diffcor.one {diffcor}

Fisher's z-test of difference between an empirical and a hypothesized correlation

Description

The function tests whether an observed correlation differs from an expected one, for example, in construct validation. All correlations are automatically transformed with the Fisher z-transformation prior to computations. The output provides the compared correlations, a z-score, a p-value, a confidence interval, 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.one(emp.r, hypo.r, n, alpha = .05, cor.names = NULL,
alternative = c("one.sided", "two.sided"), digit = 3)

Arguments

emp.r

Empirically observed correlation

hypo.r

Hypothesized correlation which shall be tested

n

Sample size in which the observed effect was found

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

r_exp

Vector of the expected correlations

r_obs

Vector of the empirically observed correlations

LL

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

UL

Upper limit of the confidence interval of the 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.one(c(.76, .53, -.32), c(.70, .35, -.40),
  c(225, 250, 210),
  cor.names = c("a-b", "c-d", "e-f"), digit = 2, alternative = "one.sided")