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 ttest 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 guide.
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 pvalue associated to a parametric test will be lower than the pvalue 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 ttest  One sample Wilcoxon signed rank test 
Compare two independent means  ttest on two independent samples  MannWhitney’s test 
Compare several independent means  ANOVA  KruskalWallis test / Mood’s test 
Compare two observed dependent means  ttest on two paired samples  Wilcoxon’s test 
Compare several observed dependent means  Repeated measures ANOVA / mixed models  Friedman’s test / Durbin, SkillingsMack’s test / Page test 
Test the association between two qualitative variables  Chisquare 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 ttest.

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, onesample Wilcoxon signed rank test.
You can find more precisions regarding our tests in this article.
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 pvalues…
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