A regression Discontinuity design is a design in which the two groups, are distingished by a cut-off point. This is considered the most ethical of the stuy designs.
If you assign your groups by a cut-off point, you are able to give your treatment or program to those who really need it. Take, for example , a study on cholesterol. If we give the treatment (say some drug ) to those with HDL>150, and no treatment to those with HDL<150, those who need the treatment actually get it, as opposed to groups that were assigned randomly, or that were pre-existing groups (i.e. non equivalent).
Here is the model for the design:
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Ct-> Pr->I->Po
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Cc-> Pr-> Po
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Ct=Cut-off Assigned treatment group
Cc=Cut-off assigned comparison group
I=intervention
Pr=pre-test (baseline measurement)
Po=Post-test measurement.
***if you have looked at the randomized (infer causal inference) section, randomized , will notice that the design can be done with or without a pre test.
The standard regresion discontinuity design , always has a pretest, as to get an idea of the differences between the cut-off assigned groups before the intervention.
Statistical Analysis of RDD:
The statistical analysis of the Regression discontinuity Design is the standard Pre-Post test design analysis. ANCOVA analysis (see below) is similar in method to that of the randomized pre-post analysis, and the cut-off point analysis. The differences in the analysis are in how you account for the differences in how the treatment and comparison groups were asigned (i.e. randomly ,non-equivalently, or by cut-off point).
Analysis of RDD with a Pre and Post Test.
Designs with both pre and post tests must be analyzed using Analysis of Covariance (ANCOVA). What is ANCOVA? ANCOVA is statistical a method that allows you to covary the pretest measurement with the outcome meaurement. ANCOVA is basically a linear regression model that allows you to adjust for the pretest measure. In other words, we are just removing the effect of the pretest measure so that we can just look at the difference between the post test measurements between the treatment and comparison groups.
For example, The ANCOVA model looks like this:
Outcome= intercept + (constant1)Pretest + (constant2)Z[t or c] + Error term
Where Z is used to indicate you treatment verses your comparison group (Z=1 treatment, Z=0 comparison).
Here is an example of an ANCOVA analysis in MINITAB statistical Package
(I made up this data!)
The regression equation is posttest = 0.107 - 0.053 pretest + 0.069 Z Predictor Coef StDev T P Constant 0.1071 0.1466 0.73 0.230 pretest -0.0530 0.1009 -0.53 0.100 Z 0.0687 0.1995 0.34 0.042 S = 0.9942 R-Sq = 0.57 R-Sq(adj) = 56.2%
We can see from the P-values, that P<.05 for the Z predictor, so we know that Z is significant, and therefore,
there is a difference between the treatment and comparison groups.
The information above describes a basic ANCOVA model. When the groups are assigned by cut-off, there are other
things you must consider.
A good reference about the specifics of this RDD is "The regression Discontinuity design"-W. Trochim
In L. Sechrest, E. Perrin, and J. Bunker (Eds.) 1990.
Research Methodology:Design and Analysis for Non-experimental data.
U.S. Dept of HSS, DHHS Number (PHS) 90-3454 pps. 119-139
If you would like more information on ANCOVA, Applied Linear Statistical Models, by Neter, Kutner, Nachshem, and Wasserman is a great reference. This book also discusses P-values, and significance levels if you need a refresher.
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4/9/97