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How do I quantify the comparability of two treatment groups?
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Generally, if two groups, the treated and untreated, are considered to be comparable if they have the same distribution of covariates. Comparability of these two groups can be done at the model or site levels.

Due to the random assignment into these groups, the resulting control and treatment groups should be composed of eligible individuals that on average are very similar at the time of application on any observed or unobserved characteristic.

This lack of pre-existing differences between treatments and controls implies that the control group yields reliable estimates of what would have happened to clients in the absence of channeling, and when these estimates are compared to outcomes for clients, reliable estimates of channeling impacts are obtained.

Only two factors can lead to differences in the true mean values of the pre-application characteristics of the treatment and control groups: deviation from the randomization procedures and normal sampling variability. Deviations from the carefully developed randomization procedures could be either deliberate (e.g., site staff purposely misrecording as treatments some applicants who are randomly assigned to the control group, but who have especially pressing needs for assistance) or accidental (e.g., misrecording of a sample member's status).

The dedication and professionalism of this site staff and the safeguards built into the assignment procedure make either occurrence very unlikely. Site staff were extremely cooperative in faithfully executing the procedures. Sampling variability, on the other hand, is the difference between the two groups that occurs simply by chance. For the sample sizes available at the model level, such differences between the two groups should be very small, and statistically insignificant.

source: https://aspe.hhs.gov/basic-report/comparability-treatment-and-control-groups-randomization
by Diamond (62,118 points)

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