The Cramer-von Mises statistic was used to compare distributions in factorial experiments. By ranking data instead of using original observations, a new test statistic was developed that can detect differences in distributions other than the mean. This statistic does not require the assumption of normality and can be easily implemented in practice. It allows for accurate critical test null values to be generated regardless of sample size using Monte-Carlo sampling. The approach was illustrated with a simulation trial where operators assessed their workload under different conditions.