parametric tests and non-paramet
Most of the tests that we study in this website are based on some distribution. These are called parametric tests. Parametric tests require that certain assumptions are satisfied. We now look at some tests that are not linked to a particular distribution. These non-parametric tests are usually easier to apply since fewer assumptions need to be satisfied.
In general, non-parametric tests:
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make few or no assumptions about the distribution of the data
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reduce the effect of outliers and heterogeneity of variance
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can often be used even for ordinal, and sometimes even nominal, data
Since non-parametric tests do not estimate population parameters, in general, there are -
no estimates of variance/variability
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no confidence intervals
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fewer measures of effect size
Also, non-parametric tests are generally not as powerful as parametric alternatives when the assumptions of the parametric tests are met.
In this part of the website we study the following non-parametric tests:
- Sign Test – primitive non-parametric version of the t-test for a single population
- Mood’s Median Test (for two independent samples) – primitive non-parametric version of the t-test for two independent populations
- Wilcoxon Signed-Rank Test for a Single Sample – non-parametric version of the t-test for a single population
- Wilcoxon Rank Sum Test for Independent Samples – non-parametric version of t-test for two independent populations
- Mann-Whitney Test for Independent Samples – an alternative non-parametric version of t-test for two independent populations
- Wilcoxon Signed-Rank Test for Paired Samples – non-parametric version of t-test for paired samples
- Fligner-Policello Test – used to determine whether the population medians corresponding to two independent samples are equal.
- McNemar Test – similar to the sign test for before and after studies
- Runs Test – to determine whether a sequence of number is randomly ordered
- Resampling Procedures – using Monte Carlo random number techniques
Elsewhere on the website we look at the following additional non-parametric tests:
- Chi-square Test of Independence
- Kolmogorov-Smirnov (KS) test
- Kruskal-Wallis Test
- Jonckheere-Terpstre Test
- Mood’s Median Test
- Spearman’s Rank Correlation
- Kendall’s Tau Correlation
- Friedman Test
- Cochran’s Q Test
As we will see, many of the non-parametric tests are based on analysis of the ranks of the data elements, often comparing the median instead of the mean.
