randomizationSuccess: Computations for successful randomization
In userfriendlyscience: Quantitative Analysis Made Accessible

Description Usage Arguments Details Value Author(s) References See Also Examples

prob.randomizationSuccess computes the probability that two groups are equivalent given a specific sample size, number of nuisance variables, and definition of 'equivalence' (in terms of the Cohen's d expressing the maximum acceptable difference between the groups on any of the nuisance variables).

pwr.randomizationSuccess computes the sample size required to make randomization succeed in a specified proportion of the studies with a two-cell design. 'Success' is defined as the two groups differing at most with a specified effect size on any of a given number or nuisance variables.

prob.randomizationSuccess(n = 1000,
                          dNonequivalence = .2,
                          nNuisanceVars = 100)
pwr.randomizationSuccess(dNonequivalence = 0.2,
                         pRandomizationSuccess = 0.95,
                         nNuisanceVars = 100)

`n`	The sample size.
`dNonequivalence`	The maximum difference between the two groups that is deemed acceptable.
`pRandomizationSuccess`	The desired probability that the randomization procedure succeeded in generating two equivalent groups (i.e. differing at most with `dNonequivalence`).
`nNuisanceVars`	The number of nuisance variables that the researchers assumes exists.

For more details, see Peters & Gruijters (2017).

For prob.randomizationSuccess, the probability that the two groups are equivalent. The function is vectorized, so returns either a vector of length one, a vector of length > 1, a matrix, or an array.

For pwr.randomizationSuccess, the required sample size. The function is vectorized, so returns either a vector of length one, a vector of length > 1, a matrix, or an array.

Gjalt-Jorn Peters

Maintainer: Gjalt-Jorn Peters <gjalt-jorn@userfriendlyscience.com>

Peters, G. J.-Y. & Gruijters, S. Why your experiments fail: sample sizes required for randomization to generate equivalent groups as a partial solution to the replication crisis (2017). http://dx.doi.org/

dCohensd

### To be on the safe side: sample size required to
### obtain 95% likelihood of success when assuming
### 100 nuisance variables exist.
pwr.randomizationSuccess(dNonequivalence = 0.2,
                         pRandomizationSuccess = 0.95,
                         nNuisanceVars = 100);

### Living on the edge:
pwr.randomizationSuccess(dNonequivalence = 0.2,
                         pRandomizationSuccess = 0.60,
                         nNuisanceVars = 10);

### For those with quite liberal ideas of 'equivalence':
pwr.randomizationSuccess(dNonequivalence = 0.5,
                         pRandomizationSuccess = 0.95,
                         nNuisanceVars = 100);

### And these results can be checked with
### prob.randomizationSuccess:
prob.randomizationSuccess(1212, .2, 100);
prob.randomizationSuccess(386, .2, 10);
prob.randomizationSuccess(198, .5, 100);

### Or in one go:
prob.randomizationSuccess(n=c(198, 386, 1212), c(.2, .5), c(10, 100));