A non-equivalent group design, is a design in which your two groups are not ,Probabilisticly Equivalent . An example of this is, a study that looks at reading comprehension in junior high students.
Here is the model for the design:
----------------------
Nt-> Pr->I->Po
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Nc-> Pr-> Po
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Nt=Nonequivalent treatment group
Nc=nonequivalent 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.
Thestandard NEGD, always has a pretest, as to get an idea of the differences between the non-equivalent groups before the intervention. This is not as big of an issue with a randomized experiment, due to probalistic equivalence (see link above).
Statistical Analysis of NEGD:
The statistical analysis of the NEGD 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 NEQDwith 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 non-equivalent, you must also adjust for error
the pretest measurement by adjusting the scores with a reliability (reliability=how much of your measurement is true,
and how much is due to error) meaurement.
How to adjust the pre-test
New pretest score= Average of all pretest scores-(original pretest score-average of all prtest scores)*(Reliability)
Reliability can be calculated in a number of ways,or it may alrady be known for your measurements.
This is something you wil have to calculate for each study you do.
The reason that this is necessary in the
NEGD is that the pre-test error might be different between groups, as opposed to a design where the groups are considered
more similar.
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