# Parametric and Nonparametric Tests

According to Zikmund and Babin (2010), specific conditions define a parametric test because the parameters used in the test have a unique mathematical distribution. Hebel (2002) describes the conditions necessary for a non-parametric test to include using data characterized by independent observations with variables measured on an interval scale. According to Hebel (2002) and Zikmund and Babin (2010) the data used in the non-parametric test lacks a specific distribution. In this case, there are no specific assumptions made about the data used to study a specific population. Zikmund and Babin’s (2010) contrast of a parametric test from a non-parametric distribution to be that relies on data with a specific distribution. According to Zikmund and Babin (2010) the models used in non-parametric tests change according to the changes in the characteristics of the population under investigation. Zikmund and Babin’s (2010) shows that the model used for parametric tests does not increase in size. The variables used in non-parametric statistical tests have probability distributions based on the assumptions made about the data while parametric distributions rely on assumptions made about the data. It is important to note that non-parametric tests have data that is applicable in ordinal and non-ordinal scales while parametric tests use ratio or interval scales. When conducting tests with non-parametric tests, the most appropriate test to use is the spearman’s test while for the parametric test is the Pearson test.

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Examples of non-parametric tests by Zikmund and Babin (2010) include situations where tests done on data provide information about n observations drawn from a population having a hypothesized value equal to the median of the population having an output value as the null median. Another area of application is the Wilcoxon Matched Pairs Signed-Ranks Test to decide if the media of the data is zero, and Kendall’s Rank Correlation Coefficient (Kendall’s τ) to decide the correlation between two variables. On the other hand, parametric tests are suitable for population with a normal distribution and a homogenous variance. According to Zikmund and Babin (2010), the data set being investigated has independent relationship and the mean of the data provides a central measure. Zikmund and Babin (2010) and Hebel (2002) describe a non-parametric test to be defined by any form of assumed distribution of data, with any type of variance, and having an ordinal or nominal characteristic, and the median as a measure of central tendency.

In addition, non-parametric tests are applicable in situations with statistical problems of hypothesis tests and estimation of population parameters such as in behavioral science and can be done without automated tools. On the other hand, if assumptions about the data under test are met, then a parametric test is the most applicable.

The advantages of non-parametric tests include ability to get exact probability statements irrespective of the population characteristics, observations from a range of samples, and easy to learn and apply. Disadvantages include low precision and low power. According to Hebel (2002) the advantages of parametric tests include the ability to accommodate more assumptions, use a specific probability model, are precise, secure, and have high power. Never substitute parametric tests for non-parametric tests and vice versa.

In conclusion, non-parametric tests provide better results in situations where parametric tests are inapplicable. Each test provides accurate results if applied on the correct data.

## References

Hebel, A. (2002). Parametric versus Nonparametric Statistics – When to use them and which is more powerful? Web.

Zikmund, W., G., & Babin, B. (2010). Exploring marketing research (10th ed.). Mason, Ohio: Thomson South-Western.

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