PAGE 1 of 1: Hypothesis Testing using Kruskal-Wallis
A psychological test is used to measure self-esteem to three different groups of
individuals based on birth order. The scores range from 0 to 50, 50 being the most
confident. At 5% level of significance, is there a difference in the scores? Which child is
the most and least confident? If the test is done by pairs (i.e., oldest child vs youngest
child), which pair has significant difference on scores?
Step 1: State the Null and Alternative Hypothesis
• Null hypothesis: All groups have equal self-esteem score based on birth
order. (H0: η1 = η2)
• Alternative Hypothesis: Not all groups have equal self-esteem score.
(H1: η1 > η2)
Step 2: Set the Level of Significance or Alpha Level (α)
• α = 0.05
Step 3: Determine the Test Distribution to Use
• Dependent Variable: Self-esteem scores (ranging from 0 to 50)
• Independent Variable: Birth order (with three categories: oldest, middle,
youngest)
Since we are comparing the median of two or more independent groups, we will use
the Kruskal-Wallis.
Step 4: Calculate Test Statistic or p - value.
Normality Test:
Conducting Kruskal-Wallis
Step 5: Make Statistical Decision
• If p-value ≤ α, reject H0, otherwise failed to reject H0.
• The p-value of 0.632 is greater than the alpha value of 0.05. Hence, we failed
to reject the null hypothesis.
Step 6: Draw Conclusion
At 5% level of significance, is there a difference in the scores?
• At 5% level of significance, the results indicate that the scores of the three
groups are equal. Therefore, the three groups of individuals based on birth order
have equal confidence.
Which child is the most and least confident?
• Based on the results, it indicates that the Middle Child has the highest mean rank
while the Oldest has the lowest mean rank. Therefore, the most confident group
is the Middle while the least confident group is the Oldest.
Hypothesis Testing using
If the test is done by pairs (i.e., oldest child vs youngest child), which pair has significant
difference on scores? Guys pahelp HAHAHAHAHA ang hirap HUHU
Step 1: State the Null and Alternative Hypothesis
• Null hypothesis: There is no significant difference in self-esteem scores
between the oldest and middle children. (H0: η1 = η2)
• Alternative Hypothesis: There is a significant difference in self-esteem
scores between the oldest and middle children. (H1: η1 ≠ η2)
Step 2: Set the Level of Significance or Alpha Level (α)
• α = 0.05
Step 3: Determine the Test Distribution to Use
• Dependent Variable:
• Independent Variable:
Step 4: Calculate Test Statistic or p - value.
Normality Test:
Since the set of data for oldest and youngest child is normal, we will use
parametric test. We have two independent samples; therefore we will use Independent
Sample T-test.
As for the set of data of the middle child, since it shows that it is not normal, we
will then use non-parametric test. We have two independent samples; therefore we will
use Mann-Whitney
Conducting Mann-Whitney
Conducting Independent Sample T-Test
Step 5: Make Statistical Decision
If p-value ≤ α, reject H0, otherwise failed to reject H0.
Oldest Child vs Middle Child
• The p-value of 0.368 is greater than the alpha value of 0.05. Hence, we failed
to reject the null hypothesis.
Middle Child vs Youngest Child
• The p-value of 0.596 is greater than the alpha value of 0.05. Hence, we failed
to reject the null hypothesis.
Oldest Child vs Youngest Child
• The p-value of 0.5758 is greater than the alpha value of 0.05. Hence, we failed
to reject the null hypothesis.
Step 6: Draw Conclusion
If the test is done by pairs (i.e., oldest child vs youngest child), which pair has
significant difference on scores?
• Based on the results, it indicates that all pairs have no significant difference on
scores, therefore, all pairs have equal self-esteem scores.
