# 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.The other spreadsheet allocates subjects as they are recruited, giving equal importance to all characteristics.In simulations the spreadsheets on average outperform randomized allocation, especially for mean differences between groups and for allocation after recruitment.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.With randomization the inaccuracy depends on the typical difference in the means of the two groups, which is therefore √2.SD/√n (because the groups are independent and each has the same standard error of the mean, SD/√n).In the more common pre-post parallel-groups design (the kind exemplified by the data in Figures 1 and 2), there has to be a sufficiently large correlation between the characteristic and the change score of the dependent variable for the error to be appreciable.Such correlations are likely to be less frequent than those between the characteristic and the raw score of the dependent, but in general there is no way of knowing at the design stage whether there is such a correlation. The controlled trials with the smallest errors arising from group-mean subject characteristics are crossovers, because there would have to be an interaction between the subject characteristic and any order effect in the efficacy of the treatment.I will discuss shortly whether this difference will have a substantial effect on the outcome.Meanwhile consider the typical difference between the means with allocation by minimization (not shown in the figure).

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