## Prozac for Reducing Relapses in Anorexia Nervosa?Before we analyze the data you should read about the study. Note that the language used below very closely agrees with the language of the article. By and large the question is: Do patients on prozac
have a greater likelihood of maintaining weight and
reducing depression or obsessions about losing weight
than do patients on placebo? We have 35 subjects, each is
randomly allocated to one of two treatment groups
(placebo, prozac). _{1}
be the proportion of persons on placebo who maintain
weight and reduce depression or obsessions about losing
weight; let p_{2} be the proportion of persons on
prozac who maintain weight and reduce depression or
obsessions about losing weight. The researchers wish to
determine how much evidence there is in favor of the
claim p_{1}<p_{2}. This statement
becomes the alternative (research) hypothesis. The null
hypothesis (hypothesis of no difference) has the two
proportions equal. Then, in formal terms,
We estimate p Where'd these numbers come from? Note the unequal sample sizes. This is most likely due to subjects dropping out of the study. Your textbook undoubtedly has a section covering
"comparing two proportions." The method used in
that section (the two-sample Your textbook's method is an approximation to the
method that is used in practice (an approximation that
works quite well when the criteria for using it are
satisfied). The "real method" is not presented
in textbooks because it is somewhat more complicated
computationally. However, the idea is similar. The method
I describe below is We note that 13 of 35 people "maintained." P-value
or observed significance level (OSL) for the test. My
calculations (I suspect they're correct) obtain P-value
= 0.0417 (about 1 in 24). In fact, Fisher's exact test
results in an exact P-value;
61,634,860/1,476,337,800 which, to the nearest 0.0001 is
0.0417.If the null hypthesis is in fact true and the experiment is replicated there is a 1 in 24 chance of obtaining results at least as favorable to the alternative hypothesis as is the observed result (10 of 13 maintainers in the prozac group of 19). The result is statistically significant at level 0.05--but just so. The result is not statistically significant at level 0.01. I would conclude that while there is evidence in favor of the alternative hypothesis (that the likelihood of maintaining is greater when prozac is used) the evidence is not irrefutably strong, and that more investigation should be done before using prozac as a treatment for relapses in anorexia. Finally. . .before accepting the results of this study there are a number of issues that should be examined. Can you think of any? |