Nonparametric Tests: Definition And Types
Nonparametric tests or techniques include a series of statistical tests which have in common the absence of assumptions about the probability law followed by the population from which the sample was taken. Thus, these techniques are applied when it is not known whether the population from which the sample is taken is normal or approximately normal.
These non-parametric techniques are frequently used because many variables do not follow the setting conditions. These are the use of continuous quantitative variables, the normal distribution of samples, similar variances and balanced samples.
When these prerequisites are not met or there are serious doubts about their fulfillment, non-parametric or free distribution tests are used. Thus, nonparametric tests have the following characteristics:
- They are used much less than one would recommend (they are less well known to researchers)
- They are applicable to hierarchical data
- Also, they can be used when two sets of observations come from different populations (populations in which the variable is not equally distributed)
- They are the only realistic alternative when the sample size is small
Classification of these tests
In this classification of nonparametric tests, there is no consensus as to their grouping. The authors Berlanga and Rubio (2012) summarized the main parametric tests.
Nonparametric Tests of a Sample
Pearson’s chi-square test
This is a test widely used when the researcher wants to analyze the relationship between two quantitative variables. It is also widely used to assess the extent to which the data collected in a categorical variable (empirical distribution) does not correspond (or does not resemble) a certain theoretical distribution (uniform, binomial, multinomial, etc.).
Binomial test
This test allows us to know whether or not a dichotomous variable follows a certain probability model. It contrasts the hypothesis according to which the observed proportion of hits corresponds to the theoretical proportion of a binomial distribution.
Series test
This is a test to determine whether the number of series (S) observed in a sample of size n is large enough or small enough to reject the hypothesis of independence (or randomness) between observations.
A series is a sequence of observations with the same attribute or the same quality. The fact that there are more or less periods than expected by chance in a data series can be an indicator that there is an important variable that conditions the results and that we do not take into account.
Kolmogorov-Smirnov test (KS)
This test makes it possible to contrast the null hypothesis according to which the distribution of a variable corresponds to a certain theoretical probability distribution (normal, exponential or Poisson). Whether or not the distribution of the data matches a certain distribution will suggest certain techniques for analyzing the data over others.
Nonparametric tests for two related samples
McNemar test
McNemar’s test is used to test hypotheses about equality of proportions. It is used when there is a situation where the measurements of each subject are repeated. Thus, the response of each of them is obtained twice: once before and once after a specific event.
Sign test
It makes it possible to contrast the hypothesis of equality between two population medians. It can be used to find out if one variable tends to be larger than another. Or to test the trend followed by a series of positive variables.
Wilcoxon test
It makes it possible to contrast the hypothesis of equality between two population medians.
Nonparametric Tests for Related K Samples
Friedman test
It is an extension of the Wilcoxon test. Thus, it is used to include data recorded over more than two time periods or groups of three or more subjects, one subject from each group being randomly assigned to one of three or more conditions.
Cochran test
It is identical to the previous one, but applies when all the responses are binary. Cochran’s Q supports the hypothesis that several related dichotomous variables have the same mean.
Kendall’s Coefficient W
It has the same indications as the Friedman test. However, its use in research has been primarily to find concordance between ranks.
Nonparametric tests for two independent samples
Mann-Whitney U test
It is equivalent to the Wilcoxon range sum test as well as to the Kruskal-Wallis two group test.
Kolmogorov-Smirnov test
This test is used to verify the hypothesis that two samples come from the same population.
Test of Wald-Wolfowitz suites
Contrast if two samples with independent data come from populations with the same distribution.
Moses extreme reaction test
It is used to investigate whether there is a difference in the degree of dispersion or the variability of two distributions. It emphasizes the distribution of the control group and measures the number of extreme values of the treatment group that influence the distribution when combined with the control group.
Nonparametric Tests for Independent K Samples
Median test
Contrast the differences between two or more groups against their median. Averages are not used, either because they do not meet normal conditions or because the variable is discrete quantitative. It is similar to the Chi-square test.
Jonckheere-Terpstra test
It is the most powerful for analyzing the ascending or descending order of the K populations from which the samples are taken.
Kruskal-Wallis H test
Finally, the Kruskal-Wallis H test is an extension of the Mann-Whitney U test and represents an excellent alternative to the one-way ANOVA test.
Thus, these tests are used when the distribution of the data is not normal. We can use it when we have data that is not based on a scale of reason or when, therefore, we doubt that the distribution of either variable corresponds to the normal curve.
On the other hand, it is true that many parametric tests are relatively robust against violation of assumptions ; however, if there are better tests, why not use them?
Our thoughts One of the most important parts of an intervention is evaluation. This often depends on the tests that have been carried out.
