Parametric tests: definition and characteristics

The larger the sample, the more accurate the estimate. On the contrary, the smaller the sample, the more distorted the mean of the samples will be by extreme rare values.

Parametric tests are a type of statistical significance tests that They quantify the association or independence between a quantitative variable and a categorical variable. (1). Let us remember that a categorical variable is one that differentiates individuals into groups. However, this type of test requires certain prerequisites for its application. What are these?

Let’s say, for example, we want to compare two groups. To check if we can apply parametric tests, we will first have to check if the distribution of the groups in the quantitative variable is normal.

Furthermore, we will also have to check the homogeneity of the variances in the populations from which the groups come. Finally, the number of subjects, called n In statistics, it will have to be greater than 30 per group, favoring the results of the hypothesis contrast the fact that the groups are balanced.

In the event that these requirements are not met, we will resort to non-parametric tests. If they are met, then we can use parametric tests: the test t (for one sample or for two related or independent samples) and ANOVA test (for more than two independent samples).

Conditions to apply them

There are many investigations that need to determine what has to do with what. That is, they need to know if the variables being studied are associated with each other or not. In any case, we need to know some things before applying one test or another. Thus, in detail, The requirements to be able to use these parametric tests are (1):

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The study variable must be numerical

This is, The dependent variable must be measured on a scale that is, at least, interval. It’s better even if it’s right.

Normal

Mostly, the dependent variable values They must follow a normal distribution. This must occur, at a minimum, in the population that belongs to the sample.

The normal or Gaussian distribution (due to the Gaussian bell) is the best studied theoretical distribution and it owes its importance fundamentally to the frequency with which different variables associated with natural and everyday phenomena follow, approximately, this distribution. Some examples, such as weight or psychological characteristics such as IQ, are examples of variables that are normally assumed to follow a normal distribution.

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

The variances of the dependent variable in the compared groups must be more or less equal. That is why it is necessary to know if this homogeneity of variances is met, since the formulation we use in the contrast of means depends on it. Some tests that allow us to compare this homogeneity of variances are:

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

The n sample

The n is the size of the population. In this case, the sample population size cannot be less than 30, and the closer it is to the better, the better. n of the entire population.

So, The larger the sample, the more accurate the estimate. On the contrary, the smaller the sample, the more distorted the mean of the samples will be by extreme rare values.

Types of parametric tests

Depending on the contrast proposed, one type or another of parametric test is used (2):

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Contrast typeEvidenceA sampleTest tTwo independent samplesTest t for two independent samplesTwo related samplesTest t for related dataMore than two independent samplesANOVA

Proof t for a sample

The proof t For a sample, it is concerned with contrasting whether the mean of a population differs significantly from a given known or hypothesized value. Thus, the test calculates descriptive statistics for the contrast variables along with the test t (1).

Proof t for two independent samples

This test is used when the comparison is between the means of two independent populations.. That is, the individuals of one of the populations are different from the individuals of the other. An example of this is a comparison between men and women (1).

Proof t for two related samples

This test is another alternative to contrast two means. This refers mainly to the supposed case in which the two populations are not independent. In this case, these are populations that are related to each other. This situation occurs, for example, when a group of individuals is observed before and after a certain intervention.

ANOVA test for more than two independent samples

In the case of having to compare more than two samples, we will have to resort to analysis of variance or ANOVA. It is a statistical test developed to simultaneously compare the means of more than two populations.

These tests are very recurrent in psychology research, abusing them on many occasions.. However, we must always remember its prerequisites, which will tell us if we can use parametric tests or if we should resort to non-parametric tests.