Testing statistical hypotheses using standard error bars and confidence intervals

Abstract

When agricultural researchers construct figures or graphs displaying sample means from an experiment, a popular technique to display the relative variation is to include standard error bars. This technique can be very informative but misleading. Researchers will sometimes try to draw inference to the equality of their means by using these standard error bars. This paper explores the use of standard error bars in comparing population parameters and exhibits how conclusions drawn by this method will often be faulty. The use of confidence intervals to test hypotheses is also presented. Some simple mathematical derivations are presented, along with a small computer simulation study. If a researcher utilizes standard error bars in an attempt to test a hypothesis, he or she will be performing a test with an approximate type I error rate of α=0.16. In situations in which it is difficult to perform a test, but confidence intervals are available, an alternative for performing a=0.05 test is to evaluate 85% confidence intervals and reject the hypothesis that the parameters are equal if the intervals fail to overlap.