# Parametric and nonparametric relationship

### Parametric vs. non-parametric tests

Correlation is a bivariate analysis that measures the strengths of association Kendall rank correlation: Kendall rank correlation is a non-parametric test that. Parametric and Non-parametric tests for comparing two or more groups Statistics: are testing some presupposed relationship), and which are exploratory (are. It's safe to say that most people who use statistics are more familiar with parametric analyses than nonparametric analyses. Nonparametric tests.

The outcome variable is the five point ordinal scale. Each person's opinion is independent of the others, so we have independent data.

Note, however, if some people share a general practitioner and others do not, then the data are not independent and a more sophisticated analysis is called for.

Note that these tables should be considered as guides only, and each case should be considered on its merits.

Table 2 Choice of statistical test for independent observations a If data are censored. However, they require certain assumptions and it is often easier to either dichotomise the outcome variable or treat it as continuous.

Parametric tests are those that make assumptions about the parameters of the population distribution from which the sample is drawn. This is often the assumption that the population data are normally distributed. Table 3 shows the non-parametric equivalent of a number of parametric tests.

**Correlation: Pearson vs. Spearman**

Table 3 Parametric and Non-parametric tests for comparing two or more groups Non-parametric tests are valid for both non-Normally distributed data and Normally distributed data, so why not use them all the time? It would seem prudent to use non-parametric tests in all cases, which would save one the bother of testing for Normality.

### Nonparametric statistics - Wikipedia

Parametric tests are preferred, however, for the following reasons: We are rarely interested in a significance test alone; we would like to say something about the population from which the samples came, and this is best done with estimates of parameters and confidence intervals.

It is difficult to do flexible modelling with non-parametric tests, for example allowing for confounding factors using multiple regression.

Parametric tests usually have more statistical power than their non-parametric equivalents. In other words, one is more likely to detect significant differences when they truly exist. Do non-parametric tests compare medians? It is a commonly held belief that a Mann-Whitney U test is in fact a test for differences in medians. However, two groups could have the same median and yet have a significant Mann-Whitney U test.

### Parametric and Non-parametric tests for comparing two or more groups | Health Knowledge

Consider the following data for two groups, each with observations. Only if we are prepared to make the additional assumption that the difference in the two groups is simply a shift in location that is, the distribution of the data in one group is simply shifted by a fixed amount from the other can we say that the test is a test of the difference in medians.

However, if the groups have the same distribution, then a shift in location will move medians and means by the same amount and so the difference in medians is the same as the difference in means.

Thus the Mann-Whitney U test is also a test for the difference in means. How is the Mann- Whitney U test related to the t-test?

## Parametric vs. non-parametric tests

If one were to input the ranks of the data rather than the data themselves into a two sample t-test program, the P value obtained would be very close to that produced by a Mann-Whitney U test. Statistics at Square One 11th ed. Hypothesis c was of a different nature, as no parameter values are specified in the statement of the hypothesis; we might reasonably call such a hypothesis non-parametric. Hypothesis d is also non-parametric but, in addition, it does not even specify the underlying form of the distribution and may now be reasonably termed distribution-free.

Notwithstanding these distinctions, the statistical literature now commonly applies the label "non-parametric" to test procedures that we have just termed "distribution-free", thereby losing a useful classification. The second meaning of non-parametric covers techniques that do not assume that the structure of a model is fixed.

- Parametric and Non-parametric tests for comparing two or more groups

Typically, the model grows in size to accommodate the complexity of the data. In these techniques, individual variables are typically assumed to belong to parametric distributions, and assumptions about the types of connections among variables are also made.

These techniques include, among others: Applications and purpose[ edit ] Non-parametric methods are widely used for studying populations that take on a ranked order such as movie reviews receiving one to four stars.

## Nonparametric statistics

The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of measurementnon-parametric methods result in ordinal data.

As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust. Another justification for the use of non-parametric methods is simplicity.

In certain cases, even when the use of parametric methods is justified, non-parametric methods may be easier to use. Due both to this simplicity and to their greater robustness, non-parametric methods are seen by some statisticians as leaving less room for improper use and misunderstanding. The wider applicability and increased robustness of non-parametric tests comes at a cost: In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.