# Statistical tests

Most scientific fields require that each researcher or postgraduate student familiarize themselves with the most frequently used types of statistical tests, because his study’s access to accurate logical results is linked to his good selection of these tests.

Statistical tests are used in testing hypotheses, where the researcher chooses the appropriate statistical test in order to ensure that the variable has statistically significant relationships, or to estimate the differences between two groups or between more than two groups.

Appropriate statistical tests are studied with the aim of the study that confirms the existence of null hypotheses that show the absence of relationships, or other hypotheses that prove the existence of differences between variables or groups.

Statistical analysis is one of the processes that a scientific researcher performs after he finishes collecting information and data for his research study, and it relies heavily on the processes of organizing and preparing the data, and then he chooses one of the most used types of statistical tests.

This helps to reach sound and useful results and solutions that help reach the goals of scientific research.

#### Statistical testing mechanisms

The statistical test works by calculating final results for statistical measures, and the results can be through numbers that reveal that:

There is no relationship between the variables (zero relationship), as these numbers can reveal:

The extent of the difference between the variables so that it shows that the relationship between the variables is a negative or positive relationship.

The probability value calculates the difference described using a statistical measure commensurate with the nature of the research data and the sample from which the information and data were collected.

#### When do you use statistical tests?

Statistical tests are conducted on information and data that are properly collected, whether from probability samples or through tests and experiments.

The success of the statistical test and its arrival at correct results depends on:

The size of the research sample should be large enough relative to the size of the study community, to approximate the realistic distribution of the research community.

In order to determine which of the most used types of statistical tests to be relied upon, it is assumed that:

Ensure that research data meets specific assumptions, and ensure the types of variables are dealt with.

#### Statistical assumptions

Statistical tests make a number of common assumptions associated with the data being tested, including:

Homogeneity of variance: It indicates the similarity between the different groups that are compared within each group, and that is when the group has a greater degree of diversity than the others, because this leads to limiting the amount of test effectiveness.

Observational independence (lack of autocorrelation): where the measurements of different test subjects are independent, and multiple measurements associated with the same test subject are not independent.

The nature of the data that follows the realistic and natural distribution of the data, and this type of assumptions that can only be applied with quantitative data exclusively.

When the research data does not meet the nature of the realistic data or the homogeneity of the variance, it is possible to rely on non-parametric statistical tests, which allow the researcher to make comparisons without making assumptions related to the distribution of the data.

When research data are not sufficient to assume independence of observations, it is possible to use tests that consider structure in research data.

#### Types of statistical variables in scientific research

Statistical variables in scientific research can be mainly divided into:

Quantitative variables, or qualitative variables, according to the following figure

#### quantitative variables

Quantitative variables represent the amount or quantity of something (such as the number of animals in a forest), and qualitative variables have several types, most notably:

Discrete variables, which some call “integer variables,” represent numbers that cannot be divided into units smaller than one, such as (one phone).

A continuous variable, which some call “ratio variables,” captures various measures that can usually be divided into units less than one (0.40 grams, for example).

#### Qualitative variables

It is the one that includes multiple types of things (such as the types of plants in a region), and the qualitative variables have several types, the most prominent of which are:

First: the nominal variable that represents the names of certain things or groups, such as the names of sports teams in a country.

Second: the ordinal variable, through which the research data is represented in a specific order.

Third: the binary variable, which represents the data through a result such as (agree, disagree), (win or lose), (yes or no).

When conducting the test, the researcher should choose one of the most used types of statistical tests

Which is commensurate with the types of the expected variable, and with the variables of the results that the researcher collected. When the scientific researcher performs an experiment, he uses the independent and dependent variables.

#### The most commonly used types of statistical tests

We can divide the most common statistical tests into two main types:

Parametric tests, and non-parametric tests, which in turn have conditions and classifications, according to the form that we will learn about in our next paragraphs.

#### First – Parametric (parametric) tests

It is one of the most widely used types of statistical tests, which are mainly used to ensure:

The safety of hypotheses that are associated with specific parametric values (so that the dependence is on the parameters of the research community).

Among the conditions for these tests is that the study sample in the research should be:

significant, not less than thirty, and that the selection for this sample was done randomly

With the moderate distribution of the study population, and that the dependent variable be a quantitative variable.

Parametric tests are used to calculate the differences between the means, the t-test, or the analysis of variance test, while the correlation coefficient is calculated by calculating the correlation coefficient

i pearson.

T-test

It is one of the parametric statistical methods that are used to calculate the differences between averages, and it has three types:

Some of them are for one sample, or for two independent samples, or for two interrelated samples.

1. One-sample t-test

The aim of using it is to test the hypothesis associated with the average of one population, through a test that shows whether

The sample mean is significantly different from the default value of the population mean.

This test, which is classified among the most widely used types of statistical tests, is used:

If the researcher has numerical data obtained from one study sample, and he wishes to compare between

The average of the sample that was able to be obtained with the average of the study population that has a previously known value.

It is also used with the null hypothesis, which shows that there are no statistically significant differences between the average of the community and the average of the study sample.

In addition, it is used with alternative hypotheses that show that there are no statistically significant differences between the average of the community and the average of the study sample.

The most prominent conditions of the (T) test are that the sample was chosen randomly, and that the dependent variable is a relative continuous quantitative variable.

Or categorical, and the distribution of the dependent variable in the study community should not be normal (normal).

2.T-test for two independent samples

Here, it is used to test the hypothesis associated with the averages of two groups or two independent samples

This is to ensure that the difference between the averages of the two independent study samples is really different from the difference between the averages of the community.

Among the most important conditions for this test, which is classified as one of the most widely used types of statistical tests, is that:

The independent variable is a nominal variable of two types, such as whether the person is (employee or non-employee), (smoker or non-smoker), (male or female).

And that both samples were chosen randomly, and that they were independent, with the need for the dependent variable of the study to be quantitative.

(relative or categorical), and that the numerical, quantitative dependent variable be of moderate values and its distribution is realistic and natural.

3.T-test of two correlated samples

It is one of the tests of hypotheses related to the averages of two groups that have a correlation, through a test through which it is confirmed that:

The difference between the mean of the two samples is really and realistically different from the difference between the mean of the two research communities.

This test is used when post or pre-tests are applied to the same group, with the aim of:

Knowing the difference between the averages of the post and pretests, and two degrees are used for each individual that measure what is before and what is after.

The most prominent conditions of this test are the interdependence of the two study samples, and that they were selected randomly, and that the independent variable be a classification variable with two levels, with the need for the dependent research variable to be a continuous quantitative variable (relative or categorical), and the distribution of the difference in this test between the values of the variable is normal .

#### Secondly – non-parametric tests (non-parametric)

It is one of the most widely used types of statistical tests, which are mainly used to verify that the validity of hypotheses associated with communities of parametric values is not specific, that is, it depends on the parameters of the community.

One of the most important conditions of these tests is that they apply to all sizes of samples, whether large or small, although they are used more with small samples.

In it, it is not required that the selection of the scientific researcher for the sample was made randomly, nor does it stipulate any of the conditions of society, including moderation, and the dependent variable in it is ordinal or nominal.

According to these tests, the calculation of the differences between the averages is using the method of the Mann-Whitney test, the Wilcoxon test, or the Kruskal-Wallis test, while the correlations are calculated using the “Spearman” correlation coefficient.