Randomly assign study participants across strata to represent prognostic characteristics
When it comes to choosing variables by which to stratify the randomization of study participants, think about what characteristics, if found to be significantly different between the treatment groups, would detract from the validity of your study results. Experimental research designs require that treatment groups possess equipoise (similar characteristics) so that true causal effects can be detected.
Or, think like a reviewer of a scientific manuscript. If the reviewer looks at the baseline and prognostic variables in a "Table 1" and see a significant difference, would they call the study results of the experimental research design into question based on this difference?
Stratified randomization is a strong deterrent of confounding in applied research. If the groups are comparable across important baseline and prognostic variables, then the chance of treatment effects being confounded by measured and unmeasured factors is greatly diminished.
Another positive attribute of stratified randomization is that the groups tend to be less varied within themselves (homogeneous), which increases statistical power.
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