WebPower (version 0.6)

wp.correlation: Statistical Power Analysis for Correlation

Description

This function is for power analysis for correlation. Correlation measures whether and how a pair of variables are related. The Pearson Product Moment correlation coefficient (r) is adopted here. The power calculation for correlation is conducted based on Fisher's z transformation of Pearson correlation coefficent (Fisher, 1915, 1921).

Usage

wp.correlation(n = NULL, r = NULL, power = NULL, p = 0, rho0 = 0,
  alpha = 0.05, alternative = c("two.sided", "less", "greater"))

Arguments

n

Sample size.

r

Effect size or correlation. According to Cohen (1988), a correlation coefficient of 0.10, 0.30, and 0.50 are considered as an effect size of "small", "medium", and "large", respectively.

power

Statistical power.

p

Number of variables to partial out.

rho0

Null correlation coefficient.

alpha

Significance level chosed for the test. It equals 0.05 by default.

alternative

Direction of the alternative hypothesis ("two.sided" or "less" or "greater"). The default is "two.sided".

Value

An object of the power analysis.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed). Hillsdale, NJ: Lawrence Erlbaum Associates.

Fisher, R. A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10(4), 507-521.

Fisher, R. A. (1921). On the probable error of a coefficient of correlation deduced from a small sample. Metron, 1, 3-32.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

Examples

# NOT RUN {
wp.correlation(n=50,r=0.3, alternative="two.sided")
#  Power for correlation
#
#     n   r alpha     power
#    50 0.3  0.05 0.5728731
#        
#  URL: http://psychstat.org/correlation

#To calculate the power curve with a sequence of sample sizes:
res <- wp.correlation(n=seq(50,100,10),r=0.3, alternative="two.sided")
res
#  Power for correlation
#
#      n   r alpha     power
#     50 0.3  0.05 0.5728731
#     60 0.3  0.05 0.6541956
#     70 0.3  0.05 0.7230482
#     80 0.3  0.05 0.7803111
#     90 0.3  0.05 0.8272250
#    100 0.3  0.05 0.8651692
#
#  URL: http://psychstat.org/correlation

#To plot the power curve:
plot(res, type='b')

#To estimate the sample size with a given power:
wp.correlation(n=NULL, r=0.3, power=0.8, alternative="two.sided")
#  Power for correlation
#
#           n   r alpha power
#    83.94932 0.3  0.05   0.8
#
#  URL: http://psychstat.org/correlation

#To estimate the minimum detectable effect size with a given power:
wp.correlation(n=NULL,r=0.3, power=0.8, alternative="two.sided")
#  Power for correlation
#
#           n   r alpha power
#    83.94932 0.3  0.05   0.8
#
#  URL: http://psychstat.org/correlation
#
#To calculate the power curve with a sequence of effect sizes:
res <- wp.correlation(n=100,r=seq(0.05,0.8,0.05), alternative="two.sided")
res
#	 Power for correlation
#
#      n    r alpha      power
#    100 0.05  0.05 0.07854715
#    100 0.10  0.05 0.16839833
#    100 0.15  0.05 0.32163978
#    100 0.20  0.05 0.51870091
#    100 0.25  0.05 0.71507374
#    100 0.30  0.05 0.86516918
#    100 0.35  0.05 0.95128316
#    100 0.40  0.05 0.98724538
#    100 0.45  0.05 0.99772995
#    100 0.50  0.05 0.99974699
#    100 0.55  0.05 0.99998418
#    100 0.60  0.05 0.99999952
#    100 0.65  0.05 0.99999999
#    100 0.70  0.05 1.00000000
#    100 0.75  0.05 1.00000000
#    100 0.80  0.05 1.00000000
#
#	 URL: http://psychstat.org/correlation
# }