To determine whether a new sleeping pill has an effect that varies with dosage, a researcher randomly assigns adult insomniacs, in equal numbers, to receive either 4 or 8 grams of the sleeping pill. The amount of sleeping time is measured for each subject during an 8-hour period after the administration of the dosage. What type of design is this, and what type of statistic is needed to analyze the data?

Response 1:

I think that each group is an independent group. Since they are both being given the same drug (just in different dosages), I believe that we can compare population means between the two groups by conducting a 2-way ANOVA. The ANOVA’s f-test can be used to analyze the data collected. Maybe, we could use a t-statistics and “simply” (I use this word lightheartedly) compare the means of both groups to identify differences in effect of the medicine.

Response 2:

This situation uses a new sleeping drug 4 grams (treatment1) or 8 grams (treatment2) as the independent variable (nominal data; both sleeping pill). The samples are the adult who live with insomnia that they were assigned equally numbers but we do not know how much. The dependent variable is the amount of sleeping time (nominal data; sleep and do not sleep) that researchers have to measure after the sample groups took this medicine 8 hrs. So, I think I select to use a two-variables (X2) test.

The null hypothesis is H0: There is not a relationship between the dosage of new pills and sleeping.

The alternative is H1: H0 is false.

Sleep after taking the drug in 8 hours.new sleeping drugs 4 g. (n1)new sleeping drugs 8 g. (n2)sleepABnot sleepCD

P.S. I am not sure that I can understand the situation correctly. So, as I understood this situation I think I should use an X2 test. If I am wrong please discuss.

Response 3:This study involves two different independent variables, which are the two different dosages that are being administered. Because there are two different independent variables here, a two-way ANOVA test is needed. You would need to use an f-statistic so that you can look at the statistical significance of the results of the test. The best way to determine if there’s a big different between taking a smaller dose verses taking a larger dose, the means of the test results will need to be compared. This can be done with a two-way ANOVA test.