Sample size calculations for a functional human motion analysis: Application to vehicle ingress discomfort prediction

The ease of entering a vehicle, known as ingress, is one of the important ergonomic factors that car manufacturers consider during the process of vehicle design. Manufacturers frequently conduct human subject tests to assess ingress discomfort for different vehicle designs. Using subject tests, manufacturers are able to estimate the proportion of participants that report that they are discomfortable entering a vehicle, referred to in this paper as fraction disaccommodated (FD). Manufacturers then conduct statistical tests in order to determine if the FD of two vehicle designs are significantly different, and to determine the required sample size in testing the FD difference between two vehicle designs under pre-specified testing power. Since conducting human subject tests is often expensive and time consuming, another alternative is to estimate the FD using simulated human motion data. Determining the number of simulations that is required is an important statistical question that is dependent on the prediction performance of the simulation analysis. In this paper, a dual bootstrap approach is proposed to obtain the standard deviation of the estimated FD based on functional predictors. This standard deviation is then used to calculate the power in testing the difference between two estimated FDs.