# Non-parametric Analysis

Non-parametric analysis or test is also known as a distribution-free test. This type of test does not assume anything about the underlying distribution. An example of common assumptions is that data comes from a normal distribution. Parametric tests, on the other hand, makes assumptions about the parameters of the population. In statistics, non-parametric does not mean that you know nothing about the population. Instead, it means you know that the population data does not have a normal distribution.

For example, one-way ANOVA assumes that the data comes from a normal distribution. This means that if your data is not normally distributed, you cannot run ANOVA. However, you can run an alternative which is non-parametric – the Kruskal-Wallis test.

You should always use parametric tests whenever it is possible because they tend to be more accurate. Also, parametric tests possess greater statistical power. This means that these tests can find a true significant effect. You should consider non-parametric tests only if you have to. In other words, you know when the assumptions like normality are being violated. If you have a sufficiently large sample size, then non-parametric tests can perform well.

When do we use non-parametric tests?

You should only use non-parametric tests when your data is not normal. So finding out if you have a normally distributed data is the key. For example, you could do this by looking at the distribution of your data.  You should use parametric statistical tests if your data is normally distributed.

A question that most students usually ask is “how do I figure out if my data is normally distributed when I don’t have a graph?” Well, the answer is pretty straightforward. You could check the kurtosis and skewness of the distribution using software like Excel. Basically, a normal distribution has no skew. It is symmetrical in shape and centered. We can define kurtosis as how much of the data is in the tails and the center.

You should use a non-parametric test like Chi-square if your distribution is not normal. You run the risk of getting meaningless results if you don’t.

Data Types

If you are worried whether your data allows for a parametric test or you want to use a non-parametric test like Chi-square, you should apply the following rule of thumb:

• Use non-parametric statistics for nominal scales or ordinal scales
• Use parametric statistics for interval scales or ratio scales

Reasons why you should run a non-parametric test

• When one or more assumptions of a parametric test have been violated
• You have a small sample size that cannot be run by a parametric test
• The outliers in your data cannot be removed
• You have a very skewed distribution and want to test for the median instead of the mean

What are some of the examples of Non-parametric tests?

Parametric is used in stats to refer to tests like ANOVA or a t-test, which assume that the population data has a normal distribution. Non-parametric tests operate in the opposite way. They do not assume that the data is normally distributed. The only non-parametric test taught in elementary stats in the Chi-square. There are more complicated ones like the Kruskal-Willis test which is a non-parametric test alternative for the one way ANOVA and the Mann Whitney test which is the non-parametric test alternative for the two-sample t-test. Our online experts have outlined the main non-parametric tests below:

• The 1-sample sign test

This test is used to estimate the median of a population and compare it to a reference value or a target value.

• 1-sample Wilcoxon signed-rank test

It is also used to estimate the population median and compare it to a target value or reference. This test, however, assumes that the data comes from a symmetric distribution.

• The Friedman test

The Friedman test checks for differences between groups with ordinal dependent variables. If the one-way ANOVA with repeated measures is appropriate, the Friedman can also be used for continuous data.

• Goodman Kruskal’s Gamma

Goodman Kruskal’s Gamma test for association in ranked variables.

• Kruskal-Wallis test

It is the non-parametric test equivalent of the one-way ANOVA. The Kruskal-Wallis test is used to determine if two or more medians are different. Instead of the data points themselves, the ranks of the data points are used for calculations.

• The Mann-Whitney test

This test compares differences between two independent groups when dependent variables are either continuous or ordinal.

• Mood’s Median test

It is used instead of the sign test when there are two independent samples.

• Spearman Rank Correlation

It is used to find a correlation between two datasets

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