Sample size (part II)

Regression

(This is the part II on sample size calculation)

Correlation

Correlation coefficient is used for effect size measure. Usse 0.1, 0.3, 0.5 to represent small, medium and large sizes.

# correlation coeff
pwr::pwr.r.test(r = 0.3, sig.level = 0.05, power = 0.8, alternative = 'two.sided')

     approximate correlation power calculation (arctangh transformation) 

              n = 84.07364
              r = 0.3
      sig.level = 0.05
          power = 0.8
    alternative = two.sided

Linear regression (F-test)

F-test for linear regression is testinng whether \(R^2\) is greater than zero (one-sided). \(R^2\) is the explained variance by using the predictors, \(R^2 = 0.3\) means that 30% of the variance are explained by the model.

Cohen’s f2, based on \(R^2\), goodness of fit (\(f2 = R^2/(1-R^2)\)). use 0.02, 0.15, 0.35 to represent small, medium and large effect sizes.

• u: number of predictors
• v: n-u-1
• as a result, sample size n = v+u+1

# effect size f2 = 0.15; use u=3 predictors
pwr::pwr.f2.test(u = 3, f2 = 0.3, sig.level = 0.05, power = 0.8)

     Multiple regression power calculation 

              u = 3
              v = 36.47078
             f2 = 0.3
      sig.level = 0.05
          power = 0.8

Here v = 73, sample size is 73+3+1 = 77.

Alternatively, can use pwrss::pwrss.f.reg(). The parameter is r2 rather than f2 (but can also use f2).

pwrss::pwrss.f.reg(r2 = 0.3, k = 0.3, power = 0.8, alpha = 0.05)

 Linear Regression (F test) 
 R-squared Deviation from 0 (zero) 
 H0: r2 = 0 
 HA: r2 > 0 
 ------------------------------ 
  Statistical power = 0.8 
  n = 14 
 ------------------------------ 
 Numerator degrees of freedom = 0.3 
 Denominator degrees of freedom = 12.415 
 Non-centrality parameter = 5.878 
 Type I error rate = 0.05 
 Type II error rate = 0.2 

# should be equivalent to
# pwr::pwr.f2.test(u = 3, f2 = 0.3/0.7, sig.level = 0.05, power = 0.8)

GLM

Resources

• Sample size calculation in clinical trial using R.
  Park et al. 2023. https://doi.org/10.7602/jmis.2023.26.1.9

• Bulus, M (2023) pwrss: Statistical Power and Sample Size Calculation Tools. R package version 0.3.1. https://CRAN.R-project.org/package=pwrss. Vignette documentation