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Intervalles de confiance pour une proportion : lesquels doit-on enseigner ?

The most frequently taught confidence intervals for a proportion are the classical Wald (Ws) and the Clopper-Pearson (CP) ones because of the simplicity of their definition. However, their actual coverage probability of the parameter p is erratic, often quite far from the nominal probability which is aimed at. Other confidence intervals are clearly preferable to the former, but their expression is generally complex and they are difficult to interpret. But nevertheless, through a simple modification of the definition of the Ws and CP intervals, we obtain some confidence intervals with much better coverage probabilities. Namely, these confidence intervals are the Agresti-Coull and Mid-P intervals that we present here. We highly recommend them in a basic Statistics course.