In general, the power of parametric tests are greater than the power of the alternative nonparametric test when assumptions are met. As the sample size increases and becomes larger, the power of the nonparametric test approaches it parametric alternative.

In other words, when using a non-parametric test more data is needed to detect the same size difference as a parametric equivalent t tests or ANOVA tests.

- The center for parametric tests is the
**mean** - The center for nonparametric tests is the
*median*

Nonparametric tests also assume that the underlying distributions are symmetric but not necessarily normal. The assumption is these test statistics are "distribution-free. In other words, there aren't any assumptions made about the population parameters.

When the choice exist on whether to use the parametric or nonparametric test, if the distribution is fairly symmetric, the standard parametric test are better choices than the nonparametric alternatives.

For example, if you are not sure if two data sets are normally distributed it may be safer to substitute the Mann-Whitney test to reduce the risk of drawing a wrong conclusion when testing two means.

**Nonparametric tests are used when:**

- Parametric criteria are not met or if distribution is unknown
- These test are used when analyzing nominal or ordinal data
- Nonparametric test can also analyze interval or ratio data
- Quantitative, ranked, and qualitative data. Parametric is for only quantitative data.

**Advantages of nonparametric tests:**

- Offer more power when assumptions for the parametric tests have been violated. And they can be almost as powerful when assumptions haven't been violated.
- Fewer assumptions about the data
- Work with smaller sample sizes
- They can be used for all data types or data containing outliers

**Disadvantages of nonparametric tests:**

- Less powerful than parametric tests if assumptions haven’t been violated.
- Critical value tables for many tests aren’t included in many computer software packages or textbooks

- Data can not be assumed to meet normality assumptions and can not be practically transformed to approximate normality.
- With qualitative data of nominal scale or ranked data of ordinal scale.
- When comparing Median values for skewed data (such as right or left skewed data). See Histograms for more insight on skewed data.
- When there are very few, if any, assumptions regarding the shape of the distribution. However, if there is a bi-modal distribution, the data should be reviewed and separated to correctly analyze the true process performance.
- Don't be forceful or careless and rush into a nonparametric test when there is clearly two (or more) unique situations in within the data. Use the Runs Test to verify the nonnormality is related to random causes and not a results of special causes.
- When unsure whether to use parametric or nonparametric, you can easily run both tests. See what the difference is in the outcomes and it may not be a meaningful difference in your Six Sigma project. Therefore, don't sweat it. Make a decision and move on to the IMPROVEments Often times you''ll find the results very similar and the hypothesis decision is the same for both.

These are the most commonly used nonparametric equivalents. There are many more nonparametric tests but these are most likely to arise on a Six Sigma project and a certification exam.

**A sample and a target (or given value) **

Parametric - One Sample t test (testing means)

Nonparametric - One Sample Wilcoxon or One Sample Sign (testing medians)

**Two independent samples **

Parametric - Two Sample t test (testing means)

Nonparametric - Mann-Whitney (testing medians)

**>2 independent samples**

Parametric - ANOVA (testing means)

Nonparametric - Mood's median or Kruskal-Wallis test (testing medians)

**Three of more matched (dependent) samples**

Parametric - Two way ANOVA for matched samples

Nonparametric - Friedman Test

Use the Runs Test to examine the randomness of the data

Follow these steps when you believe the data does not meet normality assumptions:

- Attempt to transform the data such as through a Box-Cox transformation.
- Use the Runs Test to verify the data the is random (void of special causes)
- If the transformation doesn't work, the apply the nonparametric test

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