The ability to choose the correct statistical test to analyze data is an expectation for a Six Sigma Project Manager.
In general, the power of these standard parametric tests are greater than the power of the alternative nonparametric test. As the sample size increase and becomes very large the power of the nonparametric test approaches its parametric alternative.
Nonparametric test also assume that the underlying distributions are symmetric but not necessarily normal. When the choice exist on whether to use the parametric or nonparametric, if the distribution is fairly symmetric, the standard parametric tests are better choices than the non-parametric alternatives.
These Parametric Test Flowcharts shown below indicate commonly applied tests but there are more. Visit Basic Statistics for more information on the frequently applied types of tests.
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