Student's t test and the glasgow coma scale

Study objective: To explore how Student's t test, which assumes normal errors, is affected by the nonnormal distribution of Glasgow Coma Scale (GCS) scores. Methods: A sample of 145,295 GCS scores from the Pennsylvania Trauma Systems Foundation was assumed to represent the true GCS distribution. Four Monte Carlo simulations, each based on 40,000 replications, were conducted to approximate the distribution of t values arising from samples drawn from the GCS distribution, using sample sizes of 10, 30, 60, and 100 per group. Results: The histograms of t values derived from the GCS distribution resembled the corresponding Student t distributions for sample sizes of 30 or more per group. The t test was conservative in samples of size 10, conservative to acceptable in samples of sizes 30 and 60, and acceptable in samples of size 100. In no case was the t test liberal. Conclusion: The trust can be applied to GCS data with a type I error rate that never exceeds the investigator's chosen significance level. However, a sample size exceeding 30 per group is required for the error rate to adequately approximate the chosen significance level.