#Statistical calculations to prove normal distribution full#

#Statistical calculations to prove normal distribution full#

Normality tests should be run on the full data without removing any outliers, unless the reason for the outlier is known and its removal from the analysis as a whole can be readily justified (e.g. Using a statistical test designed under the assumption of Normal or NIID data when the data is not normal renders the statistical model inadequate and the results meaningless, regardless if one is dealing with experimental or observational data (regressions, correlations, etc.). Tests for normality like the Shapiro-Wilk are useful since many widely used statistical methods work under the assumption of normally-distributed data and may require alteration in order to accommodate non-normal data. Separate tests for independence and heterogeneity can be performed to rule out those possibilities. The Null hypothesis can generally be stated as: 'data can be modelled using the normal distribution', but since some normality tests also check if the data is independent and identically distributed (IID) a low p-value from these tests may be either due to a non-normal distribution or due to the IID assumption not holding.

Normality tests can be based on the 3-rd and 4-th central moments (skewness and kurtosis), on regressions/correlations stemming from P-P and Q-Q plots or on distances defined using the empirical cumulative distribution functions (ecdf). The Shapiro-Wilk test / Shapiro-Francia testДЄ test of normality in statistics and probability theory is used to quantify if a certain sample was generated from a population with a normal distribution via a process that produces independent and identically-distributed values.

Interpreting the outcome of tests for normality.