How to Use Percentiles to Better Understand Standardized Mean Difference (SMD) as a Measure of Effect Size

The standardized mean difference (SMD) is the difference between the means of a variable, expressed not in its original unit but in the unit of standard deviation (SD). SMDs of 0.2, 0.5, and 0.8 are conventionally considered to be small, medium, and large, respectively. The reader, however, obtains no real world understanding of an SMD from these adjectives. This article suggests a solution: SMDs and their 95% confidence intervals can be better understood if they are converted into percentile scores. The procedure is explained, step by step, with reference to a meta-analysis that found that cholinesterase inhibitors (ChEIs) significantly attenuated delusions and hallucinations in Alzheimer disease and Parkinson disease with SMDs that ranged from -0.08 to -0.14. After conversion of these SMDs to percentile scores, the reader is shown that the average patient in the ChEI treatment arms would have improved by just 3 to 7 percentile places relative to the average patient in the placebo arms. So, whereas the findings were statistically significant, they would perhaps be so small as to be clinically unobservable in the average patient. All that the reader needs to do to convert an SMD into a percentile score is to locate a table that presents area under the normal curve, understand how the table presents what it does, look up the SMD value in the table, and obtain the percentile score from the value in the table. The entire procedure is very easily understood and takes less than a minute, starting from locating the table through an online search to obtaining the percentile score for the SMD.