Mental Wellbeing Analysis: Two-Way ANOVA, Data Interpretation Report

This assignment presents a statistical analysis of mental wellbeing using a two-way ANOVA. The analysis investigates the impact of self-efficacy and gender on mental wellbeing. The study begins by outlining the assumptions of the two-way ANOVA, including normality, independence, and homogeneity of variance. Tests such as the Kolmogorov-Smirnov and Shapiro-Wilk are used to assess normality. Levene's test is employed to evaluate the homogeneity of variances. The results, presented in tables, reveal that while some assumptions are met, others are not. The ANOVA results indicate a significant main effect for self-efficacy, suggesting that individuals with high self-efficacy have different levels of mental wellbeing compared to those with low self-efficacy. However, the interaction effect between self-efficacy and gender is not statistically significant. The report concludes that there is no evidence to suggest that male and female participants differ in their mental wellbeing levels, but there is strong evidence of a relationship between self-efficacy and mental wellbeing.

Running head: MENTAL WELLBEING
Mental Wellbeing
Name
Course Number
Date
Faculty Name

Running head: MENTAL WELLBEING
Mental Wellbeing
Two-Way ANOVA
Assumptions
 Two-Way ANOVA assumes that the samples were obtained from an approximately normally
distributed population.
 Independence of the samples
 Same sample size for the groups
 Homogeneity
Table 1: Normal Distribution and outliers
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
gender
Statistic Degrees of
freedom
Sig. Statistic Degrees of
freedom
Sig.
Mental
Wellbeing
male .124 29 .200* .926 29 .044
female .079 85 .200* .976 85 .113
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
According to the Kolmogorov-Smirnov test, the results show that the sample of mental wellbeing
was obtained from approximately normally distributed populations for both male and female participants
because the p-value is greater than significance level. However, regardless of the results obtained from
the Kolmogorov-Smirnov, we will rely on Shapiro-Wilk because it is referred as the most power
normality test. The test is significant for the made group and insignificant for the female. This shows
that males were not obtained from a normally distributed population, while the female participants were.
Since the data on female participants was found to be normally distributed, we can state in case the
outliers, they did do not affect the distribution significantly. On the other side, the presence of outliers
might have significantly affected the distribution of the male sample.

MENTAL WELLBEING 3
Table 2: Test of Homogeneity
Levene's Test of Equality of Error Variancesa
Dependent Variable: Mental Wellbeing
F df1 df2 Sig.
1.638 36 77 .036
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
The results in table 2 indicate that the samples do not have equal variances (p-value = 0.036).
Table 3: Between-Subjects Factors
Value Label N Percent
Gender 1 male 29 25.44%
2 female 85 74.56%
Self-Efficacy Category 1 High 52 45.61%
2 low 62 54.39%
Two-way ANOVA
Table 4: Two-way ANOVA analysis output
Tests of Between-Subjects Effects
Dependent Variable: Mental Wellbeing
Source Type III Sum of
Squares
Degrees
of
freedom
Mean Square F Sig.
Corrected Model 4348.021a 36 120.778 2.208 .002
Intercept 139190.854 1 139190.854 2544.803 .000
Self-efficacy 2907.644 20 145.382 2.658 .001
gender .243 1 .243 .004 .947
Self-efficacy * gender 1213.269 15 80.885 1.479 .134
Error 4211.602 77 54.696
Total 308039.000 114
Corrected Total 8559.623 113
a. R Squared = .508 (Adjusted R Squared = .278)

MENTAL WELLBEING 4
The interaction effect is the focus on a two-way fixed effects model. In this case, the interaction
between self-efficacy and gender not statistically significant (p-value = 0.134), at 95% confidence level.
Therefore, if the interaction effect is not significant, it is dropped and the main effects interpreted.
According to table 4, only one main effect (self-efficacy) is statistically significant with 95%
confidence. Also, the intercept coefficient is significant (p-value < 0.001) at 5% significance level.
Generally, the corrected model is very significant with a p-value of 0.002. We can conclude that there
was not enough evidence to conclude that male and female participants in the study are different in their
levels of mental wellbeing. On the other side, we can state that there is enough evidence to conclude that
individuals with high efficacy levels have different mental wellbeing capacity compared to those with
low efficacy levels.