Note that these tables should be considered as guides only, and each case should be considered on its merits. 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. 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. 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.
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. 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? 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.
Skip to main content. There is no requirement for any distribution of the population in the non-parametric test. Also, the non-parametric test is a type hypothesis test that is not dependent on any underlying hypothesis. In the non-parametric test, the test depends on the value of the median. This method of testing is also known as distribution-free testing.
Test values are found based on the ordinal or the nominal level. The parametric test is usually performed when the independent variables are non-metric. This is known as a non-parametric test. Parametric Test. Non-Parametric Test. Yes, assumptions are made. No, assumptions are not made.
Value for central tendency. The mean value is the central tendency. The median value is the central tendency. Pearson Correlation. Spearman Correlation. Probabilistic Distribution. Normal probabilistic distribution. Arbitrary probabilistic distribution. Population Knowledge. Population knowledge is required. Population knowledge is not required. Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in this grid.
Nonparametric tests are more robust than parametric tests. In other words, they are valid in a broader range of situations fewer conditions of validity. The advantage of using a parametric test instead of a nonparametric equivalent is that the former will have more statistical power than the latter.
In other words, a parametric test is more able to lead to a rejection of H0. Most of the time, the p-value associated to a parametric test will be lower than the p-value associated to a nonparametric equivalent that is run on the same data.
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