Exploring the relationship between Emotional Intelligence (EI) and academic performance

• Emotional Intelligence (EI) refers to the ability to perceive, understand, and manage emotions, both in oneself and others.
• In educational psychology, EI has been linked to:
  • Better stress management
    
  • Higher motivation and resilience
    
  • Improved social relationships
    
  • Stronger academic performance
• Understanding the statistical relationship between EI and academic performance (e.g., GPA) can help identify emotional factors contributing to student success.

Research Question

Does higher emotional intelligence predict better academic performance among students?

Our goal here is not to answer the research question but rather, to perform a meta-analysis of various studies conducted on this particular topic.

We use the maccann2020 dataset from the psymetadata package. Some of the relevant variables for this metastudy are:

yi (Effect Size)

vi (Variance of yi)

n (Sample Size)

pub_year (Publication Year)

country (Country of Study)

perc_female (Percentage of Female Participants)

age (Mean Age)

subject (Subject)

data("maccann2020")
str(maccann2020)
vars <- c("yi", "vi", "n", "pub_year", "perc_female", "age", "subject", "humanities")
heatmap_vars <- c("yi", "vi", "n", "pub_year", "perc_female", "age")
df <- na.omit(maccann2020[, heatmap_vars])

The correlation heatmap is not very encouraging. It seems that most of the variables do not necessarily effect one another in this meta-study.

We expect studies with larger sample sizes (n) to have smaller effect variances (vi), indicating more precise estimates. This is a very basic expected result in statistics and will serve as a sort of sanity check for the purposes of our data exploration.

In classical statistics, the variance of an estimator decreases as the sample size increases.
This relationship explains the negative correlation observed between vi (effect variance) and n (sample size).

Sampling Variance and Precision

For an estimator \(\hat{\theta}\) (such as the sample mean or an effect size),
the variance is inversely proportional to the sample size:

\[ \mathrm{Var}(\hat{\theta}) = \frac{\sigma^2}{n} \]

where: - \(\sigma^2\) = population variance
- \(n\) = number of observations (sample size)

Thus, as \(n \to \infty\), \(\mathrm{Var}(\hat{\theta}) \to 0\).

Implication for Our Data

In the context of the Maccann (2020) meta-analysis:

\[ v_i \propto \frac{1}{n_i} \]

Each study’s reported effect variance (\(v_i\)) becomes smaller for larger sample sizes,
which aligns with theoretical expectations and increases the precision of the estimated effect size (\(y_i\)).

We now explore how effect sizes (yi) and their variances (vi) differ across study categories (subject, humanities).

maccann2020$country <- as.factor(maccann2020$country)
# Plot object
plot3d <- plot_ly(
  data = maccann2020, x = ~n, y = ~country,
  z = ~yi, color = ~country, 
   colors = c("steelblue", "tomato", "darkorange", "forestgreen", "purple"), 
  type = "scatter3d", mode = "markers",
  marker = list(size = 4, opacity = 0.8)
) %>% layout(
    scene = list(
      xaxis = list(title = "Number of Observations"),
      yaxis = list(title = "Country"),
      zaxis = list(title = "Effect Size (yi)")
    ),
    title = "3D Scatter Plot: Effect Size across Countries and Observation Count"
  )

From the graph it is clear that the results of the study don’t necessarily change based on country, but as number of observations increase, the effect size narrows towards 0. This indicates that the higher confidence studies must have found results that were increasingly inconclusive. This raises a question on the veracity of the other studies that seem to have found higher effect sizes.