Is caffeine dependence real?

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.

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 using the Stata Command window at the bottom of the string.  Your command will take the form:

gen new_var= caffeine_score-placebo_score

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, 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.  Use alpha=.01.

To do a t-test in Stata for a single mean, first run Statistics--Summaries, Tables, and Tests--Classical tests of hypotheses--One sample mean comparison test.  Put your variable to test and null hypothesis in the appropriate boxes.  

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.  You get a confidence interval automatically when you ask for a t-test in as in (1b).  

Remember: The matched-pairs t-test is a one-sample test for the difference between two sets of pairs.  You would follow the same instructions to do a regular one-sample t-test.

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

Part 2:

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 .  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?  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, the p-value, and your conclusions.  Use a one-sided alternative hypothesis, alpha=.05.

To do a t-test in Stata for a difference of two means, first run Statistics--Summaries, Tables, and Tests--Classical tests of hypotheses--Group mean comparison test.  Put your continuous variable and group variable in the appropriate boxes.   Be sure to check the box for unequal variances and the box for Welch approximation.

4.  Give a 90% confidence interval for the difference in average improvement when viewing the positive subliminal message versus when viewing the neutral message.  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.