Psychology dissertation regression discontinuity design can estimate a local treatment effect when access to an intervention changes at a known threshold. The design compares people just above and below that cutoff, where treatment assignment changes sharply but other characteristics should vary smoothly. Its strength comes from the assignment rule, not from fitting a flexible curve to observational data.
This guide covers sharp and fuzzy designs, the running variable, continuity assumptions, bandwidth selection, local polynomial estimation, manipulation checks, covariate balance, sensitivity analysis, reporting, and ethical interpretation. It develops the short introduction in the site’s quasi-experimental design guide without duplicating its broader comparison of methods.
What regression discontinuity estimates
A regression discontinuity, or RD, design begins with a continuous or ordered assignment variable and a cutoff. An intervention is offered on one side of that threshold. For example, students scoring 14 or higher on a distress screening scale may be offered an enhanced counselling pathway, while students scoring below 14 receive usual support.
If potential outcomes would otherwise change smoothly through score 14, a sudden outcome difference at that cutoff can identify an intervention effect. The comparison is local. Students scoring 13.9 and 14.1 may be similar, but students scoring 4 and 24 may not be. The estimate therefore concerns people at or very near the threshold rather than every student in the population.
The US Institute of Education Sciences’ regression discontinuity standards describe the design as assignment by a continuous scoring rule and identify the effect as the difference between fitted outcome relationships at the cutoff. The standards emphasise assignment-variable integrity, attrition, continuity, functional form, bandwidth, and complete reporting.
| Design feature | Meaning | Psychology example |
|---|---|---|
| Running variable | Score that determines eligibility | Distress screening score |
| Cutoff | Threshold where assignment changes | Score of 14 |
| Treatment | Intervention offered or received | Enhanced counselling pathway |
| Outcome | Post-assignment response | Anxiety score after three months |
| Local estimand | Effect for units at the cutoff | Effect for students close to 14 |
Decide whether psychology dissertation regression discontinuity design fits
RD is appropriate only when a real assignment rule changes treatment probability at a known threshold. A researcher cannot create a credible design by choosing a convenient split in an existing predictor after looking at outcomes. The cutoff must determine eligibility, encouragement, dosage, or another well-defined intervention contrast.
Useful psychology settings include support allocated above a symptom threshold, educational services triggered by test scores, programme grants awarded from ranked applications, or legal age rules affecting access to services. The forcing variable should be measured before treatment and recorded with enough precision to distinguish observations around the cutoff.
If an intervention begins for everyone at one time, use an interrupted time series. If treated and untreated groups are compared across common pre/post periods, consider difference-in-differences. RD is about discontinuous assignment at a score threshold, not merely a visible break over time.
Define treatment and the cutoff before analysing outcomes
Document the formal rule and how staff applied it in practice. State whether the threshold controls treatment offer, treatment receipt, or intensity. Archive policy documents, scoring instructions, eligibility exceptions, and the dates during which the rule operated. If the rule changed, separate cohorts or justify a multi-cutoff analysis.
Do not treat an arbitrary median split as RD. Dichotomising a continuous scale at its sample median creates groups but no externally imposed assignment discontinuity. Similarly, a diagnostic threshold is not sufficient if clinicians ignore it and treatment probability does not change at that point.
Choose an outcome and follow-up window
Specify one primary outcome, its scale, measurement procedure, and follow-up time. Measurement must be comparable on both sides of the threshold. An outcome collected more intensively for eligible participants can produce a discontinuity in observation rather than wellbeing.
Define whether the estimand concerns eligibility, offer, or receipt. Eligibility effects may remain policy-relevant even when some people refuse treatment. Effects of receipt in a fuzzy design require additional assumptions and usually have a complier interpretation. Do not switch between these meanings in the results chapter.
Understand sharp and fuzzy RD designs
Sharp regression discontinuity
In a sharp design, treatment status changes deterministically at the cutoff: everyone on one side is assigned treatment and everyone on the other side is not. Perfect compliance is uncommon in applied psychology, but eligibility or offer may still follow a sharp rule even if participation does not.
The sharp RD estimate is the jump in the expected outcome at the threshold. It can be interpreted causally for units at the cutoff when the running variable and potential outcomes satisfy the design assumptions and no other intervention changes at the same value.
