Introduction

The Chi-Square test is an important statistical method for determining the relationship between two categorical variables. It is particularly useful in hypothesis testing and in analyzing the dependency between the variables in a contingency table. In this article, we will discuss the step-by-step process of how to calculate the chi-square test statistic.

Steps to Calculate Chi-Square Test Statistic

1. Create a Contingency Table:

To begin, you need to create a contingency table that represents the observed frequencies of each category in your dataset. The different categories should be arranged in columns and rows based on the respective variables.

2. Determine Expected Frequencies:

Next, you need to determine the expected frequency for each cell in the table. To do this, use the following formula for each cell:

Expected Frequency = (Row Total x Column Total) / Grand Total

Calculate the expected frequency for all cells in your table.

3. Compute the Residuals:

Now that you have both observed and expected frequencies, compute the residuals for each cell. The residual is simply the difference between observed frequency and expected frequency:

Residual = Observed Frequency – Expected Frequency

4. Square Each Residual:

Because we want our test statistic to only consider non-negative values, we simply square each residual value:

Squared Residual = (Resistance)^2

5. Calculate the Contribution of Each Cell:

To find out how much each cell contributes to the overall chi-square statistic, divide the squared residual by its corresponding expected frequency:

Contribution for Each Cell = Squared Residual / Expected Frequency

6. Sum Contributions to Get Chi-Square Test Statistic:

Finally, sum all individual contributions from each cell to obtain your chi-square test statistic value:

Chi-Square Test Statistic = Σ (Contribution for Each Cell)

7. Compare with Chi-Square Distribution Table

Now that you have your chi-square test statistic, compare it with the critical value from the Chi-Square distribution table corresponding to the predetermined level of significance (usually 0.05) and degrees of freedom [(rows – 1)*(columns – 1)]. If your test statistic is greater than the critical value, there is a significant relationship between the variables, and you can reject the null hypothesis.

Conclusion

Calculating the chi-square test statistic is an essential step in identifying possible relationships between categorical variables. By following these steps, you’ll be well-equipped to analyze your data and draw meaningful conclusions about the associations between variables in your study. Don’t forget to use your conclusions responsibly and consider other factors that may be influencing your results.