Parametric vs. Nonparametric Test
To make the generalization about the population from the sample, statistical tests are used. A statistical test is a formal technique that relies on the probability distribution, for reaching the conclusion concerning the reasonableness of the hypothesis. These hypothetical testing related to differences are classified as parametric and nonparametric tests.The parametric test is one which has information about the population parameter.
On the other hand, the nonparametric test is one where the researcher has no idea regarding the population parameter. So, take a full read of this article, to know the significant differences between parametric and nonparametric test.
Comparison Chart
| BASIS FOR COMPARISON | PARAMETRIC TEST | NONPARAMETRIC TEST |
| Meaning | A statistical test, in which specific assumptions are made about the population parameter is known as parametric test. | A statistical test used in the case of non-metric independent variables, is called non-parametric test. |
| Basis of test statistic | Distribution | Arbitrary |
| Measurement level | Interval or ratio | Nominal or ordinal |
| Measure of central tendency | Mean | Median |
| Information about population | Completely known | Unavailable |
| Applicability | Variables | Variables and Attributes |
| Correlation test | Pearson | Spearman |
Definition of Parametric Test
The parametric test is the hypothesis test which provides generalizations for making statements about the mean of the parent population. A t-test based on Student’s t-statistic, which is often used in this regard.
The t-statistic rests on the underlying assumption that there is the normal distribution of variable and the mean in known or assumed to be known. The population variance is calculated for the sample. It is assumed that the variables of interest, in the population are measured on an interval scale.
Definition of Nonparametric Test
The nonparametric test is defined as the hypothesis test which is not based on underlying assumptions, i.e. it does not require population’s distribution to be denoted by specific parameters.
The test is mainly based on differences in medians. Hence, it is alternately known as the distribution-free test. The test assumes that the variables are measured on a nominal or ordinal level. It is used when the independent variables are non-metric.
Equivalent Tests
| PARAMETRIC TEST | NON-PARAMETRIC TEST |
| Independent Sample t Test |
Mann-Whitney test |
| Paired samples t test |
Wilcoxon signed Rank test |
| One way Analysis of Variance (ANOVA) |
Kruskal Wallis Test |
| One way repeated measures Analysis of Variance |
Friedman’s ANOVA |
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