diffpwr.two {diffcor}

Monte Carlo Simulation for the correlation difference between two correlations that were observed in two independent samples

Description

Computation of a Monte Carlo simulation to estimate the statistical power the correlation difference between the correlation coefficients detected in two indepdenent samples (e.g., original study and replication study).

Usage

diffpwr.two(n1, n2, r1, r2, alpha = .05, n.samples = 1000, seed = 1234)

Arguments

n1

Sample size to be tested in the Monte Carlo simulation for the first sample.

n2

Sample size to be tested in the Monte Carlo simulation for the second sample.

r1

Correlarion observed in the first sample.

r2

Correlarion observed in the second sample.

alpha

Type I error. Default is .05.

n.samples

Number of samples generated in the Monte Carlo simulation. The recommended minimum is 1000 iterations, which is also the default.

seed

To make the results reproducible, a random seed is specified.

Details

Depending on the number of generated samples ('n.samples'), correlation coefficients of the sizes 'r1' and 'r2' are simulated. For each simulated pair of coefficients, it is then checked whether the confidence intervals (with given alpha level) of the correlations overlap. All correlations are automatically transformed with the Fisher z-transformation prior to computations. The ratio of simulated non-overlapping confidence intervals equals the statistical power, given the actual sample sizes ('n1' and 'n2'; see Robert & Casella, 2010 <doi:10.1007/978-1-4419-1576-4>, for an overview of the Monte Carlo method).

Value

r1

Correlation observed in sample 1.

n1

The sample size of the first sample.

cov1

Coverage. Ratio of simulated confidence intervals including r1.

bias1

Average relative difference between r1 and simulated correlations.

r2

Correlation observed in sample 2.

n2

The sample size of the second sample.

cov2

Coverage. Ratio of simulated confidence intervals including r2.

bias2

Average relative difference between r2 and simulated correlations.

pwr

Statistical power as the ratio of simulated non-verlapping confidence intervals.

Biases should be as close to zero as possible and coverage should be ideally between .91 and .98 (Muthén & Muthén, 2002 <doi:10.1207/S15328007SEM0904_8>).

Author(s)

Christian Blötner [e-mail]

References

Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling: A Multidisciplinary Journal, 9(4), 599–620. https://doi.org/10.1207/S15328007SEM0904_8

Robert, C., & Casella, G. (2010). Introducing Monte Carlo methods with R. Springer. https://doi.org/10.1007/978-1-4419-1576-4

Examples

diffpwr.two(n.samples = 1000, n1 = 1000, n2 = 594, r1 = .45, r2 = .39,
            alpha = .05, seed = 1234)