Fuzzy regression discontinuity
In a fuzzy design, crossing the threshold changes the probability of treatment without determining it perfectly. Some eligible students may decline counselling, and some below the threshold may receive it through clinical judgement. Plot and estimate the treatment-probability jump before interpreting the outcome jump.
The fuzzy RD ratio divides the outcome discontinuity by the treatment-receipt discontinuity. Under exclusion, monotonicity, continuity, and a sufficiently strong first-stage jump, it estimates a local effect for people whose treatment status is changed by crossing the threshold. This is not necessarily the effect for always-treated, never-treated, or distant participants.
| Feature | Sharp RD | Fuzzy RD |
|---|---|---|
| Assignment at cutoff | Treatment changes from 0 to 1 | Treatment probability changes |
| Main contrast | Outcome jump | Outcome jump divided by treatment jump |
| Interpretation | Local assignment effect | Local effect for threshold compliers |
| Primary diagnostic | Verify deterministic rule | Estimate a strong first-stage discontinuity |
| Common risk | Undocumented exceptions | Weak or ambiguous treatment jump |
State the identifying assumptions
Continuity of potential outcomes
The key assumption is that, without treatment, expected outcomes would change smoothly through the cutoff. Other determinants of the outcome should not jump at the same threshold. If score 14 also triggers financial support, a diagnostic label, and extra monitoring, the observed discontinuity reflects that bundle unless the estimand is defined as the entire policy package.
Continuity is supported by knowledge of the assignment process, balance in predetermined covariates, absence of other rules at the cutoff, and credible measurement. It is not proven by including many polynomial terms. Draw a causal diagram and list every service or classification tied to the score.
No precise manipulation of the running variable
People should not be able to sort precisely across the cutoff based on expected treatment gains. A student who can retake a screening measure until eligible, or a clinician who rounds borderline scores upward, can create selected groups on either side. Audit how scores were produced, who saw them, and whether exceptions were possible.
Plot the running-variable distribution and inspect heaping, gaps, and a density change at the cutoff. A formal density test is useful but should not replace institutional evidence. Discrete scales may produce mass points and require methods that acknowledge limited support. A non-significant test does not establish that manipulation is absent.
Local comparability and stable measurement
Predetermined covariates should evolve smoothly at the threshold. Estimate discontinuities in age, prior symptoms, socioeconomic indicators, or baseline outcomes using the same transparent approach as the main analysis. A single small p-value among many checks can occur by chance, so present effect sizes, intervals, plots, and multiplicity context.
The outcome must be recorded consistently. If eligible students complete clinician-rated measures while ineligible students receive an online questionnaire, assessment mode changes at the cutoff. That violates the interpretation even when the underlying construct is the same. The site’s reliability and validity guide helps document measurement quality.
Prepare and visualise the data
Create one auditable variable for the original running score, one centred score equal to the original value minus the cutoff, treatment assignment, treatment receipt, outcomes, baseline covariates, clusters, and exclusions. Never replace the original score with a recoded version without retaining provenance.
Report the number of observations at each distinct score, especially near the cutoff. Verify whether units share the same score, whether clusters were assigned, and whether outcomes are missing differentially. Use the site’s missing-data guide to plan attrition and sensitivity analyses rather than deleting incomplete cases silently.
Construct an honest RD plot
An RD plot should show binned outcome means and separate smooth fits on each side of the cutoff. Mark the threshold clearly and show the data range used. Do not connect observations across the cutoff or select bins to exaggerate a jump. Plot treatment receipt and predetermined covariates separately.
A graph is a diagnostic, not the final estimator. The maintained rdrobust project provides rdplot for data-driven plots, rdbwselect for bandwidth selection, and rdrobust for point estimation and robust bias-corrected inference in R, Stata, and Python.
Choose the bandwidth and estimator
The bandwidth defines how close observations must be to the cutoff to contribute to the local estimate. A narrower window reduces reliance on modelling distant scores but includes fewer observations and increases uncertainty. A wider window increases precision while risking bias if the score-outcome relationship is misspecified.
