Compute Chi-Square for Job Position and Work Motivation Scores
Introduction
The Chi-square (χ²) test is a non-parametric statistical method used to test the relationship between two categorical variables. It compares the observed frequencies in a contingency table with the expected frequencies that would occur if there were no relationship between the variables. In this question, we analyze the relationship between job position and motivation levels using the Chi-square test.
Given Data
| High Motivation | Low Motivation | |
|---|---|---|
| Junior Managers | 10 | 15 |
| Senior Managers | 10 | 10 |
Step 1: Calculate Totals
Row Totals:
Junior Managers = 10 + 15 = 25
Senior Managers = 10 + 10 = 20
Column Totals:
High = 10 + 10 = 20
Low = 15 + 10 = 25
Grand Total = 45
Step 2: Calculate Expected Frequencies
Expected frequency (E) = (Row Total × Column Total) / Grand Total
- E for Junior–High = (25 × 20) / 45 = 11.11
- E for Junior–Low = (25 × 25) / 45 = 13.89
- E for Senior–High = (20 × 20) / 45 = 8.89
- E for Senior–Low = (20 × 25) / 45 = 11.11
Step 3: Apply Chi-Square Formula
χ² = Σ[(O – E)² / E]
Where O = Observed frequency, E = Expected frequency
- Junior–High: (10 – 11.11)² / 11.11 ≈ 0.111
- Junior–Low: (15 – 13.89)² / 13.89 ≈ 0.087
- Senior–High: (10 – 8.89)² / 8.89 ≈ 0.139
- Senior–Low: (10 – 11.11)² / 11.11 ≈ 0.111
Total χ² ≈ 0.111 + 0.087 + 0.139 + 0.111 = 0.448
Step 4: Conclusion
Degrees of Freedom (df) = (Rows – 1)(Columns – 1) = (2 – 1)(2 – 1) = 1
Critical value of χ² at df = 1 and α = 0.05 is 3.84
Since 0.448 < 3.84, we fail to reject the null hypothesis.
Final Interpretation
The Chi-square test shows no significant association between job position and motivation levels among employees. The observed difference in motivation between junior and senior managers could be due to chance. Thus, based on this sample, job role does not significantly impact motivation level.