Parametric Tests: Definition And Characteristics

The larger the sample, the more precise the estimate. Conversely, the smaller the sample, the more uncertain the sample mean is due to extreme marginal values.

Parametric tests are statistical tests that measure the degree of association between a quantitative variable and a categorical variable. Recall that a categorical variable is a variable that differentiates individuals into groups. However, for this type of testing, certain prerequisites are required.

Suppose, for example, that we want to compare two groups. In order to check that it is possible to apply the method of parametric tests, we will first have to check whether the distribution of the groups in the quantitative variable is normal.

In addition, it is also necessary to verify the homogeneity of the variations of the populations from which the groups come. Finally, the number of subjects, called n in statistics, must be greater than 30 per group. This validates the hypothesis that groups are fair.

If these requirements are not met, then we will resort to non-parametric tests. On the other hand, if they are satisfied, one can then use the parametric tests. These are the t-test (for one sample or for two related or independent samples) and the ANOVA test (for more than two independent samples).

The conditions for the application of parametric tests

In order to determine the relationship between different elements, a lot of research is needed. These studies seek to establish whether certain variables are associated with each other or not. To do this, you need to know the type of test you can apply. Let’s see what are the necessary conditions to implement the parametric tests.

The study variable of the parametric tests must be numeric

That is, the variable should be measured on an interval scale. It’s even better if it’s a ratio scale.

The normality

The values of the dependent variable must follow a normal distribution. This should at least concern the population belonging to the sample.

The normal or Gaussian distribution (so called because of the Gaussian bell) is the most studied theoretical distribution. It is mainly due to the fact that many natural and common phenomena approximately follow this distribution.

This is particularly the case with weight or psychological characteristics such as the intelligence quotient for example. These variables generally follow a normal distribution.

Homoscedasticity (the homogeneity of variances) between the groups to be compared

The variances of the dependent variable within the groups compared should be more or less equal. The contrast of the means depends on the homogeneity of the variances, which is why it is necessary to ensure that this is respected. Here are now some tests that allow us to compare this homogeneity of variances:

Levene test.
Fisher’s F test.
Hartley’s Fmax.
Barlett test.

Sample n

Sample n represents the size of the population. In this case, the sample size should not be less than 30. It will be all the better it will be close to n of the total population.

The larger the sample, the more precise the estimate. Conversely, the smaller the sample, the more the sample mean will be distorted by irregular extreme values.

Types of parametric tests

Type	Tests
A sample	Your t t
Two independent samples	T test for two independent samples
Two related samples	T- test for related data
More than two independent samples	ANOVA

T test for a sample

The one-sample t-test aims to determine whether the mean of a population differs significantly from a known or assumed defined value. Thus, the test calculates descriptive statistics for the contrast variables at the same time as the t (1) test.

T test for two independent samples

This test is used when the comparison is made between the means of two independent populations. That is, the individuals of the two populations are different. For example, the comparison between men and women (1).

T test for two related samples

This test is an alternative to compare two means. This is mainly the supposed case where the two populations are not independent.

In this case, we are dealing with populations that are related to each other. This situation occurs, for example, when a group of individuals is observed before a certain intervention and then after that intervention.

ANOVA test for more than two independent samples

If more than two samples have to be compared, analysis of variance also called ANOVA should be used. It is thus a statistical test which makes it possible to simultaneously compare the means of more than two populations.

All of these tests are very common in psychology research, but they are often abused. However, we must always keep in mind that the preconditions are important. Indeed they tell us if we can use parametric tests or if we need to resort to nonparametric tests.