STATISTICAL METHOD
Regression Discontinuity Analysis
Statistical Consulting for Cutoff-Based Designs
We apply regression discontinuity analysis within your study design, testing for manipulation of the score, choosing the bandwidth and local model with sensitivity checks, and reporting the effect at the cutoff with its 95% confidence interval.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Regression Discontinuity?
A regression discontinuity design estimates the effect of a treatment given, wholly or partly, according to whether a continuous score crosses a cutoff. Units just below and just above the cutoff are comparable if their potential outcomes change smoothly there and they cannot precisely control their own score, so the jump in the outcome at the cutoff estimates the effect. In a sharp design everyone above the cutoff is treated, and in a fuzzy design the cutoff only changes the probability of treatment. The estimate is local to the cutoff. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides regression discontinuity analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is a Regression Discontinuity Design Appropriate?
The design fits a program or treatment offered according to a score threshold, and these are the research situations in which researchers most often ask us to apply or confirm it.
Eligibility Set by a Score A program, drug or service is offered to people above or below a threshold on a test, risk score or age, and its effect on later outcomes is the question.
Cutoff Rule With Partial Uptake Crossing the threshold makes treatment much more likely but not certain, which calls for a fuzzy design and an estimate for those moved by the rule.
Worry About Score Manipulation Staff or applicants may be able to nudge scores past the threshold, and the researcher needs to show whether the units near it remain comparable.
Reviewing a Completed RD Analysis An effect at a cutoff has been reported and a reviewer has questioned the bandwidth or the model. Independent Statistical Review re-examines the specification.
ANALYTICAL APPROACH
How We Apply Regression Discontinuity
Within the family of Clinical, Survival & Epidemiological, a cutoff design is judged on whether the units either side of it are credibly comparable.
Treatment Rule and Continuity We confirm how the rule worked, sharp or fuzzy, and that nothing else changes at the cutoff. Continuity of potential outcomes is argued from the setting, as no test can confirm it.
Manipulation and Balance We run a density test of the score at the cutoff and check that baseline covariates do not jump there. Precise control of the score by units, or by staff, would undermine the design.
Bandwidth and Local Model We fit local linear models within a data-driven bandwidth, avoid high-order global polynomials that let distant data drive the jump, and show how the estimate moves with the bandwidth.
Local Effect and Robustness We report the effect at the cutoff with robust bias-corrected intervals, run placebo cutoffs and a donut-hole check, and state that the result does not extend far from the threshold.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the cutoff analysis is delivered with the diagnostics, estimates and files needed to report and defend it.
Data & Variable Review The running variable, its measurement and any heaping or rounding, the treatment rule, the outcome timing and missing data are reviewed before any model is fit.
Method-Specific Checks A density test of the score, covariate balance at the cutoff, placebo cutoffs and sensitivity to bandwidth, kernel and polynomial order are examined and recorded.
Statistical Results The estimated discontinuity with its 95% confidence interval, the bandwidth and effective sample either side, and for a fuzzy design the first-stage jump in treatment.
Publication-Ready Tables & Figures An RD plot with binned means and fitted lines, a bandwidth sensitivity figure and results tables, formatted to the journal's requirements, ready to insert.
Interpretation The result is written as a local effect at the cutoff, with the comparability argument and its limits explained, and no claim about units far from the threshold.
Reproducible Analysis Files R scripts, Stata do-files or Python code for the estimation and checks are provided where applicable, so each figure and estimate can be rerun if the data change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
A cutoff design needs a clear threshold and enough observations near it. These methods fit when treatment follows no rule, when an instrument drives it or when the running variable is time.
01
Instrumental Variable Analysis
When something other than a threshold shifts who is treated, and it affects the outcome only through treatment, an instrument can identify an effect for compliers.
02
Propensity Score Matching (PSM)
When treatment was chosen, not set by a rule, and the main confounders were measured, matching compares similar patients but cannot address unmeasured differences.
03
Difference-in-Differences (DiD)
When a policy reaches one group and not another, and both are observed before and after, comparing their changes does not need a score or a threshold.
04
Interrupted Time Series
When the cutoff is a date, such as a policy start, and one population is followed over many periods, a segmented model of the series is the closer fit.
CASE EXAMPLE
How We Work in Practice
An illustration of how a cutoff analysis moves from a prespecified specification to a local estimate and its robustness checks.
ILLUSTRATIVE EXAMPLE · SCHOOL-BASED HEALTH PROGRAM · UNITED STATES
A school-based health program offered counseling to students above a screening score and wanted to know whether the offer affected later school attendance.
Only students at or above a fixed screening score were offered counseling, which made a cutoff design natural. Before attendance data were opened, we specified a local linear model, a data-driven bandwidth and the density test. A concern arose that staff rescoring borderline students might have moved some across the threshold. We examined the score distribution near the cutoff, checked baseline covariates for jumps and planned a donut specification that drops scores nearest the line. The plan said that the estimate would describe students near the threshold only, not all enrolled students.
Outcome: The program received the estimated change in attendance at the cutoff with its 95% confidence interval, the density and balance checks, the donut specification and the analysis scripts.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Cutoff Designs
R, Stata and Python have dedicated packages for local polynomial estimates and density tests, and SAS can fit the local regressions, with scripts provided.
RESEARCH DISCIPLINES
Cutoff Designs Across Research Fields
Regression discontinuity designs appear across research fields, each with its own eligibility rules, outcomes and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from an epidemiologist who wanted the setup checked against the study design and the decisions explained plainly.
“I had already started the Regression Discontinuity (RD), but I was not confident about how to evaluate discrimination and choose a threshold without overstating accuracy. The team checked the setup against our study design, explained the decisions in plain language, and returned results we could actually use. The final output was concise, clearly interpreted, and ready to use in our research reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your cutoff analysis, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your discontinuity design, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The research question, the policy or clinical meaning of the cutoff and your conclusions remain with you, and our interpretation stays within what the estimates and the design support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Regression Discontinuity
Short answers to what researchers ask before analyzing a cutoff, from manipulation and bandwidth to confidentiality and the assessment process.
How do you check whether the score was manipulated?
The design needs units that cannot precisely control their score near the cutoff. We test for a jump in the density of the score at the cutoff and for jumps in baseline covariates, and we ask how the score was produced. A passed test supports the design but does not prove it, so the institutional account is part of the evidence.
How is the bandwidth chosen, and does it change the result?
We use a data-driven bandwidth, usually with a local linear fit, and then show the estimate across narrower and wider bandwidths and other kernels. If conclusions change materially with reasonable choices, we say so. High-order global polynomials are avoided, because they weight observations far from the cutoff and can produce spurious jumps.
Why not compare matched groups instead of using the cutoff?
In a sharp design, treated and untreated units never share the same score values, so the overlap that matching needs is absent by design. Regression discontinuity uses the rule instead, comparing units just either side of the cutoff and relying on continuity there, not on measuring every confounder. The price is a local treatment effect that describes units near the threshold, not the whole population.
Can you review an analysis that has already been completed?
Yes, we can review a completed discontinuity analysis before submission or a response to reviewers. We check the treatment rule, the manipulation and balance checks, the bandwidth and polynomial choices, the confidence interval method and how the local estimate was worded, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With a
Regression Discontinuity Design?
Share your research question, the cutoff rule and your data. We assess whether the design fits your study and confirm the approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014