The misconception that the normality assumption
applies to the response and/or predictor variables is
problematic in that there are certainly situations where
the response and/or predictors are not normally
distributed, but a normal distribution for the errors is
still plausible. As one example, dichotomous predictors
are often used in multiple regression; although such
predictors are clearly not normally distributed, the
errors of regression models using dichotomous
predictors may still be normally distributed, allowing
for trustworthy inferences. Furthermore, dichotomous
variables that are particularly strong predictors of a
response variable may induce a bimodality to the
marginal distribution of the response variable, even if
the errors are normally distributed. This is one situation
in which neither predictor nor response variable has a
normal distribution, despite the model errors being
normally distributed.
The misconception that the normality assumptionapplies to the response and/or predictor variables isproblematic in that there are certainly situations wherethe response and/or predictors are not normallydistributed, but a normal distribution for the errors isstill plausible. As one example, dichotomous predictorsare often used in multiple regression; although suchpredictors are clearly not normally distributed, theerrors of regression models using dichotomouspredictors may still be normally distributed, allowingfor trustworthy inferences. Furthermore, dichotomousvariables that are particularly strong predictors of aresponse variable may induce a bimodality to themarginal distribution of the response variable, even ifthe errors are normally distributed. This is one situationin which neither predictor nor response variable has anormal distribution, despite the model errors beingnormally distributed.
การแปล กรุณารอสักครู่..
