a Textbook references we suggest for these statistical tests include the following: for basic statistical methods try Ramsey and Schafer (2002) or Ott (1993); for regression try Montgomery et a/. (2001); for categorical methods try Agresti (1996); for nonparametric methods try Conover (1999); for time-to-event (survival) analysis try Lee and Wang (2003).
b The statistical and graphical methods used to verify these assumptions are beyond the scope of this chapter. Most of these methods are detailed in the text by Ramsey and Schafer (2002). A reference for categorical data methods is the text by Agresti (1996).
c Observations must be free of cluster and serial effects. Random sampling from the population of interest implies that the observations will be independent of one another. d Standard deviation must be the same between groups being compared, and the variance of a dependent variable should be homogeneous over the range of the independent variable(s) being considered.
e This assumption may be ignored if the sample sizes involved are large enough. How large depends on how far from normality the data seem to stray.
f Adequate model fit typically requires that the dependent response varies as a linear function of the independent predictors and no insignificant (nuisance) parameters are allowed to remain in the model.
g Both variables must be from random samples.
h Loess local regression is a nonparametric technique for describing bivariate relationships where the functional form is not known in advance. i This method has underlying distributional requirements but not necessarily that of normality. 1 Censored observations are typically assumed to be censored at random.
k Assumes that the hazard functions of different individuals are proportional and independent of time.
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