Section 2.3 is about a 2017 study where 20 volunteers agreed to be exposed to a treatable strain of malaria. Before exposure, 14 of the volunteers had been randomly assigned to get an experimental malaria vaccine, while the other 6 volunteers got a placebo. Here are the results of the study.
| Placebo | Vaccine | Total | |
| Infected | 6 | 5 | 11 |
| Not infected | 0 | 9 | 9 |
| Total | 6 | 14 | 20 |
What was the population of interest?
Were the 20 people in the study a random sample from the population?
Was this an experiment or an observational study?
Were individuals randomly assigned to the treatment groups?
Does the vaccine appear to work? How can you tell?
The results of the study look good, but could they just be a random fluke? There are two possibilities: Either the explanatory variable (treatment) and the response variable (infection) are associated or independent.
In statistics we call the first possibility the null hypothesis and the second possibility is called the alternative hypothesis. How can we tell which is correct? One way is to simulate re-doing the study many times and see how often we get such extreme results.
To simulate how the study could have turned out differently, we assume that the vaccine has no affect on whether someone gets infected. Then we randomly select 11 people to get infected (like what happened in the original study).
| Placebo | Vaccine | Total | |
| Infected | 11 | ||
| Not infected | 9 | ||
| Total | 6 | 14 | 20 |
It is very rare to get a result where all six members of the placebo group get infected. In fact, that only happens in about 1 out of 84 simulations. That is pretty strong evidence that the original results of the study were not a random fluke.