What is parametric test
A parametric test is a statistical test which makes certain assumptions about the distribution of the unknown parameter of interest and thus the test statistic is valid under these assumptions. A significance test under a Simple Normal Model for example has the assumption that the parameter has a normal distribution behaves like an independent variable (is the result of an independent process) is identically distributed and has a constant mean and variance.
Some Parametric tests
- ANOVA
- Z-test
- F-test
- t-test
When to use Parametric tests
| Tests | condition to use |
|---|---|
| ANOVA | comparing the means of ( more than two samples) |
| F-test | Comparing variances of two samples |
| t-test | Comparing mean to a value , or the means of two samples |
| Z-test | as t-test for large samples |
Non- Parametric Test
In statistics, nonparametric tests are methods of statistical analysis that do not require a distribution to meet the required assumptions to be analyzed (especially if the data is not normally distributed). Due to this reason, they are sometimes referred to as distribution-free tests. Nonparametric tests serve as an alternative to parametric tests such as T-test or ANOVA that can be employed only if the underlying data satisfies certain criteria and assumptions.
Some Non- Parametric Test
- Wilcoxon Signed Rank Pair test
- Mann-Whitney U test
- Mc Nemars test
- Chi-Squared Test
1. Mann-Whitney U Test
The Mann-Whitney U Test is a nonparametric version of the independent samples t-test. The test primarily deals with two independent samples that contain ordinal data.
2. Wilcoxon Signed Rank Test
The Wilcoxon Signed Rank Test is a nonparametric counterpart of the paired samples t-test. The test compares two dependent samples with ordinal data.
3. The Kruskal-Wallis Test
The Kruskal-Wallis Test is a nonparametric alternative to the one-way ANOVA. The Kruskal-Wallis test is used to compare more than two independent groups with ordinal data.
| Parametric Test | Non Parametric Test |
|---|---|
| These tests are applied only to the data which are measured in ratio and interval scale | These tests are applied only to the data which are measured in Nominal and ordinal scale |
| These tests are more powerful | These tests are less powerful than parametric tests |
| It requires complicated sampling theory | It doesn’t required complicated sampling theory |
| It requires complicated computation | It requires simple computation and gives result quicky |
| These test are designed to test the hypothesis of one or more parameters of the population | These test are designed to test the hypothesis which doesn’t involve any parameter . |
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