Using t-Test to Find Significant Difference in Achievement Motivation Scores Between Male and Female Students

Introduction

The t-test is a widely used parametric test in statistics for comparing the means of two independent groups. In psychology, it helps determine whether the differences in test scores, behaviors, or psychological traits between groups are statistically significant or due to random variation. In this task, we apply the independent samples t-test to determine whether male and female students differ significantly in their achievement motivation scores.

Given Data

Male Students: 45, 32, 25, 57, 36, 42, 35, 55, 66, 65, 30, 35, 22, 27, 26
Female Students: 36, 53, 64, 55, 52, 34, 62, 73, 61, 34, 45, 38, 36, 25, 45

Step 1: Calculate the Means

Male:
Sum = 628; n = 15
Mean (M1) = 628 / 15 ≈ 41.87

Female:
Sum = 713; n = 15
Mean (M2) = 713 / 15 ≈ 47.53

Step 2: Calculate Standard Deviations

Using formula for standard deviation (s):
s = sqrt[ Σ(x – mean)² / (n – 1) ]

Male SD:
Σ(x – M1)² ≈ 3214.93
s1 = √(3214.93 / 14) ≈ √229.64 ≈ 15.15

Female SD:
Σ(x – M2)² ≈ 2428.8
s2 = √(2428.8 / 14) ≈ √173.49 ≈ 13.17

Step 3: Apply Independent t-Test Formula

t = (M1 – M2) / √[(s1²/n1) + (s2²/n2)]
t = (41.87 – 47.53) / √[(229.64/15) + (173.49/15)]
t = -5.66 / √(15.31 + 11.57) = -5.66 / √26.88 = -5.66 / 5.18 ≈ -1.09

Step 4: Degrees of Freedom and Significance

df = n1 + n2 – 2 = 15 + 15 – 2 = 28
At 0.05 significance level (two-tailed), critical t ≈ ±2.048

Since -1.09 lies within the range -2.048 to +2.048, the result is not significant.

Conclusion

The independent samples t-test shows that there is no statistically significant difference between the achievement motivation scores of male and female students in this sample. While the female group shows a higher mean score, the difference is not large enough to be considered statistically significant at the 5% level. Therefore, the observed difference could be attributed to random variation rather than a true difference in achievement motivation.