Case studies  /  Education

Multilevel Modelling of Student Performance Across Twenty Departments

Accounting for students clustered within courses and departments, where ignoring the hierarchy would have manufactured significance.

EducationSector
Multilevel (hierarchical) linear modellingMethod
R (lme4)Software
~8,500 students across 20 departmentsScale
About five weeksDuration

The challenge

What the organisation came with

An educational organisation wanted to understand which factors had the greatest impact on student performance, across roughly 8,500 students in 20 departments.

The structure of the data made this harder than it looks. Students are grouped within courses, and courses within departments. Students in the same department share teaching, assessment practice, intake and culture, so their outcomes are more similar to each other than to students elsewhere. The observations are not independent.

Ignoring that hierarchy has a specific and well-understood consequence: standard errors are underestimated and statistical significance is overstated. An analysis that treats 8,500 clustered students as 8,500 independent observations will find effects that are not there.

The approach

How it was analysed, and why that method

Why multilevel rather than ordinary least squares

Multilevel — hierarchical — linear modelling was used, with random effects for the grouping structure. This partitions the variance into the part attributable to differences between students and the part attributable to differences between departments, and adjusts the standard errors accordingly.

Ordinary least squares regression was rejected because it assumes independent observations and cannot account for clustering. With 20 departments and a strongly grouped outcome, the difference between the two approaches is not cosmetic — it changes which findings survive.

What the hierarchy revealed

Separating student-level from department-level variance answers a question a single-level model cannot: how much of the difference in performance is about individual students, and how much is about where they study.

Interpreting the model for a non-technical audience

Fixed effects were reported for the student-level factors the organisation could act on, alongside the variance components showing how much departmental variation remained once those factors were accounted for. Visualisations were produced so that departmental differences could be seen rather than inferred from a coefficient table.

Delivered

What the client received

Statistical report with fixed effects and variance components
Predictive models of student performance
Visualisations of variation between departments
Reproducible R code

The value

What changed as a result

The organisation used the findings to improve academic support initiatives and to evaluate teaching interventions.

Because the model separated what varies between students from what varies between departments, support could be directed at the level where the variation actually sat.

About this case study

Written from the assigned statistician's own project notes. The client is not named and no identifying detail, data or figures are published. Scale and timeframe are approximate.

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