Power Analysis for One-Sample Correlation (Exact)

Calculates power, sample size, or minimum detectable correlation (only one can be NULL at a time) to test a (Pearson) correlation against a constant using exact method described in Barabesi and Greco (2002).

Formulas are validated using G*Power.

Usage

power.exact.onecor(
  rho = NULL,
  req.sign = "+",
  null.rho = 0,
  n = NULL,
  n.max = 10000,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  verbose = 1,
  utf = FALSE
)

Arguments

rho: correlation.
req.sign: whether estimated rho is smaller or larger than the null.rho (when minimum detectable rho is of interest).
null.rho: correlation when null is true. Only 0 is allowed for now.
n: sample size.
n.max: max. number of observations in the sample (default: 500).
power: statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as \(1 - \beta\).
alpha: type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).
alternative: character; the direction or type of the hypothesis test: "two.sided" or "one.sided".
verbose: 1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.
utf: logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Value

parms: list of parameters used in calculation.
test: type of the statistical test (Z-Test)
rho.alpha: critical value(s).
es: minimum detectable correlation.
power: statistical power\((1-\beta)\).
n: sample size.

References

Barabesi, L., & Greco, L. (2002). A Note on the Exact Computation of the Student t, Snedecor F and Sample Correlation Coefficient Distribution Functions. Journal of the Royal Statistical Society. Series D (The Statistician), 51(1), 105–110. https://www.jstor.org/stable/3650394

Examples

# expected correlation is 0.20 and it is different from 0
# it could be 0.20 as well as -0.20
power.exact.onecor(rho = 0.20,
                   power = 0.80,
                   alpha = 0.05,
                   alternative = "two.sided")
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> One-Sample Correlation (Exact)
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : rho - null.rho  = 0
#>   H1 (Alternative) : rho - null.rho != 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Target Effect (rho)  = 0.200 (vs. null.rho = 0)
#>   Sample Size          = 193  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#> 

# expected correlation is 0.20 and it is greater than 0
power.exact.onecor(rho = 0.20,
                   power = 0.80,
                   alpha = 0.05,
                   alternative = "one.sided")
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> One-Sample Correlation (Exact)
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : rho - null.rho <= 0
#>   H1 (Alternative) : rho - null.rho  > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Target Effect (rho)  = 0.200 (vs. null.rho = 0)
#>   Sample Size          = 153  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.198
#>   Statistical Power    = 0.802
#>