Differences
Parametric tests normally assume observations are independent, and that when they are paired and data is drawn from normally distributed population of variables the dependent variable is interval-level data. The populations must also bear similar variances and the variables involved bear measurements from an interval scale (Pett, 2015). Conversely, non-parametric tests assume that observations are independent while been randomly extracted from the population. They, however, differ in the sense that they do not require the population to be normally distributed. This explains why they are commonly referred to as distribution free statistics. They also differ from parametric tests in the sense that they apply to data in an ordinal scale. Besides, they do not require measurements that are as strong as the parametric tests.
Examples
The Student t-Test is a good example of the parametric test since it is the most widely used. A statistician working at a Guinness brewery came up with the test ( Hebel, 2002 ). A single sample t-test can be used to come up with a determination on whether the mean differs from the known average. A 2 sample t-test, on the other hand, the difference between to differing sets of data. An example of a non-parametric t-test is the Chi-Squared which is used to come up with a comparison between multiple groups whereby the input variables and output are binary (Pett, 2015). In this case, a determination can be made on whether a frequency distribution is to occur as a definite cause or by chance.
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Assumptions
One of the assumptions of the tests is the assumption of normality. This implies that data has to bear a normal distribution or be symmetric. The homogeneity of variances is also another assumption requiring that data obtained from multiple groups should display similar variance. Another assumption is based on linearity requiring that data bears a liner relationship. Finally, there is an independence assumption requiring that variables used are independent.
References
Hebel, A., 2002. Parametric Versus Nonparametric Statistics-When to use them and which is more powerful? Department of Natural Sciences University of Maryland Eastern Shore.
Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions . Sage Publications.
