diffpwr.one {diffcor}

Monte Carlo Simulation for the correlation difference between an expected and an observed correlation

Description

Computation of a Monte Carlo simulation to estimate the statistical power the correlation difference between an observed correlation coefficient and an a fixed value against which the correlation should be tested.

Usage

diffpwr.one(n,
            r,
            rho,
            alpha = .05,
            n.samples = 1000,
            seed = 1234)

Arguments

n

Sample size to be tested in the Monte Carlo simulation.

r

Assumed observed correlation.

rho

Correlation coefficient against which to test (reflects the null hypothesis).

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, it is recommended to set a random seed.

Details

Depending on the number of generated samples (n.samples), correlation coefficients of size r are simulated. Confidence intervals are constructed around the simulated correlation coefficients. For each simulated coefficient, it is then checked whether the hypothesized correlation cofficient (rho) falls within this interval. All correlations are automatically transformed with the Fisher z-transformation prior to computations. The ratio of simulated confidence intervals excluding the hypothesized coefficient equals the statistical power, given the intended alpha-level and sample size (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

r

Empirically observed correlation.

rho

Correlation against which r should be tested.

n

The sample size entered in the function.

cov

Coverage. Indicates the ratio of simulated confidence intervals including the assumed correlation r. Should be between .91 and .98 (Muthén & Muthén, 2002 <doi:10.1207/S15328007SEM0904_8>).

bias_M

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

bias_Md

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

pwr

Statistical power as the ratio of simulated confidence intervals excluding rho.

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.one(n = 500,
            r = .30,
            rho = .40,
            alpha = .05,
            n.samples = 1000,
            seed = 1234)