The Difference Between Chi-Square Test and Fisher’s Exact Test — When to Use and How They Differ

In quantitative research, especially when analyzing categorical data, researchers often want to determine whether two categorical variables are related — for example:

• Is there a relationship between gender and healthcare choices?

• Is smoking associated with heart disease?

Two statistical methods commonly used to analyze such relationships are the Chi-Square Test of Independence and the Fisher’s Exact Test. While both aim to determine whether two variables are associated, they differ in their assumptions, sample size requirements, and calculation methods.น

The Difference Between Chi-Square Test and Fisher’s Exact Test

What Is the Chi-Square Test?

The Chi-Square Test of Independence (χ²) is a non-parametric test used to determine whether two categorical variables are significantly associated.It compares the observed frequencies in each category with the expected frequencies that would occur if there were no relationship between the variables.

The result of the test provides a Chi-Square statistic (χ²) and a p-value, which indicate whether the observed differences are statistically significant.

Key Assumptions

1. Both variables must be categorical (nominal or ordinal).

2. Observations must be independent of one another.

3. The expected frequency in each cell should ideally be 5 or greater.

Example

Research Topic: “The Relationship Between Gender and Type of Exercise Preference”

• Independent Variable: Gender (male / female)

• Dependent Variable: Exercise type (yoga / running / weight training)

If the sample size is large enough and each expected frequency is greater than or equal to 5, the Chi-Square Test is suitable for analysis.

What Is Fisher’s Exact Test?

The Fisher’s Exact Test is also used to analyze relationships between two categorical variables but is ideal for small sample sizes or when some cells in the contingency table have expected frequencies below 5.

Unlike the Chi-Square Test, which uses an approximation, Fisher’s Exact Test calculates the exact probability of obtaining the observed distribution, making it more accurate when sample sizes are limited.

Example

Research Topic: “Is the Use of Contraceptives Associated with Side Effects?”

• Independent Variable: Use of contraceptives (yes / no)

• Dependent Variable: Occurrence of side effects (yes / no)

If the total number of participants is fewer than 30, or if one or more cells have expected frequencies below 5, the Fisher’s Exact Test should be used instead of the Chi-Square Test.

How to Choose Between Chi-Square Test and Fisher’s Exact Test

The choice depends primarily on sample size and expected cell frequencies.

• Use the Chi-Square Test when the sample size is large and all expected frequencies are 5 or more in each cell.

• Use the Fisher’s Exact Test when the sample size is small or when one or more cells have expected frequencies below 5.

• For 2x2 contingency tables with small samples, the Fisher’s Exact Test is always preferred for its accuracy.

In summary:

Chi-Square Test is suitable for large samples and for testing associations between categorical variables.Fisher’s Exact Test is suitable for small samples or when low expected frequencies make the Chi-Square Test unreliable.

Why You Should Use Data Investigator

Choosing between Chi-Square and Fisher’s Exact Test requires a proper understanding of data structure, statistical assumptions, and sample size requirements.Using the wrong test can lead to inaccurate conclusions or invalid interpretations of relationships between variables.

With over 15 years of experience in SPSS-based statistical analysis, Data Investigator provides professional expertise to ensure your statistical tests are correctly chosen, applied, and interpreted.

Our Services Include

• Conducting categorical data analysis using SPSS

• Checking expected frequencies and sample adequacy before selecting tests

• Applying Chi-Square Test or Fisher’s Exact Test accurately

• Providing detailed interpretations of statistical results

• Issuing official Certificates of Statistical Analysis

Whether you are a thesis student, medical researcher, or government organization,Data Investigator ensures your statistical results are accurate, reliable, and clearly presented.

For more information:

E-mail: info@datainvestigatorth.com

Line: @datainvestigator