Understanding the Effect Size of ADHD Medications: Implications for Clinical Care

Stephen V. Faraone, PhD


September 18, 2003

In This Article

Comparing Studies

The concept of effect-size was developed to facilitate comparisons of efficacy between studies. Without using this concept, comparing 2 studies can be difficult. Consider this example. If one study measures efficacy using the Conners ADHD Rating Scale and another uses the SNAP ADHD rating scale and both report improvement scores, we cannot compare the results because a 1-point improvement on the Conners Scale is not equivalent to a 1-point improvement on the SNAP scale. Even if two studies use the same scale, we cannot simply compare mean change scores between drug and placebo because these studies may differ in their precision of measurement. We should have more faith in precise measures than imprecise ones. These problems of differing scales of measurement and differing precision of measurement make it difficult to compare treatment studies. Fortunately, these problems are overcome by the computation of effect-size, which give us the difference in improvement between drug and placebo, adjusted for the scale and accuracy of the measurements used in each study.

Table 1 summarizes several measures of effect size. The standardized mean difference (SMD) is used when studies report efficacy in terms of a continuous measurement such as a score on an ADHD rating scale. The SMD is easy to compute with this formula:

SMD = Drug Improvement - Placebo Improvement
Standard Deviation

The standard deviation is a measure that adjusts the drug vs placebo differences for the scale and precision of measurement. An SMD of zero means that a drug and placebo have equivalent effects. SMDs greater than zero indicate the degree to which a drug is more efficacious than placebo, and SMDs less than zero indicate the degree to which a drug is worse than placebo. The SMD can range in value from negative infinity to positive infinity, but values are typically between -3 and 3.

Because the job of the SMD is to compare results across different studies using different measures, it cannot be interpreted as a difference in rating scale points or percent improvement. How, then, are we to interpret SMDs? One approach is to use the widely accepted guidelines of Cohen.[3] For SMDs computed by research in the behavioral sciences, he defined 0.2 as small, 0.5 as medium, and 0.8 as large. He gives the mean height difference between 15- and 16-year-old girls, which is half an inch, as an example of a small effect size. The height difference between 14- and 18-year-old girls (about 1 inch) is his example of a medium effect size, and the height difference between 13- and 18-year-old girls (about 1.5 inches) is a large effect size. Another example can be made from differences in intelligence as measured by the Wechsler IQ scales. If a medication increased IQ by 3 points, we would say it had a small effect. We would call an increase of 7.5 IQ points a medium effect and an increase of 12 IQ points a large effect. It is easy to compute the IQ point equivalent of any SMD. You simply multiply the SMD by 15.


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