wp.correlation: Statistical Power Analysis for Correlation

Description Usage Arguments Value References Examples

View source: R/webpower.R

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

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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

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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

Example output

Loading required package: MASS
Loading required package: lme4
Loading required package: Matrix
Loading required package: lavaan
This is lavaan 0.6-3
lavaan is BETA software! Please report any bugs.
Loading required package: parallel
Loading required package: PearsonDS
Power for correlation

     n   r alpha     power
    50 0.3  0.05 0.5728731

URL: http://psychstat.org/correlation
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 0.8272251
    100 0.3  0.05 0.8651692

URL: http://psychstat.org/correlation
Power for correlation

           n   r alpha power
    83.94932 0.3  0.05   0.8

URL: http://psychstat.org/correlation
Power for correlation

           n   r alpha power
    83.94932 0.3  0.05   0.8

URL: http://psychstat.org/correlation
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 0.86516920
    100 0.35  0.05 0.95128318
    100 0.40  0.05 0.98724540
    100 0.45  0.05 0.99772996
    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

WebPower documentation built on May 1, 2019, 8:19 p.m.