Pitfalls of statistical hypothesis testing: type I and type II errors

Researchers investigated the effects of a multidimensional lifestyle intervention on aerobic fitness and adiposity in predominantly migrant preschool children. A cluster randomised controlled trial study design was used. Intervention included a physical activity programme, plus lessons on nutrition, media use (use of television and computers), and sleep and adaptation of the built environment of the preschool class. The study lasted from August 2008 to June 2009. The control group did not receive any intervention and continued their regular school curriculum, which included one 45 minute physical activity lesson a week in the gym.1

In total, 40 preschool classes were recruited in areas with a high migrant population in the German and French speaking regions of Switzerland. Classes were randomised to intervention or control after stratification for linguistic region. The primary outcomes were aerobic fitness as measured by the 20 minute shuttle run test and body mass index (BMI). Secondary outcomes included motor agility, percentage body fat, and waist circumference.

The critical level of significance for statistical testing was set at 0.05 (5%). Intervention resulted in significantly increased aerobic fitness compared to control (intervention minus control) (mean difference: 0.32 stages; 95% confidence interval 0.07 to 0.57; P=0.01), but no difference in BMI (−0.07 kg/m², −0.19 to 0.06; P=0.31). The authors concluded that a multidimensional intervention increased aerobic fitness and reduced body fat but not BMI in predominantly migrant preschool children.

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

• a) If in the population there was no difference between intervention and control in mean aerobic fitness, then a type I error occurred …