Measurement error in footwear research biomechanics

Abstract

Study designs for the biomechanical evaluation of running footwear often encompass repeated measurements of subjects running in a laboratory setup. During post-processing, within-subject variance is usually discarded by pooling subjects’ data, although it can be used in a beneficial way to derive intervals for relevant effect magnitudes. These are essentially required for the a priori calculation of sample size as well as the interpretation of statistical test results.

Based on the calculation of the random error component of repeated measurements, a sample dataset on rearfoot eversion measurements was used to demonstrate the concept of detecting practically relevant effect magnitudes. This paper provides calculation procedures as well as the interpretational concept, which can both be easily adapted to many other research scenarios.

Keywords:

• practical relevance
• repeatability
• measurement error
• bias
• random error

Notes

1. We can check this assumption visually by plotting the standard deviation between measurements against their mean value – see Figure 1. This procedure relates to the Limits of Agreement concept introduced by Bland and Altman (1999).

2. It is important to note that we do not employ hypothesis testing, which is usually involved when an ANOVA is performed. Since almost every statistical software package is capable of performing ANOVA, we felt this to be the most simple way to obtain the desired results. Interested readers are referred to statistical textbooks to obtain the formulae that comprise an ANOVA procedure (Sheskin 2007, Howell 2010).

3. We do not focus on the particular advantages and drawbacks of this instrumentation in this paper.

4. A two-factor ANOVA, with the subjects being one of the factors, is equivalent to a repeated measures ANOVA on the remaining factor. It is recommended to perform the two-way ANOVA procedure, as some statistical software packages will omit the output of the mean squares for the subjects when a repeated measures ANOVA is performed. However, this subjects mean square can be useful in interpreting the obtained results (see Section 3).

5. If the focus is put on differences between two measurements, the factor  × 1.96 = 2.77 has to be included (Freedman et al. 2007).