wp.correlation | R Documentation |
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).
wp.correlation(n = NULL, r = NULL, power = NULL, p = 0, rho0 = 0,
alpha = 0.05, alternative = c("two.sided", "less", "greater"))
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 ( |
An object of the power analysis.
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.
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
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.