Statistical Power for the Generic F-Test

Determines the power or the non-centrality parameter for the generic F-Test with (optional) Type 1 and Type 2 error plots.

Usage

power.f.test(
  power = NULL,
  ncp = NULL,
  null.ncp = 0,
  df1,
  df2,
  alpha = 0.05,
  plot = TRUE,
  verbose = 1,
  utf = FALSE
)

Arguments

power: statistical power \((1 - \beta)\); either power or ncp needs to be NULL (and is then estimated).
ncp: non-centrality parameter for the alternative; either power or ncp needs to be NULL (and is then estimated).
null.ncp: non-centrality parameter for the null.
df1: integer; numerator degrees of freedom.
df2: integer; denominator degrees of freedom.
alpha: type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).
plot: logical; FALSE switches off Type 1 and Type 2 error plot. TRUE by default.
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

power: statistical power \((1-\beta)\).
ncp: non-centrality parameter under alternative.
null.ncp: non-centrality parameter under null.
df1: numerator degrees of freedom.
df2: denominator degrees of freedom.
f.alpha: critical value(s).

Examples

# power is defined as the probability of observing a test statistics greater
# than the critical value
power.f.test(ncp = 1, df1 = 4, df2 = 100, alpha = 0.05)

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic F-Test
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : lambda = 0
#>   H1 (Alternative) : lambda > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Target NCP (lambda)  = 1 (vs. null.lambda = 0)
#>   Presumed Sample S.   = 105
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.897
#>   Statistical Power    = 0.103  <<
#> 
power.f.test(power = 0.80, df1 = 4, df2 = 100, alpha = 0.05)

#> +--------------------------------------------------+
#> |       MINIMUM DETECTABLE NCP CALCULATION         |
#> +--------------------------------------------------+
#> 
#> Generic F-Test
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : lambda = 0
#>   H1 (Alternative) : lambda > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Target NCP (lambda)  = 12.514 (vs. null.lambda = 0)  <<
#>   Presumed Sample S.   = 105
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#>