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You could also state that the effect of the treatment could be confounded by the characteristic, but arguably bias and confounding should be used when a method of subject allocation produces only consistent differences in group means.While it should now be obvious that minimization of differences in group means of characteristics can result in better precision in the estimate of a treatment effect, it is less obvious that the calculated width of the confidence interval is on average the same as that with randomization when the analysis does not account for the differences in means.The other spreadsheet allocates subjects as they are recruited, giving equal importance to all characteristics.
The standardized difference is therefore √(2/n), which is The worst design in this respect is the post-only parallel groups, where the dependent variable is measured once only, after the treatment.
This kind of design is required if the outcome is a new event (e.g., illness, death) or a count of new events (e.g., injuries, wins), although it can also be used for continuous dependent variablessee the article on a It is not unusual to have a substantial correlation between a characteristic and the dependent variable, and this correlation multiplied by the standardized group mean difference becomes the error in the treatment effect (because , where Y is the dependent variable, X is the subject characteristic, and r is the correlation coefficient).
Randomization was long considered the best way to allocate subjects to the treatment and control groups, but it is now apparent that non-random allocation aimed specifically at minimizing differences in group means of subject characteristics is superior .
However, many clinical and non-clinical trials offer the opportunity to enhance minimization by allocation after all subjects have been recruited, and I have been unable to find software for this approach.
I have devised for such assignment gives primary importance to minimizing differences between the means of one characteristic, first by ranking the subjects on this characteristic, then by assigning each subject in a cluster of contiguous subjects to each group.
Educational Dissertations Principals Perceptions - Random Assignment Minimizes
An analysis that takes this extra level of repeated measurement into account produces narrower confidence intervals than the usual analysis: in essence, the confidence interval for the difference in the effect of the treatment between groups should be based on the paired t statistic rather than the unpaired t statistic.
If the effect of the treatment depends on the subject characteristic (e.g., greater reduction in blood cholesterol in heavier overweight subjects), the mean effect of the treatment in the group will differ substantially from the mean effect in the population.
The resulting error in the estimate of the effect of the treatment depends on what happens in the comparison group.
If minimization is perfect, there is no difference between the group means of the subject characteristic, so the typical difference of a group mean from the population mean is given by the standard error of the mean of a sample of size 2n with two groups, 3n with three groups, and so on.
for a randomized controlled trial of the effect of two types of exercise on blood cholesterol.