Afsnitsforfatter: Danielle J. Navarro and David R. Foxcroft

Running the hypothesis test in practice

At this point some of you might be wondering if this is a “real” hypothesis test, or just a toy example that I made up. It is real. In the previous discussion I built the test from first principles, thinking that it was the simplest possible problem that you might ever encounter in real life. However, this test already exists. It is called the binomial test, and it is implemented by jamovi as one of the statistical analyses available when you hit the Frequencies button. To test the null hypothesis that the response probability is one-half p = 0.5,[1] and using data in which x = 62 of n = 100 people made the correct response, available in the binomialtest data set, we get the results shown in figur 84.

figur 84 Binomial test analysis and results in jamovi

Right now, this output looks pretty unfamiliar to you, but you can see that it is telling you more or less the right things. Specifically, the p-value of 0.02 is less than the usual choice of α = 0.05, so you can reject the null. We will talk a lot more about how to read this sort of output as we go along, and after a while you will hopefully find it quite easy to read and understand.

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[1]

Note that the p here has nothing to do with a p-value. The p argument in the jamovi binomial test corresponds to the probability of making a correct response, according to the null hypothesis. In other words, it is the θ value.