To make the generalisation about the population from the sample, statistical tests are uses. These hypothetical testing related to differences are classified as parametric and nonparametric tests. On one hand, the parametric test is one which has information about population parameter while on the other hand, nonparametric tests, 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.

## Content: Parametric Test Vs 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 generalisations 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.

## Key Differences Between Parametric and Nonparametric Tests

The fundamental differences between parametric and nonparametric test are discussed in the following points:

- A statistical test, in which specific assumptions are made about the population parameter is known as the parametric test. A statistical test used in the case of non-metric independent variables is called nonparametric test.
- In the parametric test, the test statistic is based on distribution. On the other hand, the test statistic is arbitrary in the case of the nonparametric test.
- In the parametric test, it is assumed that the measurement of variables of interest is done on interval or ratio level. As opposed to the nonparametric test, wherein the variable of interest are measured on nominal or ordinal scale.
- In general, the measure of central tendency in the parametric test is mean, while in the case of the nonparametric test is median.
- In the parametric test, there is complete information about the population. Conversely, in the nonparametric test, there is no information about the population.
- The applicability of parametric test is for variables only, whereas nonparametric test applies to both variables and attributes.
- For measuring the degree of association between two quantitative variables, Pearson’s coefficient of correlation is used in the parametric test, while spearman’s rank correlation is used in the nonparametric test.

### Hypothesis Tests Hierarchy

### 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 |

### Conclusion

To make a choice between parametric and the nonparametric test is not easy for a researcher conducting statistical analysis. For performing hypothesis, if the information about the population is completely known, by way of parameters, then the test is said to be parametric test whereas, if there is no knowledge about population and it is needed to test the hypothesis on population, then the test conducted is considered as the nonparametric test.

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