Testing statistical hypotheses using standard error bars and confidence intervals

When agricultural researchers construct figures or graphs displaying sample means from an experiment, a popular technique to display the relative vari ation is to include standard error bars. This technique can be very informa tive but misleading. Researchers will sometimes try to draw inference to th e equality of their means by using these standard error bars. This paper ex plores the use of standard error bars in comparing population parameters an d exhibits how conclusions drawn by this method will often be faulty. The u se of confidence intervals to test hypotheses is also presented. Some simpl e mathematical derivations are presented, along with a small computer simul ation 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 alpha=0.16. In situations in which it is difficult to perform a test, but confidence intervals are available, an alternative for performing alpha=0.05 test is to evaluate 85% confidence intervals and reje ct the hypothesis that the parameters are equal if the intervals fail to ov erlap.