5 - One-Sample Studies with Ordinal or Numeric Responses

Summary

The chapter covers inferences with ordinal or numeric responses, with the focus on medians or means. We discuss choosing between the mean and median for describing the central tendency. We give an exact test and associated exact central confidence interval for the median that is applicable without making assumptions on the distribution. For the mean, we show the need for making some restrictive assumptions on the class of distributions for testing the mean, otherwise tests on the mean are not possible. We discuss the one-sample t-test, and how with the normality assumption it is uniformly most powerful unbiased test. We show through some asymptotic results and simulations that with less restrictive assumptions the t-test can still be approximately valid. By simulation, we compare the t-test to some bootstrap inferential methods on the mean, suggesting that the bootstrap-t interval is slightly better for skewed data. We discuss making inferences on rate or count data after making either Poisson or overdispersed Poisson assumptions on the counts. Finally, we discuss testing the variance, standard deviation, or coefficient of variation under certain normality assumptions.