# What Type of Data Is Used in a Chi-Square Test?

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Angela Bailey

What Type of Data Is Used in a Chi-Square Test?

The chi-square test is a statistical test used to determine if there is a significant association between two categorical variables. It is commonly used in research and analysis to understand the relationship between variables and make predictions.

However, not all types of data are suitable for a chi-square test. In this article, we will explore the types of data that can be used in a chi-square test and how to analyze them.

## 1. Categorical Data

In order to perform a chi-square test, you need categorical data. Categorical data consists of distinct categories or groups that cannot be ordered or ranked. For example, the gender (male or female) of individuals or the type of car (sedan, SUV, truck) owned by people are categorical variables.

To illustrate this further, let’s consider an example:

• Research Question: Is there an association between smoking habits and lung cancer?
• Data Variables:
• Smoking Habits: Non-smoker, Occasional smoker, Regular smoker
• Lung Cancer: Yes, No
• Data Collection: Gather information about individuals’ smoking habits and whether or not they have been diagnosed with lung cancer.

## 2. Contingency Table

A contingency table is used to organize categorical data for analysis in a chi-square test. It displays the frequencies or counts of observations for each combination of categories. The rows represent one variable, while the columns represent another variable.

To continue with our example, the contingency table for smoking habits and lung cancer would look like this:

Non-smoker Occasional smoker Regular smoker
Lung Cancer: Yes 50 30 70
Lung Cancer: No 100 80 120

## 3. Assumptions of the Chi-Square Test

In order to interpret and draw valid conclusions from the chi-square test, certain assumptions need to be met:

• The data should be collected using random sampling techniques.
• The observations should be independent of each other.
• The expected frequency counts for each cell in the contingency table should be at least 5.
• The variables being analyzed should have a clear relationship or association.

## 4. Interpreting the Chi-Square Test Results

The chi-square test calculates a test statistic and compares it to the critical value from a chi-square distribution. Based on this comparison, we can determine whether there is a significant association between the variables or not.

If the calculated test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant association between the variables. On the other hand, if the calculated test statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant association.

### Conclusion

The chi-square test is a powerful statistical tool for analyzing categorical data and determining if there is a significant association between variables. By understanding the types of data that can be used in a chi-square test and following the assumptions, researchers can gain insights into relationships and make informed decisions based on the results.