Chi-square test: what it is and how to do it

The Chi-square test, also known as Pearson's chi-square test or Fisher's exact test, is one of the methods used to test a hypothesis in research.

In this article we will introduce you to what it consists of, what types there are and how you can use it in practice.

What is a Chi-Square Test?

The chi-square test is a statistical procedure that can be used to determine whether there is a significant difference between expected and observed results in one or more categories.

It is a non-parametric test used by researchers to To examine differences between categorical variables in the same population. It can also be used to validate observed frequencies or provide additional context.

The basic idea of ​​the test is that the actual data values ​​are compared with the values ​​that would be expected if the null hypothesis were true.

The purpose of this is to determine whether a difference between the observed and expected data is due to chance or whether it is due to a relationship between the variables under study.

It also explains what the t test from student is.

The importance of the chi-square test in research

The chi-square test is an excellent way to understand and interpret the relationship between two categorical variables.

The crosstab displays the distributions of two categorical variables simultaneously, with the intersections of the variable's categories appearing in the cells of the table.

Calculating the chi-square statistic and comparing it to a critical value of the chi-square distribution allows the researcher to assess whether the observed cell numbers differ significantly from the expected cell numbers.

Because of the way the chi-square value is calculated, it is extremely sensitive to sample size: if the sample size is too large (~500), almost every small difference will appear statistically significant.

It is also sensitive to distribution within cells. This problem can be solved by always using categorical variables with a limited number of categories.

Types of Chi-Square Tests

There are different types of chi-square tests: goodness-of-fit test, independence test and homogeneity test. We will now introduce you to what the individual tests consist of:

Goodness-of-fit test

The chi-square goodness-of-fit test is used to compare a randomly drawn sample containing a single categorical variable to a larger population.

This test is most commonly used to compare a random sample to the population from which it was potentially collected.

Test for independence

The chi-square test of independence looks for an association between two categorical variables within the same population.

In contrast to the goodness-of-fit test, the independence test does not compare a single observed variable with a theoretical population, but rather two variables within a series of samples.

Chi-square homogeneity test

The chi-square homogeneity test is structured and carried out in the same way as the independence test.

The main difference is that the independence test looks for an association between two categorical variables within the same population, while the homogeneity test determines whether the distribution of a variable is the same in each of multiple populations (and thus uses the population itself as a second categorical variable).

How do you perform a chi-square test?

Now that you know a little more about what a chi-square test is, let's introduce you to how to do it in 5 steps:

1. Define your null and alternative hypotheses before you start collecting data.
2. Decide what the alpha value should be. This is about the risk you are willing to take to draw the wrong conclusion. For example, let's say we set a value of α=0,05 for the independence tests. In this case, you have chosen a 5% risk of concluding that the two variables are independent when in reality they are not.
3. Check the data for errors.
4. Check the assumptions of the test.
5. Carry out the test and draw your conclusion.

Conclusion

As you can see, the chi-square test statistic consists of finding the squared difference between the actual and expected data values ​​and dividing that difference by the expected data values. This is done for each data point and the values ​​are summed.

The test statistic is then compared to a theoretical value of the chi-square distribution. The theoretical value depends on both the alpha value and the degrees of freedom of the data.

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KEYWORDS OF THIS BLOG POST

Chi-square test | Test | Research