The Alpha and Beta Errors in Randomized Trials

Abstract

The sample size required in a randomized trial depends on the alpha (or type I) error and the beta (or type II) error deemed acceptable and on the size of the treatment effect sought (called the delta). We have examined all the randomized trials published in the Journal, the British Medical Journal, and the Lancet in 1987, and have recorded the values selected by the authors for alpha, beta, and delta. Of the 113 trials, only 21 used all three variables. The selected value for the alpha error — the risk of saying there is a difference when there is none — was always 0.05. The value for the beta error — the risk of saying there is no difference when there is one — was 0.10 or more in all but two of these trials.^{1 , 2} None of the authors defended their choice of values for delta.