VISUAL ASSESSMENT OF THE SIGNIFICANCE OF A MEAN DIFFERENCE

Data may be graphically displayed as the mean plus or minus the standard deviation, the mean plus or minus its standard error, or by a 95% confidence interval on the mean. When two sets of data are displayed this way, questions may arise as to whether the means are significantly different or if the accompanying two-sample Student t-test has correctly assessed the significance of the difference between the means. Previously published rules of thumb for visual assessment have not included the first two types of display. In addition, the problem of unequal variances has been ignored. In this paper, the ratio of the interval lengths and the sample size of the longer interval are seen to play major roles in devising rules of thumb for these three interval types.-Author