What is Chi-Square Test and Types of Chi-Square explained for Biomedical Researchers

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Biomedical researchers often handle categorical or nominal data in their analyses (i.e., data with labels rather than numerical values, such as race, smoking status, and sex). Since categorical data cannot be summarized using means or medians, the measure of the central tendency of categorical variables is the mode. Because categorical variables can only have a few specific values, such data does not follow a normal distribution. Hence, categorical data cannot be analyzed with commonly used tests like ANOVA or Pearson’s correlation, because these tests require continuous data. Instead, categorical data is often analyzed using the chi-square test.

Different types of chi-square tests

As mentioned above, the chi-square test is a non-parametric test that is used for hypothesis testing where the variables are categorical. There are two types of chi-square tests that are commonly used:[SA1] 

1. Chi-Square Test of Differences/Independence

This is used to determine whether there is a statistically significant difference or association between two categorical variables.

2. Chi-Square Goodness of Fit Test

This is used to determine whether a categorical variable follows a hypothesized distribution.

What is the chi-square test of differences?

The chi-square test of differences is used to determine if there is a statistically significant difference between the frequencies of two or more categorical variables. When used to check whether there is a statistically significant association between the two variables, this test is also known as the chi-square test of independence.

What is the chi-square goodness of fit test?

The goodness of fit is a statistical measure used to evaluate how well a model “fits” the observed data. In other words, it measures the degree to which the predicted values from a model match the actual values from the data.

The chi-square goodness-of-fit test is commonly used in biomedical research to test whether data follows a specific distribution and is often used to verify the assumptions of statistical models.

What are the degrees of freedom in a chi-square test?

In a chi-square test, degrees of freedom refer to the number of independent pieces of information that are used to calculate the chi-square statistic. It is a measure of the number of values in the final calculation of a statistic that are allowed to vary.

How should I report the results of a chi-square test with Example?

Generally, you would report the chi-square statistic along with your sample size N and degrees of freedom. For example:

χ² (1, N = 84) = 8.9, p = .003

Some journals may ask you to subscript degrees of freedom.

Further, be sure to always use the Greek letter χ and not the English uppercase letter X for the chi-square statistic. If you’re using MS Word, the χ symbol is available in the Symbol list under the Insert menu.

Would you like further assistance in determining the most suitable statistical test for your data? Consult an expert biostatistician under Editage’s Statistical Analysis & Review Services.