Case Study: Treating Schizophrenia (Part 2)

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You might want toreview the introduction to the chapter 3 discussion forum to refresh your memory on this case study.

For the chapter 3 discussion forum, you were asked to calculate the mean and standard deviation for two groups of people: 10 folks who were given given a placebo, and 10 who were given a dose of real medication (the treatment group).

The correct answers for those calculations were as follows:

Group 1 (placebo group): Mean PANSS score= 79.5; Standard Deviation = 17.92

Group 2 (treatment group): Mean PANSS score= 75.3; Standard Deviation = 17.92

Although these summary statistics are basically accurate, the real drug trial had 150 people in each of these groups.I only gave you 10 because I didn't want you entering 150 values into your calculator (you're welcome, haha).

For drug trials, the starting assumption is always that the drug does not work, and it is up to the company to prove that it does work.For ITCI's trial of their molecule lumateperone, they were trying to show that after 4 weeks of treatment the people in the treatment group had lower scores on the PANSS test than people who got the placebo.Looking at the mean PANSS scores above, it does look like the treatment group did better, but on the other hand it could be that lower scores of the people in the treatment group occurred only due to sample variation.What is the probability that the lower scores occurred by random chance, and the drug actually doesn't work?

To estimate this probability, for now we can use the central limit theorem from section 6.5.If we assume that the drug doesn't work in the overall population, then the difference between the two groups should be zero (this is

).However, we see that in the trial which is based on samples from the whole population of people with schizophrenia, the difference was 4.2 points (this is x bar).In this case, we don't know

since that is the population mean, we only know s, the sample mean.Because of this, please use 2.0853 for (

/

n

).With these numbers in mind, please first calculate the z-score for the value of 4.2 assuming the true value should be 0.Basically just plug in these numbers in the equation for the z-score, and tell us what you get for z.Then based on this z-score, tell us what is the probability of getting4.2 or a value more extreme in our sample, assuming the actual value in the population is 0 (i.e. the drug doesn't work)?

You will see that the chance of getting 4.2 or more is low if we assume that the drug doesn't work and the difference between the two groups should be 0.Based on this, we could assume that the drug works with the chance of being wrong equal to the probability of getting 4.2 or something greater.Iknow understanding this last part is challenging, but take a few minutes and try to think it through -if you can follow that, it will help a lot in future chapters where we talk about this logic in greater depth.