# What is the difference between a parametric and a nonparametric test?

## What is the difference between a parametric and a nonparametric test?

Parametric tests assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable. For example, Student’s t-test for two independent samples is reliable only if each sample follows a normal distribution and if sample variances are homogeneous.

Nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met.

Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in this grid.

## What is the advantage of using a nonparametric test?

Nonparametric tests are more robust than parametric tests. In other words, they are valid in a broader range of situations (fewer conditions of validity).

## What is the advantage of using a parametric test?

The advantage of using a parametric test instead of a nonparametric equivalent is that the former will have more statistical power than the latter. In other words, a parametric test is more able to lead to a rejection of H0. Most of the time, the p-value associated to a parametric test will be lower than the p-value associated to a nonparametric equivalent that is run on the same data.

## How can I use parametric and nonparametric tests in XLSTAT?

XLSTAT offers several tools to generate parametric or nonparametric tests, available even in the Basic solution. Most parametric tests have an equivalent nonparametric test so you can run the same analysis regardless of the underlying statistical distributions in your data. In the following equivalence table, you can see some of the many tests contained in our software.

What is it used for? Parametric test Nonparametric test
Observed mean VS theoretical One sample t-test One sample Wilcoxon signed rank test
Compare two independent means t-test on two independent samples Mann-Whitney’s test
Compare several independent means ANOVA Kruskal-Wallis test / Mood’s test
Compare two observed dependent means t-test on two paired samples Wilcoxon’s test
Compare several observed dependent means Repeated measures ANOVA / mixed models Friedman’s test / Durbin, Skillings-Mack’s test / Page test
Test the association between two qualitative variables Chi-square test on contingency table Exact Fischer test / Monte Carlo method
Test the association between two quantitative variables Pearson’s correlation test Spearman’s correlation test
Test for outliers Dixon’s test / Grubbs test Boxplot (not really a test)

For example, if you want to compare an observed mean to a theoretical value:

• Comparing a mathematic grade average of a class to the country average? Here, we are going to use a parametric test because we can assume that the data follows a normal distribution. We are going to use a t-test.

• Comparing the median liking score of a new crisps brand to the strongest brand of the market? We cannot suppose that the liking scores follow a normal distribution so we will perform a nonparametric, one-sample Wilcoxon signed rank test.

## How can I set up a parametric - nonparametric statistical test analysis in XLSTAT?

You can customize your statistical tests using the XLSTAT dialog boxes and display various outputs such as descriptive statistics, confidence intervals… You can also generate several charts. You can choose to display the error bars, the p-values…  