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Parametric tests assume that your data are normally distributed (i.e. follow a classic bell-shaped "Gaussian" curve). Non-parametric tests make no assumption about the shape of the distribution.
Parametric tests draw conclusions based on the data that are drawn from populations that have certain distributions. Non-parametric tests draw fewer conclusions about the data set. The majority of elementary statistical methods are parametric because they generally have larger statistical outcomes. However, if the necessary conclusions cannot be drawn about a data set, non-parametric tests are then used.
Parametric statistical tests assume that your data are normally distributed (follow a classic bell-shaped curve). An example of a parametric statistical test is the Student's t-test.Non-parametric tests make no such assumption. An example of a non-parametric statistical test is the Sign Test.
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What is DC parametric tests
There are several types of hypothesis testing, primarily categorized into two main types: parametric and non-parametric tests. Parametric tests, such as t-tests and ANOVA, assume that the data follows a specific distribution (usually normal). Non-parametric tests, like the Mann-Whitney U test or the Kruskal-Wallis test, do not rely on these assumptions and are used when the data doesn't meet the criteria for parametric testing. Additionally, hypothesis tests can be classified as one-tailed or two-tailed, depending on whether the hypothesis specifies a direction of the effect or not.
In parametric analysis the underlying distributions of the variables are described by parameters. These may be known or it may be possible to estimate them from the observed data. In non-parametric analyses, the parameters are not used - either because they cannot be derived or because the tests do not require them.
In parametric statistics, the variable of interest is distributed according to some distribution that is determined by a small number of parameters. In non-parametric statistics there is no underlying parametric distribution. In both cases, it is possible to look at measures of central tendency (mean, for example) and spread (variance) and, based on these, to carry out tests and make inferences.
Parametric.
Nonparametric tests are sometimes called distribution free statistics because they do not require that the data fit a normal distribution. Nonparametric tests require less restrictive assumptions about the data than parametric restrictions. We can perform the analysis of categorical and rank data using nonparametric tests.
Most parametric and many non-parametric tests for testing the significance of hypotheses are based on the assumption of normality - or approximate normality.
Parametric are the usual tests you learn about. Non-parametric tests are used when something is very "wrong" with your data--usually that they are very non-normally distributed, or N is very small. There are a variety of ways of approaching non-parametric statistics; often they involve either rank-ordering the data, or "Monte-Carlo" random sampling or exhaustive sampling from the data set. The whole idea with non-parametrics is that since you can't assume that the usual distribution holds (e.g., the X² distribution for the X² test, normal distribution for t-test, etc.), you use the calculated statistic but apply a new test to it based only on the data set itself.