Unit 12: Comparing Two Populations

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In 1999, UCLA's student health center (The Ashe Center) conducted a survey of dorm residents based on a random sample. Load the results of the survey into Fathom and take a look at the data.

Your goal here is to tell us how men and women UCLA students differ. Describe the data set, and compare the sexes. You might also want to examine whether students who are satisfied with their body differ from those who are not. Pay careful attention to assumptions; you might not want to do hypothesis tests with some variables. Write it up in a coherent "story".

The variables are as follows:

drink --the answer to the question "Have you ever had an alcohol drink (other than a sip or two)?"

drunktimes-- "How many times have you been drunk this academic year?"

BMI -- Body-mass index; a measure of overall size. Height (cm) divided by squared weight (in kg).

gender-- 0 if female, 1 if male

bodysat -- "Are you satisfied with your body weight?" 1 if yes, 0 if no.

sex -- "F" if female, "M" if male. (I recommend you use this in your analysis since Fathom will recognize it as a categorical variable.)

bodysat2 -- "yes" if satisfied with body weight, "no" if not. Again, I recommend you use this variable.

Put your answers in a file, label is ms12yourlastname and send it to your  instructor.

How to use Fathom to do a 2-sample comparison of means

Fathom has an unusual interface that makes it quite easy to do two-sample comparisons for a data set like the one above. Suppose you have two variables. Var1 is continuous (like weight) and Var2 is categorical with exactly two categories (like sex).

Select "New Hypothesis Test" (or New estimate if you want confidence intervals.) This is the item that looks like the scales of justice on the icon bar. When you pull it down and put it on the desktop you'll get a box that has a short description of what it does. In this box there is a place to select the test you want. At the moment it will probably say "Empty Test". Select compare means.

The box now has the words "First attribute (continuous): <unassigned>" Just below that it says "Second attribute (continuous or categorical): <unassigned>" If you can't see all of these words, you might need to make your box a little larger.

Now, drop the continuous attribute, Var1, onto the word <unassigned> so that it is now assigned to the First Attribute.

Next, drop the categorical variable, Var2, onto the <unassigned> that is associated with the Second Attribute.

Fathom interprets this to mean: compare Mean of Var1 only for those cases in which Var2 is of the first group with the Mean of Var2 for those cases in which Var2 is of the second group. So, for example, it compares the weights of males with the weights of females.

If the Second Attribute had been continuous, then Fathom would have compared the Mean of Var1 with the Mean of Var2.

If the second attribute were categorical but had more than two categories, you would get an error message.

This allows us to accomodate two different structures for the data:

Structure 1
Weight Gender
160 M
100 F
200 M
113 F

This is the structure of the Milestone's data. When you drop "gender" onto the Second Attribute, Fathom knows to compare the means of those with value "M" with the means of those with value "F".

Alternatively, there's Structure 2
Men's Weight Women's Weight
160 100
200 113