Chi-Square Test Process

Problem Statement

The HR department at a large company is investigating whether there is an association between the employee department and attendance frequency. They want to determine if certain departments have higher or lower attendance frequencies and whether these differences are statistically significant. For this purpose, they have collected data from a random sample of 450 employees, categorizing them by their department and attendance frequency.

Objective

Conduct a Chi-Square test to determine if there is a significant association between the department and attendance frequency of employees at a 5% significance level.

Data

Department	Frequent Attendance	Occasional Attendance	Rare Attendance	Total
Sales	90	40	20	150
Marketing	50	80	20	150
IT	30	60	60	150
Total	170	180	100	450

Tasks

1. Set up Hypotheses:
   • Null Hypothesis (H0): There is no association between department and attendance frequency.
   • Alternative Hypothesis (H1): There is an association between department and attendance frequency.
2. Calculate Expected Frequencies: Use the formula:

   

   Calculate the expected frequency for each cell in the table.
3. Compute the Chi-Square Statistic:

   

   Sum up the values to get the total Chi-Square statistic.


4. Determine the Degrees of Freedom (df):

   Use the formula:



5. Compare with Critical Value: Find the critical value for a 5% significance level CHI-Square-Table .


6. Make a Decision:

   If the calculated Chi-Square statistic is greater than the critical value, reject the null hypothesis. If it is less than or equal to the critical value, fail to reject the null hypothesis.



7. Conclusion: Based on your findings, state whether there is a significant association between department and attendance frequency.

Summary of Findings

You correctly concluded to reject the null hypothesis because the calculated Chi-Square statistic was greater than the critical value. This indicates a significant association between employee department and attendance frequency.