Use a principled data-driven selector for the main analysis and report it in the original score units. The current CRAN rdrobust manual documents mean-squared-error bandwidth selectors, separate bandwidths, kernels, clustering, mass-point adjustments, and robust bias-corrected intervals. Do not try many windows and publish only the one with the smallest p-value.
Prefer local polynomial estimation
A common main specification uses separate local linear regressions on either side with greater weight near the cutoff. Higher-order global polynomials can behave erratically near boundaries and make distant observations overly influential. If curvature requires more flexibility, use a method justified for local estimation and compare sensitivity transparently.
Report the polynomial order, kernel, bandwidth selector, estimation bandwidth, bias-correction bandwidth, variance estimator, and confidence level. If data are clustered by school or clinician, use cluster-appropriate inference. If the running variable is discrete or has few unique values, seek specialist guidance because conventional continuous-score asymptotics may be unreliable.
Plan sample size around the cutoff
The relevant information is the number and distribution of observations within plausible bandwidths, not the total dataset. A study with 5,000 participants can be weak if only 40 lie near the cutoff. Anticipate score density, outcome variance, treatment-probability jump, clustering, expected local effect, and attrition.
Simulation can evaluate bias, precision, coverage, and weak first-stage risk under realistic score distributions. Explain assumptions and report the expected local sample. The site’s power-analysis guide shows how to avoid generic participant-per-variable rules.
Run validity and sensitivity checks
| Check | Purpose | Warning sign |
|---|---|---|
| Treatment first stage | Confirm assignment changes exposure | Small or uncertain probability jump |
| Score density | Assess sorting near cutoff | Bunching, gaps, or unexplained heaping |
| Covariate continuity | Assess local comparability | Systematic baseline discontinuities |
| Placebo cutoffs | Detect unrelated breaks | Similar jumps away from true threshold |
| Bandwidth sensitivity | Assess modelling dependence | Effect changes sign across credible windows |
| Donut RD | Examine suspicious observations at cutoff | Conclusion depends on a few manipulated scores |
Falsification checks should be chosen before inspecting the main estimate. Test plausible placebo cutoffs where treatment does not change, predetermined outcomes that treatment cannot affect, and alternative valid bandwidths. A placebo estimate need not be exactly zero; assess its magnitude and precision.
A donut RD excludes observations immediately around the threshold when manipulation or measurement heaping is suspected. It changes the target and removes the observations that normally make RD compelling, so treat it as a sensitivity analysis, not an automatic repair. Explain the excluded interval and why it is substantively plausible.
Assess whether conclusions depend on influential clusters, one score value, outcome transformation, polynomial order, or covariate adjustment. Covariates can improve precision but should not be selected because they make the effect significant. The design should identify the effect before adjustment; discontinuous covariates may instead reveal a validity problem.
Interpret a local effect correctly
An RD estimate is evaluated at the cutoff. If enhanced counselling reduces anxiety by 2.4 points locally, the result applies to students whose screening scores are near 14 under the studied assignment system. It does not establish the same effect for students with much lower or higher distress.
Report the estimate in outcome units with a confidence interval and the selected bandwidth. For fuzzy RD, report both the treatment-probability discontinuity and the ratio estimate. Avoid describing a local complier effect as the average programme effect for all eligible students.
Causal language remains conditional on continuity, score integrity, exclusion restrictions for fuzzy designs, stable measurement, and appropriate inference. Discuss how clinical discretion, concurrent services, attrition, and scale reliability could alter the conclusion. Link limitations to evidence rather than listing generic caveats.
Worked psychology dissertation example
A university offers an eight-session anxiety programme to first-year students whose baseline screening score is at least 20. The outcome is a validated anxiety measure at 12 weeks. Administrative records contain the original score, programme offer, attendance, outcome, baseline demographics, residence hall, and assessor information.
Eligibility changes sharply at 20, but some eligible students decline and a few ineligible students enter through urgent referral. The researcher therefore treats assignment as fuzzy. Policy documents confirm that no other benefit starts at 20. Scores are generated automatically from item responses before staff view eligibility.
The main plot shows an outcome drop at the cutoff and smooth trends within each side. A treatment-receipt plot shows a 62-percentage-point jump. Density and baseline-covariate diagnostics reveal no substantive discontinuities, although scores are heaped at integer values. The analysis uses mass-point-aware local linear estimation, a triangular kernel, a data-driven bandwidth, and robust bias-corrected confidence intervals.
