Compute ANOVA (Parametric Statistics) for the Given Data on Emotional Intelligence
Introduction
Analysis of Variance (ANOVA) is a powerful statistical technique used to determine whether there are any statistically significant differences between the means of three or more independent groups. In this case, we are given emotional intelligence scores of employees categorized into three groups: Group A, Group B, and Group C. We will compute a one-way ANOVA to determine if there is a significant difference in emotional intelligence among these groups.
Data Provided
Group A: 34, 32, 23, 66, 44, 44, 33, 23, 43, 33
Group B: 26, 34, 23, 13, 34, 76, 43, 35, 57, 34
Group C: 28, 56, 54, 33, 56, 54, 23, 25, 54, 34
Step-by-Step ANOVA Calculation
Step 1: Calculate the Group Means
Group A:
Sum = 34 + 32 + 23 + 66 + 44 + 44 + 33 + 23 + 43 + 33 = 375
Mean = 375 / 10 = 37.5
Group B:
Sum = 26 + 34 + 23 + 13 + 34 + 76 + 43 + 35 + 57 + 34 = 375
Mean = 375 / 10 = 37.5
Group C:
Sum = 28 + 56 + 54 + 33 + 56 + 54 + 23 + 25 + 54 + 34 = 417
Mean = 417 / 10 = 41.7
Step 2: Calculate the Grand Mean
Total sum of all values = 375 (Group A) + 375 (Group B) + 417 (Group C) = 1167
Grand Mean = 1167 / 30 = 38.9
Step 3: Calculate Sum of Squares Between Groups (SSB)
SSB = n * [(Mean of A – GM)2 + (Mean of B – GM)2 + (Mean of C – GM)2]
= 10 * [(37.5 – 38.9)2 + (37.5 – 38.9)2 + (41.7 – 38.9)2]
= 10 * [1.96 + 1.96 + 7.84] = 10 * 11.76 = 117.6
Step 4: Calculate Sum of Squares Within Groups (SSW)
We compute each group’s deviation from its mean and square it.
Group A:
- (34 – 37.5)2 = 12.25
- (32 – 37.5)2 = 30.25
- (23 – 37.5)2 = 210.25
- (66 – 37.5)2 = 812.25
- (44 – 37.5)2 = 42.25
- (44 – 37.5)2 = 42.25
- (33 – 37.5)2 = 20.25
- (23 – 37.5)2 = 210.25
- (43 – 37.5)2 = 30.25
- (33 – 37.5)2 = 20.25
Total for Group A = 1430.5
Group B:
- (26 – 37.5)2 = 132.25
- (34 – 37.5)2 = 12.25
- (23 – 37.5)2 = 210.25
- (13 – 37.5)2 = 600.25
- (34 – 37.5)2 = 12.25
- (76 – 37.5)2 = 1482.25
- (43 – 37.5)2 = 30.25
- (35 – 37.5)2 = 6.25
- (57 – 37.5)2 = 380.25
- (34 – 37.5)2 = 12.25
Total for Group B = 2878.5
Group C:
- (28 – 41.7)2 = 187.69
- (56 – 41.7)2 = 204.49
- (54 – 41.7)2 = 151.29
- (33 – 41.7)2 = 75.69
- (56 – 41.7)2 = 204.49
- (54 – 41.7)2 = 151.29
- (23 – 41.7)2 = 357.21
- (25 – 41.7)2 = 282.24
- (54 – 41.7)2 = 151.29
- (34 – 41.7)2 = 59.29
Total for Group C = 1824.27
SSW = 1430.5 + 2878.5 + 1824.27 = 6133.27
Step 5: Calculate Degrees of Freedom (df)
- dfbetween = k – 1 = 3 – 1 = 2
- dfwithin = N – k = 30 – 3 = 27
Step 6: Calculate Mean Squares
- MSB = SSB / dfbetween = 117.6 / 2 = 58.8
- MSW = SSW / dfwithin = 6133.27 / 27 ≈ 227.38
Step 7: Calculate F-Ratio
F = MSB / MSW = 58.8 / 227.38 ≈ 0.2586
Step 8: Interpretation
To determine if the F-ratio is significant, we compare it with a critical value from the F-distribution table at dfbetween = 2 and dfwithin = 27. At α = 0.05, the critical F value is approximately 3.35. Since 0.2586 < 3.35, we fail to reject the null hypothesis.
Conclusion
The one-way ANOVA analysis for the emotional intelligence scores across Group A, Group B, and Group C reveals that the calculated F value (≈ 0.26) is significantly lower than the critical value at a 5% level of significance. This indicates that there is no statistically significant difference in the mean emotional intelligence scores among the three groups of employees. In other words, any variation observed in their scores is likely due to chance rather than a real effect.
ANOVA remains a foundational technique in psychology and behavioral sciences, especially when comparing more than two groups. While in this case the means of Group A and B were identical, and Group C had a slightly higher mean, the variation was not enough to be statistically significant.