Exercises: Compare Two Treatments Using Re-Randomization Simulation

In a randomized experiment, the treatment group's mean improvement is $\bar{x}_T = 12$ points and the control group's mean improvement is $\bar{x}_C = 8$ points. What is the observed difference $\bar{x}_T - \bar{x}_C$, in points?

To test whether a treatment had a real effect, we begin by assuming a model. What is the model we assume and test?

In a drug trial, $\hat{p}_T = 0.70$ of the treatment group recovered and $\hat{p}_C = 0.55$ of the control group recovered. What is the observed difference in recovery proportions $\hat{p}_T - \hat{p}_C$? Give your answer as a decimal.

A randomized experiment finds that the treatment group's mean is 3 points higher than the control group's. A student concludes, "The treatment worked." Why is this conclusion premature?

A treatment group of 5 subjects has improvement scores 10, 12, 14, 8, 11. A control group of 5 subjects has scores 9, 7, 10, 8, 6. Compute the observed difference in means $\bar{x}_T - \bar{x}_C$, in points.

During one re-randomization shuffle, which of the following actually moves, and which stays fixed?

The dot plot shows 50 re-randomization differences built under the no-effect model. The observed difference is +4 points. (a) How many of the 50 shuffles produced a difference of +4 or more? (b) What fraction of shuffles is that (as a decimal)?

Using the same dot plot, the observed difference of +4 lands in the far upper tail, with only about 4% of shuffles at least that large. What is the significance decision?