The estimated local effect among threshold compliers is a 3.1-point reduction in anxiety, with a 95% confidence interval from a 5.4-point to a 0.8-point reduction. Plausible bandwidths produce estimates in the same direction, while placebo cutoffs show no comparable jumps. The dissertation limits inference to students near the eligibility threshold and explains that programme attendance, not universal effects, drives the fuzzy estimand.
Write the method and results chapters
The method should describe the intervention, comparison condition, setting, recruitment, assignment score, cutoff, rule enforcement, sharp or fuzzy status, outcome, follow-up, exclusions, attrition, bandwidth selection, estimator, clustering, and all validity checks. The What Works Clearinghouse reporting guide requests this context as well as the forcing-variable density, outcome-score graph, psychometric information, and fuzzy first-stage details.
The results should begin with sample flow and counts by score. Show the RD plot, treatment first stage where relevant, density graph, baseline balance, main estimate, selected bandwidth, local sample, and robust interval. Follow with preregistered alternative bandwidths, placebo cutoffs, donut analysis if justified, and other sensitivity checks.
Archive analysis code, package versions, score-construction rules, and a decision log where ethics permit. Protect participants near clinically meaningful thresholds because small-cell tables can increase disclosure risk. If analysis choices changed after seeing outcomes, label them exploratory.
Common regression discontinuity mistakes
- Creating a cutoff from the sample median without a real assignment rule.
- Ignoring whether treatment probability actually changes at the threshold.
- Claiming a population-wide effect from a local estimate.
- Fitting one high-order global polynomial across the entire score range.
- Selecting bandwidths or polynomial orders by statistical significance.
- Treating a density test as proof that scores were not manipulated.
- Ignoring heaping, few unique scores, clusters, or differential attrition.
- Using covariate adjustment to conceal baseline discontinuities.
- Failing to report the fuzzy first-stage jump and complier interpretation.
- Assuming an outcome jump is caused by treatment when another rule shares the cutoff.
Frequently asked questions
What is the running variable in psychology dissertation regression discontinuity design?
It is the pre-treatment score used to assign or encourage treatment. Examples include a symptom scale, assessment score, age, or ranked application score. Its cutoff and measurement process must be documented.
How is sharp RD different from fuzzy RD?
Sharp RD has deterministic treatment assignment at the cutoff. Fuzzy RD has a discontinuous change in treatment probability and estimates a local effect for people whose treatment changes because they cross the threshold.
How do I select the bandwidth?
Use a principled data-driven selector aligned with the estimator, report the chosen window in score units, and test credible narrower and wider alternatives. Never choose the main bandwidth because it produces significance.
Does regression discontinuity require a large sample?
It requires adequate information close to the cutoff. Total sample size can be misleading. Plan around local score density, outcome variation, clustering, treatment compliance, expected effect, and attrition.
Can I use SPSS for regression discontinuity?
Basic models and plots are possible, but robust local-polynomial bandwidth selection, bias-corrected inference, density testing, mass-point handling, and fuzzy RD are more directly supported by specialist R, Stata, or Python packages.
What if participants can manipulate their score?
Investigate the scoring process, density, heaping, and institutional evidence. Precise sorting can invalidate local comparability. Alternative designs or carefully justified sensitivity analyses may be required rather than a cosmetic statistical fix.
Can regression discontinuity prove causality?
It can support a local causal estimate when the assignment rule, continuity, score integrity, measurement, treatment contrast, and inference are defensible. Those conditions must be justified, and the effect should not be extrapolated beyond the cutoff without additional assumptions.
Conclusion
A credible psychology dissertation regression discontinuity design begins with a genuine threshold rule and a clearly defined local estimand. Verify assignment, understand sharp or fuzzy compliance, protect the running variable’s integrity, visualise the data honestly, use local estimation and principled bandwidths, and report density, balance, placebo, and sensitivity checks.
If you need methodological support, seek ethical guidance that helps you understand and defend your own design. A suitable adviser can review the assignment mechanism, code, diagnostics, and reporting while you remain responsible for the data, analytic decisions, and dissertation authorship.
