Each discussion requires a minimum of two substantive peer review posts. All posts must utilize and cite material from the unit’s course information, readings, and videos. You may also use outside resources to support your answer.

Naihla

Is it fair to say that we should use a parametric test when we can and a non-parametric test when we have to? Why or why not? What is the primary difference between parametric and non-parametric tests? Select three parametric tests and identify their counterpart. How do you determine when to use the parametric test and when to use the non-parametric counterpart?

The primary difference between the two tests is that parametric tests assume underlying statistical distributions in data and tests group means while nonparametric tests don’t rely on any distributions and tests group medians. Parametric tests also have more statistical power and will detect significant difference when they truly exist. I don’t think it’s fair to say that we should use a parametric test when we can and a non-parametric test when we have to because, both tests have specified situations that they work best for.

Parametric Test Non-Parametric Counterpart

1-Sample t-test 1-sample Sign, 1-sample Wilcoxon

2- Sample t-test Mann-Whitney Test

One-Way ANOVA Kruskal-Wallis, Mood’s median test

If the mean more accurately represents the center of the distribution of your data, and meets the sample size requirements then, parametric tests should be use. If the median is more accurate in representing the center of the distribution of your data, nonparametric tests should be use. For example, if your sample size is >20 and appropriate for conducting a 1-Sample t-test but, the median is more representative of the distribution then, a nonparametric test should be used.

Minitab Blog Editor. (2015, February 19). Choosing Between a Nonparametric Test and a Parametric Test. https://blog.minitab.com/blog/adventures-in-statistics-2/choosing-between-a-nonparametric-test-and-a-parametric-test (Links to an external site.).

Paige

A parametric test tends to hold more statistical power and therefore, is more accurate. As such, a parametric test should be used if possible. It’s use is beneficial for skewed and nonnormal distributions if the sample is large enough. A non-parametric test should only be used if you have to and is often the choice when the sample size is too small for a parametric test and if ordinal data, ranked data, or outliers are present.

The three parametric tests and their counterparts are 1) Parametric: 1-sample t test and Non-parametric: 1-sample Sign, 1-sample Wilcoxon, 2) parametric: 2-sample t test and Non-parametric: Mann-Whitney test, and lastly 3) parametric: one-way ANOVA and Non-parametric: Kruskal-Wallis, Mood’s median test.

To decide whether to use a parametric test or a non-parametric counterpart, there are a set of guidelines to follow. For example a 1-sample test guideline is if your sample size is greater than 20, for a 2-sample test each group should be greater than 15, for an ANOVA sample sizes between 2-9 groups should be greater than 15 or a sample size of 10-12 groups should be greater than 20. If the sample size guideline is not met, than a non-parametric test would be used as an alternative to a parametric test.