Statistical Power for the Generic Chi-Square Test

Determines power, the non-centrality parameter (NCP) for the generic chi-square test with (optional) Type 1 and Type 2 error plots.

Usage

power.chisq.test(
  power = NULL,
  ncp = NULL,
  null.ncp = 0,
  df = NULL,
  alpha = 0.05,
  plot = TRUE,
  verbose = 1,
  utf = FALSE
)

Arguments

power: statistical power \((1 - \beta)\); either power, ncp or df needs to be NULL (and is then estimated).
ncp: non-centrality parameter for the alternative; either power, ncp or df needs to be NULL (and is then estimated).
null.ncp: non-centrality parameter for the null.
df: integer; degrees of freedom, e.g., for the test of independence df = (nrow - 1) * (ncol - 1); either power, ncp or df needs to be NULL (and is then estimated).
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.
df: degrees of freedom.
alpha: type 1 error rate (user-specified).
chisq.alpha: critical value.

Examples

# power is defined as the probability of observing a test statistics greater
# than the critical value
power.chisq.test(ncp = 20, df = 100, alpha = 0.05)

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic Chi-square Test
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : lambda = null.lambda
#>   H1 (Alternative) : lambda > null.lambda
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Target NCP (lambda)  = 20 (vs. null.lambda = 0)
#>   Degrees of Freedom   = 100
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.619
#>   Statistical Power    = 0.381  <<
#> 
power.chisq.test(power = 0.80, df = 100, alpha = 0.05)

#> +--------------------------------------------------+
#> |       MINIMUM DETECTABLE NCP CALCULATION         |
#> +--------------------------------------------------+
#> 
#> Generic Chi-square Test
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : lambda = null.lambda
#>   H1 (Alternative) : lambda > null.lambda
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Target NCP (lambda)  = 40.556 (vs. null.lambda = 0)  <<
#>   Degrees of Freedom   = 100
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#> 
power.chisq.test(power = 0.80, ncp = 20, alpha = 0.05)

#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Generic Chi-square Test
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : lambda = null.lambda
#>   H1 (Alternative) : lambda > null.lambda
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Target NCP (lambda)  = 20 (vs. null.lambda = 0)
#>   Degrees of Freedom   = 17.673  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#>