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,
            rho1,
            rho2,
            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.

rho1

Assumed population correlation to be observed in the first sample.

rho2

Assumed population correlation to be 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 1,000 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 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 alpha-level and sample sizes (see Robert & Casella, 2010 <doi:10.1007/978-1-4419-1576-4>, for an overview of the Monte Carlo method).

It should be noted that the Pearson correlation coefficient is sensitive to linear association, but also to a host of statistical issues such as univariate and bivariate outliers, range restrictions, and heteroscedasticity (e.g., Duncan & Layard, 1973 <doi:10.1093/BIOMET/60.3.551>; Wilcox, 2013 <doi:10.1016/C2010-0-67044-1>). Thus, every power analysis requires that specific statistical prerequisites are fulfilled and can be invalid with regard to the actual data if the prerequisites do not hold, potentially biasing Type I error rates.

Value

As dataframe with the following parameters

rho1

Assumed population correlation to be observed in the first sample.

n1

Sample size of the first sample.

cov1

Coverage. Ratio of simulated confidence intervals including rho1.

bias1_M

Difference between the mean of the distribution of the simulated correlations and rho1, divided by rho1.

bias1_Md

Difference between the median of the distribution of the simulated correlations and rho1, divided by rho1.

rho2

Assumed population correlation to be observed in the second sample.

n2

The sample size of the second sample.

cov2

Coverage. Ratio of simulated confidence intervals including rho2.

bias2_M

Difference between the mean of the distribution of the simulated correlations and rho2, divided by rho2.

bias2_Md

Difference between the median of the distribution of the simulated correlations and rho2, divided by rho2.

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

Duncan, G. T., & Layard, M. W. (1973). A Monte-Carlo study of asymptotically robust tests for correlation coefficients. Biometrika, 60, 551–558. https://doi.org/10.1093/BIOMET/60.3.551

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

Wilcox, R. (2013). Introduction to robust estimation and hypothesis testing. Elsevier. https://doi.org/10.1016/C2010-0-67044-1

Examples

diffpwr.two(n1 = 1000,
            n2 = 594,
            rho1 = .45,
            rho2 = .39,
            alpha = .05,
            n.samples = 1000,
            seed = 1234)