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Abstract:
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In a clinical trial, it is common to use an ANOVA model to compare treatment effect between active and placebo group, while adjusting for interesting covariates. The estimated means and variances are based on the underlying data and the model settings, but for statistical inference, the distribution of estimation is also needed. In most cases, in order to get the critical value for statistical inference, we often assume that residuals of model fitting are normally distributed or claim that sample sizes are large enough to apply the central limit theory. In practice, in order to check these assumptions, we often use normality test, such as the Kolmogorov-Smirnov test; however, somewhat crucially, this test does not provide direct information on the actual distribution of the estimators. In this presentation, we introduce a new method for normality verification which is straight forward and can be used to decide whether a data transformation is necessary. In particular, we first utilize Bootstrapping to construct an empirical bivariate distribution on the estimated least square (LS) means of data from active and placebo groups. We then compare this with the bivariate distribution using the same LS means from an ANOVA model with a normality assumption.
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