# wp.correlation: Statistical Power Analysis for Correlation In WebPower: Basic and Advanced Statistical Power Analysis

 wp.correlation R Documentation

## 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

```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
```

WebPower documentation built on May 21, 2022, 5:05 p.m.