The importance of statistical power

The effectiveness of a home based early childhood intervention on children’s body mass index (BMI) at age 2 years was investigated. A randomised controlled superiority trial was used. The intervention consisted of eight home visits from specially trained community nurses in the first 24 months after birth. The intervention was in addition to the usual childhood nursing service from community health service nurses. The control group received the usual childhood nursing service alone. Participants were first time mothers and their infants.1

The primary outcome was children’s BMI at age 2 years. The sample size calculation was based on having 80% power to detect a difference in mean BMI of 0.38 units between treatment groups at age 2 years, using a two sided hypothesis test and critical level of significance of 0.05. It was assumed that the standard deviation of observations in each group was the same and equal to 1.5 units. A total sample size of 504 participants (252 in each treatment arm) was needed. To allow for an estimated 25% drop-out rate the sample size was increased to 630 participants. In total, 667 first time mothers and their infants were recruited to the trial, with 337 allocated to intervention and 330 to control.

At age 2 years, mean BMI was significantly lower in the intervention group compared with the control group (16.53 v 16.82; difference −0.29, 95% confidence interval −0.55 to −0.02; P=0.04).

Which of the following statements, if any, are true?

• a) The difference in mean BMI of 0.38 between treatment groups is called the smallest effect of clinical interest

• b) An increase in statistical power would require a smaller sample size

• c) The trial was overpowered …