# What is a parametric test and a non-parametric test

## Parametric tests and their prerequisite check: Our professional guide

Choosing the right statistical method is not always easy. Ideally, you have already formulated clear hypotheses and an idea of ​​the basic statistical process. But even then you still have to decide during the analysis whether you want to use parametric tests or prefer to use a non-parametric test. The decision between parametric testing or non-parametric testing is a fundamental decision for static analysis. That is why in this article we want to explain the differences between the two families of static methods and show you how to choose the right test. For more in-depth advice on the choice and implementation of the optimal procedure, simply make an appointment for statistical advice with us!

• How are parametric tests different from a non-parametric test?
• Which parametric test or non-parametric test is suitable for your project?
• How do you check the prerequisites for a parametric test?

### Parametric tests vs. non-parametric tests: It all depends on the distribution

Parametric and non-parametric tests both form a separate family of different statistical methods. Like all statistical methods, these are only valid or useful under certain conditions. For example, Pearson's correlation coefficient r assumes that both of the variables analyzed are continuous.

Parametric tests all have one thing in common: Every parametric test assumes that the data comes from a very specific distribution. Most parametric tests assume a normal distribution. Let's take a comparison of performance ratings in a company from two different departments. A possible parametric test here would be the t-test. However, this would only be permissible if the ratings of both departments are distributed more or less normally.

In contrast, non-parametric tests make no assumptions about the distribution of the data. These tests are therefore also called non-distribution tests.

### Parametric test: head start through power

So non-parametric tests are allowed in more situations than parametric tests. Therefore, non-parametric tests are also called robust Tests called. Then why should you use parametric tests at all? After all, these are permissible in fewer situations. However, parametric tests compensate for this disadvantage by having a greater test strength or power than non-parametric tests. In other words: If there is actually an effect in the population, you have a better chance of detecting this effect with a parametric test.

When in doubt, the following applies: if the distribution of the data allows, use a parametric test. However, if the distribution of the data contradicts the assumptions of a parametric test, switch to non-parametric tests.

 advantage disadvantage Parametric tests Greater test strength - if assumptions are met Assumes a certain distribution of the data (mostly normal distribution) Non-parametric tests No assumptions about distributions If assumptions for parametric test met: Lower test strength

### Which statistical test for which situation?

For your data analysis, you should first check whether a parametric method is available and whether your data has the required distribution. If this is not the case, you can always use a non-parametric method.

We have shown some frequently used procedures for you in the following table.

 situation Parametric test Non-parametric test example Compare 2 independent samples t-test for independent samples Mann-Whitney-U test Is the performance rating of department A different from department B? Compare 2 dependent samples t-test for dependent samples Wilcoxon test Do employees show better skills in Excel after a training course (comparison before and after training course)? Compare 3+ independent samples Analysis of Variance (ANOVA / ANCOVA) Kruskal-Wallis test Which of the 4 designs for our website leads to more orders? Compare 3+ dependent samples Analysis of variance with repeated measures Friedman test Does the intention to buy one of 4 cars increase after a test drive (comparison before and after training drive)?Does the effect of a test drive differ between the 4 examined car models? Relationship between 2 variables Pearson correlation Kendall's Tau or Spearman Correlation Is there a relationship between workload and sick days?

Of course, there are of course a large number of other parametric and non-parametric tests for special situations. Are you unsure which procedure is the right one for your research project? Simply contact our experts for statistical advice!

### The prerequisite check for your parametric test

Once you have identified the ideal parametric test for your hypotheses, the first step is to check that your data has the required distribution. You do this in two steps.

### 1 - Check data for outliers

Outliers very quickly falsify the distribution of your data. In addition, some non-parametric methods are also susceptible to outliers. Therefore, you should always check your data for outliers first. If necessary, you can then exclude outliers from further analysis. You can read about how to correctly check your data for outliers in our article on box plots.

In this box plot, case 30 could represent an outlier

### 2 - check distribution

You are now ready to check the distribution of your data. The vast majority of parametric tests assume a normal distribution. Therefore, in this article, we will show you how to test your data for normal distribution. A histogram can of course give you a first impression of the distribution of the data. However, depending on the width of the bars, a histogram can quickly give a false impression. For a correct check it is therefore best to rely on specialized methods: If you use SPSS for the test for normal distribution, this includes the QQ plot, the Shapiro-Wilk test and the Kolmogorov-Smirnov test. You can request both procedures in SPSS via the menu item "Descriptive Statistics Exploratory Data Analysis".

In SPSS, you can use exploratory data analysis to check data for normal distribution

Recommended settings for exploratory data analysis

For the QQ plot, the data points should roughly follow the straight line. Furthermore, the tests for normal distribution should not be significant.

In this case there are no significant deviations from the normal distribution

The data points do not deviate much from the diagonal; almost normal data are available

In order to use SPSS correctly for the test for normal distribution, we recommend using statistical tests such as the Shapiro-Wilk test only in combination with QQ plots. The test for normal distribution with formal tests has a number of weaknesses as a method. If in doubt, you should give preference to the visual test with QQ-Plot.

If the distribution of your data stands up to the verification, your data is approximately normally distributed. As long as all other assumptions for the respective test are met, you can then use parametric tests such as the t-test.

### Test for normal distribution SPSS: data is not normally distributed - what now?

If your data deviates significantly from a normal distribution, you should first consider transforming the data. Transformations such as the root or log transformation can often help to approximate the abnormal data to a normal distribution. Then you can then perform the parametric test on the transformed data.

If one transformation is not enough, the further procedure depends on the size of your sample. In the case of large samples, parametric tests are usually robust against deviation from normal distribution, and a parametric test can also be used for non-normal data if the sample is large enough. For smaller samples, however, you should switch to non-parametric tests. Because even a data analysis with non-parametric tests can lead to valuable insights! If you are unsure how to proceed with abnormal data, you can also use our statistics to be sure.

### Parametric Tests: Summary

You now know the differences between a parametric test and a non-parametric test and the advantages of a parametric test. We also showed you how to check your data for normal distribution. With this prerequisite check you can decide whether you should use a parametric test. We hope that this text has helped you in planning your data analysis. If you would like more in-depth coaching on statistical procedures, please contact us at any time!