Random Assignment Minimizes

On the other hand, sample sizes with a post-only crossover can be much smaller than those in the pre-post parallel-groups design (down to one quarter as many), so the differences between group means will be typically greater.

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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.

With minimization there is the same gain in precision from accounting for unexplained variance, but because there is little or no difference in group means, the adjustment for the difference involves little or no extrapolation with the linear covariate term.

Precision is therefore overtly a little better following adjustment with minimization than with randomization; more importantly, the adjusted estimate is less sensitive to violation of the assumption of linearity of the effect of the covariate.

When a subject characteristic substantially modifies the effect of a treatment or other intervention in a controlled trial, precision of the estimate of the treatment effect is improved by allocating subjects to control and treatment groups in a manner aimed at minimizing the differences between population and group means of the characteristic.

The usual approach of randomized allocation produces substantial differences from the population mean and between group means on average with One spreadsheet is designed for use when the characteristics of all subjects are known before allocation; it gives primary importance to minimizing differences between the means of one characteristic (usually the baseline values of the dependent variable), while up to five other characteristics are given equal secondary importance.

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.

Decisions about the clinical, practical, mechanistic or statistical significance of an effect are based on the width of the confidence interval or on the underlying probability distribution of the true value of the effect Without minimization, inclusion of a covariate adjusts away the error arising from differences in the means (or in the case of the outcome in Figure 1, the analysis reduces the effect of the difference between the group and population means).

Inclusion of a covariate also improves precision by accounting for the otherwise unexplained variance associated with the covariate.