The purpose of the lab is to use JMP to obtain confidence intervals and p-values from hypothesis tests.
Lab Procedures
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:
1a) (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.
1b) (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-testscore) 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.
2. 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.