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Commentary |

Arguments for and Against Standardized Mean Differences (Effect Sizes)

Peter Cummings, MD, MPH
Arch Pediatr Adolesc Med. 2011;165(7):592-596. doi:10.1001/archpediatrics.2011.97.
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Researchers often estimate an association to quantify a possibly causal relationship between an exposure (a treatment, habit, or experience) and an outcome (death, illness, or a continuous measurement). Statistics used to quantify associations include ratios or differences in risks, rates, or means. If the estimated association is causal, these statistics describe the effect of exposure on the outcome. The effect for a population is the average outcome if all were exposed (or at some exposure level) compared with the average outcome if all were not exposed (or at a different level of exposure).1,2

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Figure 1. The distributions of final total plasma cholesterol values for treated and control subjects are shown for 3 hypothetical randomized trials of a statin drug. Vertical lines indicate average cholesterol values for each treatment arm; SD, pooled standard deviation for the outcomes; and SMD, standardized mean difference (mean difference divided by pooled SD). The vertical scales for trials 1 and 2 have been compressed compared with the scale for trial 3. To convert total cholesterol to millimoles per liter, multiply by 0.0259.

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Figure 2. The distributions of final total plasma cholesterol values for treated and control subjects are shown for 3 hypothetical randomized trials of 3 different statin drugs. Vertical lines indicate average cholesterol values for each treatment arm; SD, pooled standard deviation for the outcomes; and SMD, standardized mean difference (mean difference divided by pooled SD). The vertical scales for trials 4 and 5 have been compressed compared with the scale for trial 6. To convert total cholesterol to millimoles per liter, multiply by 0.0259.

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