Parametric versus non-parametric tests. Which test to choose for analysis?

Statistical analysis is an integral part of scientific research and working with data. In order to draw valid conclusions, the use of appropriate statistical tests is essential. The analyst is often faced with the choice of which test to choose in a given situation. This is important because the wrong choice of test for the data can cause the results to be subject to error or have low reliability. The statistical tests we use can usually be assigned to one of two groups, i.e. parametric or non-parametric tests. In the following, I will discuss how these two groups of tests differ and what should guide the selection of a statistical test in data analysis.

Parametric tests

Parametric tests are a group of statistical data analysis techniques. They are used to test for differences between groups or sets of data. The purpose of their use is to draw conclusions about the population from which the data are drawn. As the name implies, these tests use information about population parameters such as the mean or standard deviation. The advantage of parametric tests is their statistical power. They tend to be more sensitive and accurate when testing hypotheses about means and variances, assuming certain conditions are met. For example, if we have data with a normal distribution with equal variances between groups, a t-test or ANOVA is likely to give more accurate results than non-parametric equivalents such as the Wilcoxon test or the Kruskal-Wallis test.

The main assumptions of parametric tests may include:

• normality of the data distribution - parametric tests assume that the data in the study groups are from a normal distribution. This means that the data should be close to the normal distribution curve,
• homogeneity of variances - it is assumed that the variances of the data in different groups are equal, i.e. there are no significant differences in the dispersion of data between groups,
• data type - most commonly applied to data measured at the quantitative level of measurement.

Non-parametric tests

In the case of non-parametric tests, it is difficult to indicate the main assumptions, because in this case this type of statistical technique is quite flexible. As already mentioned, for these tests we do not assume a specific distribution of the data and they can be applied to variables measured on nominal and ordinal scales. These tests also do not use information about population parameters. Non-parametric tests are often used when the data do not meet the assumptions of parametric tests or when we are dealing with data measured at a qualitative level of measurement. They are used to compare distributions, medians or ranks, and not necessarily population parameters. Non-parametric tests are less sensitive (lower test power) for detecting subtle differences between groups than parametric tests.

One non-parametric test is the Mann-Whitney U test. This is the non-parametric equivalent of the Student's t-test and is used to compare two independent groups in terms of differences in rank distribution. Another type of non-parametric test is the Kruskal-Wallis test, which is the equivalent of an analysis of variance (ANOVA).

The differences and characteristics of parametric and non-parametric tests are presented in Table 1.

Feature

Parametric tests

Non-parametric tests

Assumptions on population distribution

They require certain assumptions to be met

They do not require assumptions to be met, e.g. normality of distribution, homogeneity of variance

Population information

Use information on population parameters

Do not use information on population parameters

Power of the test

Usually more powerful than non-parametric tests

Have lower power than parametric tests

Example tests

Student's t-test, ANOVA

Wilcoxon test, Kolmogorov-Smirnov test

Table 1. Comparison of the main features of parametric and non-parametric tests

Parametric versus non-parametric testing - how to choose?

Finally, let us consider how we can make the choice of an appropriate test for data analysis. The choice between a parametric and non-parametric test depends on a number of factors, including the type of data, assumptions about the distribution of the data and the purpose of the study. Here are some factors that can help you decide which type of test is appropriate.

1. Test assumptions. Parametric tests have specific assumptions, such as normality of distribution and equality of variance. If the data are close to a normal distribution and meet the other assumptions for the test, a parametric test can be chosen. If, on the other hand, the assumptions are not met, non-parametric tests may be a better choice.
2. Level of measurement. Parametric tests are more suitable for data measured on an interval or quotient scale, where differences between values can be accurately determined. Non-parametric tests are more flexible and can be applied to different scales of measurement, including ordinal or nominal data.
3. Study sample size. For small samples, non-parametric tests may be more appropriate, as parametric tests may require meeting distribution assumptions that are more difficult to meet for small samples.
4. Study objective. If the aim is to compare medians, analyse the relationship between ordinal variables or assess differences in the distribution of the data, non-parametric tests may be a better choice.

The final choice between a parametric and non-parametric test depends on the specific research case and the data available to the analyst. It is important to carefully consider the above factors and select the appropriate test based on the context of the study and the characteristics of the data.

 Parametric tests Non-parametric tests Student's t-test (one sample) Wilcoxon test Student's t-test (two samples) Wilcoxon's test for dependent samples Student's t-test (two independent samples) Mann-Whitney U-test One-way analysis of variance (ANOVA) Kruskal-Wallis test

Table 2. Popular parametric tests and their non-parametric counterparts

Example of use in PS IMAGO PRO

Using PS IMAGO PRO, the analyst has access to tools that allow him or her to quickly and easily check assumptions for statistical tests. The programme also allows the appropriate analysis and visualisation of the data to be performed. The example we will follow concerns the parametric Student's t-test, which is used to compare the means of two independent groups. Suppose we want to test whether the average height of men is higher than the average height of women.

The hypotheses are as follows:

- Null hypothesis (H0): The average height of men is not different from the average height of women.
- Alternative hypothesis (H1): The average height of men is higher than the average height of women.

To do this, we draw random samples from the male and female populations. We then verify the assumptions to see if we can apply a t-test to the collected data.

In the first instance, it is useful to check that our comparison groups are equal. If we are in doubt about whether the groups are equidistant, then use the chi-square test of concordance. If we want to equalise the categories of a variable, we can select the Balance distribution procedure from the Predictive Solutions menu (Data > Balance distribution).

In the next step, we check the assumption of normality of the analysed variable distributions. For this purpose, in PS IMAGO PRO it is useful to use the Explore procedure (Analyze > Descriptive Statistics > Explore), which gives the analyst a full set of descriptive statistics, e.g. means, standard deviations, skewness value, kurtosis, etc. In addition, the analyst can generate histograms and normality plots with Kolmogorov-Smirnov and Shapiro-Wilk tests, which allow the analyst to clearly determine whether the assumption is met or not. If the assumption of normality of the distributions is not met, the analyst can choose one of the available non-parametric tests, in this case it would be the Mann-Whitney U test.

Next, it is necessary to verify the assumption of homogeneity of variance in the groups analysed. For this purpose, we can use the Levene's test, available in the Explore procedure.

If the above assumptions are met, we can proceed to perform the t-test for independent samples. To facilitate the analyst's work, the result table of the t-test also presents the value of the Levene's test.

If the difference in means is statistically significant, then in this example we can conclude that the two groups differ in terms of growth.

Summary

The choice of test depends on the type of data, the purpose of the analysis and meeting the assumptions of parametric tests. If the data do not meet the assumptions for parametric tests, it makes sense to choose non-parametric tests, which are less restrictive in their data requirements. However, parametric tests, when the relevant assumptions are met, often have greater statistical power. Therefore, it is important to thoroughly understand the data you want to analyse and choose the appropriate statistical test depending on the situation.

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