Sample size calculation

The sample size calculation is performed in order to estimate the number of students to include in intervention and reference schools, respectively. The standard formula for sample size calculation to test a difference between two mean values is used:

where α is the significance level in a one-sided test

1-β is the power

is the value in a standard normal distribution with area under the curve below x

is the common standard deviation in total number of injuries for a student

and are the mean number of total injuries for students in schools with normal and extra physical education (PE)

To account for clustering (i.e. students within class or school) an adjusted sample size is calculated as:

where

N’ is sample size adjusted for clustering

N is sample size when no clustering (formula above)

m is number of students within a cluster

ρ is the intraclass correlation coefficient (ICC)

The literature regarding number injuries among school children with difference in the amount of physical education is sparse(1, 2).Sports specific injury occurrences have been reported extensively but in a sports type specific environment with selected individuals and setting (3-8).

For the sample size calculation we made the following assumptions:

  • significance level, α (probability of a type I error) of 0.05 and corresponding Z-value of1.645 for a one-sided test
  • power level, 1-β (1 minus the probability of failing to reject the null hypothesis when it is false (type II error)) and corresponding Z-value of 0.84
  • mean value of total number of injuries in schools with normal PE at 1.4 injury per student during a 2-year study period
  • difference in mean value of total number of injuries between students in schools with normal and extra PE, - at 0.3-0.4
  • common standard deviation, of number of injuries for a student, at 1.0-1.5
  • clustering at school or class level
  • ICC at school level at 0.01 and ICC at class level at 0.05.

Sample size (N’) as number of students within normal and extra PE schools, respectively / Scenario
1 / 2 / 3
Common, / 1.5 / 1.0 / 1.5
Difference, - / 0.3 / 0.3 / 0.4
Clustering school level, ICC=0.01 / N’= 615 / N’= 273 / N’= 295
Clustering class level, ICC=0.05 / N’= 525 / N’= 233 / N’= 346

ICC at school level is assumed to be small as the variation between schools usually is small, whereas ICC at class level is assumed to be larger as the variation between classes usually is larger.

The sample size calculation indicated that the number of students to be included in the study in normal PE and in extra PE schools, respectively, varies between 300-600 students.

In the present study we intended to include 500-600 students in normal PE schools and 500-600 students in extra PE schools.

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2.Collard DC, Verhagen EA, Chinapaw MJ, Knol DL, van Mechelen W. Effectiveness of a school-based physical activity injury prevention program: a cluster randomized controlled trial. Arch Pediatr Adolesc Med. [Randomized Controlled Trial

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3.Soligard T, Myklebust G, Steffen K, Holme I, Silvers H, Bizzini M, et al. Comprehensive warm-up programme to prevent injuries in young female footballers: cluster randomised controlled trial. Bmj. [Multicenter Study

Randomized Controlled Trial

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4.LaBella CR, Huxford MR, Grissom J, Kim KY, Peng J, Christoffel KK. Effect of neuromuscular warm-up on injuries in female soccer and basketball athletes in urban public high schools: cluster randomized controlled trial. Arch Pediatr Adolesc Med. [Multicenter Study

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5.Wedderkopp N, Kaltoft M, Lundgaard B, Rosendahl M, Froberg K. Injuries in young female players in European team handball. Scand J Med Sci Sports. [Research Support, Non-U.S. Gov't]. 1997 Dec;7(6):342-7.

6.Powell JW, Barber-Foss KD. Injury patterns in selected high school sports: a review of the 1995-1997 seasons. J Athl Train. 1999 Jul;34(3):277-84.

7.Radelet MA, Lephart SM, Rubinstein EN, Myers JB. Survey of the injury rate for children in community sports. Pediatrics. 2002;110(3):e28.

8.Caine D, Caine C, Maffulli N. Incidence and distribution of pediatric sport-related injuries. Clin J Sport Med. [Review]. 2006 Nov;16(6):500-13.