Normality

Data Assumptions: Univariate Normality

January 14, 2015

Very brief description As one of the most basic data assumptions, much has been written about univariate, bivariate and multivariate normality. An excellent reference is by Tom Burdenski (2000) entitled Evaluating Univariate, Bivariate, and Multivariate Normality Using Graphical and Statistical Procedures. A few noteworthy comments about normality: 1. Normality can have different meanings in different contexts, i.e. sampling distribution normality and model error distribution (e.g. in Regression and GLM). Be very careful which type of normality is applicable.   2. By definition, a [READ MORE]

Data Assumptions: Its about the residuals, and not the variables’ raw data

June 3, 2013

Normality, or normal distributions is a very familiar term but what does it really mean and what does it refer to…   In linear models such as ANOVA and Regression (or any regression-based statistical procedures), an important assumptions is “normality”. The question is whether it refers to the outcome (dependent variable “Y”), or the predictor (independent variable “X”). We should remember that the true answer is “none of the above”.    In linear models where we look at the relationship between dependent and independent variables, our [READ MORE]

Data Assumption: Normality of error term distribution

May 17, 2013

We often come across requirements in procedures such as General Linear Models (GLM) used for ANOVA’s, ANCOVA’s, etc, which state “normality of error term distribution”, “normally distributed errors” or “normality of residuals”.    These all mean the same thing: Residuals (error) must be random, normally distributed with a mean of zero, so the difference between our model and the observed data should be close to zero. Not only do residuals have to be normally distributed, but they should be normally distributed at every value of the dependent [READ MORE]

Data Assumption: Bivariate and Multivariate Normality

January 16, 2013

How to test Bivariate and Multivariate Normality:   Refer to the post, Data Assumption: Univariate Normality, for general comments about normality.   There are no special tests to screen for either Bivariate or Multivariate normality. The only test I am aware of is the Mardia’s statistic test for multivariate normality. Use univariate screening and while univariate normality does not guarantee multivariate normality, most often multivariate won’t be far off if the univariate screening test was passed.    Even better than univariate tests are bivariate such as a [READ MORE]