) Prob > t. which is the p-value when the alternative has a >  sign in it; and, 3) Prob < t, which is the p-value when the alternative has a < sign in it.  Choose the one that matches your alternative hypothesis.

2)   Give a 95% confidence interval for the difference in the population average of beats for caffeine addicts not deprived of caffeine and the population average of beats for caffeine addicts deprived of caffeine.   Is there sufficient evidence to say that caffeine deprivation alters addicts' motor speed?

To get the multiplier for the t-distribution, take the following steps.  Open a new data table and add one row.  In column 1, click on Formula-Edit Formula.  Click on Probability- t Quantile.  Enter .975 for p and enter the degrees of freedom for df.  Click OK.  The result you get in the row is the t-multiplier for a 95% confidence interval.  If you want some other confidence percentage, enter as p the value half way  between the percentage and one.  For example, for an 80% confidence interval, enter p=0.90.

Reference:
Moore, D.  The Basic Practice of Statistics.  New York:  W.H. Freeman, 2000, p. 382.

Subliminal Messages (you will get this problem) and Their Effects on Math Test Scores (you will get this problem)

A subliminal message is below our threshold of awareness but may influence our behavior.  Can subliminal messages affect the way students learn math? A group of students who had failed the mathematics part of the City of New York Skills Assessment Test agreed to participate in a study of this question.  The data were originally collected in a study by John Hudesman, and the study is described in Moore (2000, p. 400).

All students received a daily subliminal message flashed on a screen too rapidly to be read consciously.  The students were randomly assigned to receive one of two messages. The treatment group received the message, "Each day I am getting better in math."  The control group received the neutral message, "People are walking on the street."  All students in both groups took a pre-test, went to a summer math skills program, and then took a post-test.

This is a study involving inferences for the difference in means of separate groups.  It's not matched pairs because there are two separate groups: the students who got the subliminal message, and the students who got the neutral message.  The data for the students' test scores are in the file subliminal (click here).  People in the subliminal group have the code "T", and people in the neutral message group have the code "C".

Questions:

3a) (not handed in)  In this problem, the outcome variable is the improvement in test scores.   For each group, examine the distribution of improvement scores.  Do normal curves appear reasonable descriptions of the distributions of improvement scores in each group?  You can get both normal curves on one plot by using Analyze - Fit Y by X.  Put the continuous variable in the Y-box and the group variable in the X-box.  After running it, click on the red arrow next to the "Oneway analysis...", and select Normal Quantile Plot - Plot Actual by Quantile.   If the data in both groups roughly follow normal curves, we can proceed with the significance test.  Otherwise, because the sample size is small, you have to use methods that we have not learned in this course.

3b)  (handed in)  The researchers claim that the positive subliminal message improves test scores.  Test their claim using the change in test score (post-test score - pre-test score) for the subliminal and neutral message groups.  Write your hypotheses, the value of the test statistic (show the numerator and denominator that go into the test statistic), the p-value, and your conclusions.  You can pick off the appropriate values for the means and standard errors by clicking on the red arrow next to "Oneway analysis..." and selecting Means and Std Dev.  Use a one-sided alternative hypothesis.

To run a hypothesis test for the difference of two means in JMP,  use  Analyze - Fit Y by X, inputting the continuous variable in the Y-box and the group variable in the X-box.  After running it, go to the red arrow next to the "Oneway analysis..."  Then select t-Test.  The output shows  the mean, the SE for the difference in means, the upper and lower limits of a 95% confidence interval, the value of the test statistics ("t-ratio") , the degrees of freedom for the t-distribution, and the p-values for the tests of different hypotheses.  As before,  Prob > |t| is the p-value when the alternative is two-sided; 2) Prob > t is the p-value when the alternative has a >  sign in it; and, 3) Prob < t is the p-value when the alternative has a < sign in it.  The graph displays the location of the test statistic on the t-curve. 

4.  Give a 90% confidence interval for the difference in average improvement when viewing the positive subliminal message versus when viewing the neutral message.  Use the degrees of freedom given in the t-test output as the multiplier.  Explain in one sentence what this confidence interval tells you about the effectiveness of the subliminal message versus the neutral message.

COMMENTS ON THIS PROBLEM:

These conclusions are valid for the subject material, message, and student populations in this study. However, they may not generalize to other subject material, messages, or other populations.  Additional studies involving other subject material, other messages, and other populations are needed before we can feel  secure with broad generalizations.

Reference:
Moore, D. The Basic Practice of Statistics. New York: W.H. Freeman and Company, 2000.