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

## 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

 ```1 2``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68``` ```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
This is lavaan 0.6-3
lavaan is BETA software! Please report any bugs.
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.