diffcor.two {diffcor}

Fisher's z-Tests for differences of correlations in two independent samples

Description

Tests whether the correlation between two variables differs across two independent studies/samples. The correlations are automatically transformed with the Fisher z-transformation prior to computations. The output provides the compared correlations, test statistic as z-score, p-values, confidence intervals of the empirical correlations, and the effect size Cohens q. According to Cohen (1988), q = |.10|, |.30| and |.50| are considered small, moderate, and large differences, respectively.

Usage

diffcor.two(r1, r2, n1, n2, alpha = .05, cor.names = NULL,
alternative = c("one.sided", "two.sided"), digit = 3)

Arguments

r1

Correlation coefficient in first sample

r2

Correlation coefficient in second sample

n1

First sample size

n2

Second sample size

alpha

Likelihood of Type I error, DEFAULT = .05

cor.names

OPTIONAL, label for the correlation (e.g., "IQ-performance"). DEFAULT is NULL

digit

Number of digits in the output for all parameters, DEFAULT = 3

alternative

A character string specifying if you wish to test one-sided or two-sided differences

Value

r1

Vector of the empirically observed correlations in the first sample

r2

Vector of the empirically observed correlations in the second sample

LL1

Lower limit of the confidence interval of the first empirical correlation, given the specified alpha level, DEFAULT = 95 percent

UL1

Upper limit of the confidence interval of the first empirical correlation, given the specified alpha level, DEFAULT = 95 percent

LL2

Lower limit of the confidence interval of the second empirical correlation, given the specified alpha level, DEFAULT = 95 percent

UL2

Upper limit of the confidence interval of the second empirical correlation, given the specified alpha level, DEFAULT = 95 percent

z

Test statistic for correlation difference in units of z distribution

p

p value for one- or two-sided testing, depending on alternative = c("one.sided", "two.sided)

Cohen_q

Effect size measure for differences of independent correlations

Author(s)

Christian Blötner [e-mail]

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.

Eid, M., Gollwitzer, M., & Schmitt, M. (2015). Statistik und Forschungsmethoden (4.Auflage) [Statistics and research methods (4th ed.)]. Beltz.

Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87, 245-251.

Examples

diffcor.two(r1 = c(.39, .52, .22),
  r2 = c(.29, .44, .12),
  n1 = c(66, 66, 66), n2 = c(96, 96, 96), alpha = .01,
  cor.names = c("a-b", "c-d", "e-f"), alternative = "one.sided")