Normal and t Distributions

Abstract

The normal and t distributions are heavily used in statistical analysis. The normal and t-tables on the Rcmdr menu can be used to look up probabilities p given quantiles (z- or t-values), or quantiles (z or t) corresponding to known p-values. Some of these probability functions are also available in Excel (as part of the Analysis toolpack), but the R functionsare more versatile and more precise.The tables can also be used to explore the relationship between an observed mean$$\bar x$$of n observations and its standard deviation s by using the standardized normal$$z=\bar x / s_{\bar x}$$where the sample standard error of the mean is given by$$s_{\bar x} = s / \sqrt{n}$$.Graphical displays can be used to explore the Type I and II errors associated with hypothesis tests and to explore the effectof sample size on the width of a confidence interval. We can access the graphs from the menus and also from an Excel workbookdescribed in Chapter 5 that communicates with the R process.