p-value from chi-squared test simulation

Generates multinomial data suitable for analysis with chisq.test.

Usage

p_chisq.test(
  n,
  w,
  df,
  correct = TRUE,
  P0 = NULL,
  P = NULL,
  gen_fun = gen_chisq.test,
  return_analysis = FALSE,
  ...
)

gen_chisq.test(n, P, ...)

Arguments

n: sample size per group
w: Cohen's w effect size
df: degrees of freedom
correct: logical; apply continuity correction?
P0: specific null pattern, specified as a numeric vector or matrix
P: specific power configuration, specified as a numeric vector or matrix
gen_fun: function used to generate the required discrete data. Object returned must be a matrix with k rows and k columns of counts. Default uses gen_chisq.test. User defined version of this function must include the argument ...
return_analysis: logical; return the analysis object for further extraction and customization?
...: additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

Value

a single p-value

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


# effect size w + df
p_chisq.test(100, w=.2, df=3)
#> [1] 0.1077823

# return analysis model
p_chisq.test(100, w=.2, df=3, return_analysis=TRUE)
#> 
#> 	Chi-squared test for given probabilities
#> 
#> data:  tab
#> X-squared = 2.48, df = 3, p-value = 0.4789
#> 

# vector of explicit probabilities (goodness of fit test)
p_chisq.test(100, P0 = c(.25, .25, .25, .25),
                   P = c(.6, .2, .1, .1))
#> [1] 1.342015e-09

# matrix of explicit probabilities (two-dimensional test of independence)
p_chisq.test(100, P0 = matrix(c(.25, .25, .25, .25), 2, 2),
                   P = matrix(c(.6, .2, .1, .1),2,2))
#> [1] 0.05475601

# \donttest{
    # compare simulated results to pwr package

    P0 <- c(1/3, 1/3, 1/3)
    P <- c(.5, .25, .25)
    w <- pwr::ES.w1(P0, P)
    df <- 3-1
    pwr::pwr.chisq.test(w=w, df=df, N=100, sig.level=0.05)
#> 
#>      Chi squared power calculation 
#> 
#>               w = 0.3535534
#>               N = 100
#>              df = 2
#>       sig.level = 0.05
#>           power = 0.8962428
#> 
#> NOTE: N is the number of observations
#> 

    # slightly less power when evaluated empirically
    p_chisq.test(n=100, w=w, df=df) |> Spower(replications=100000)
#> 
#> Execution time (H:M:S): 00:00:22
#> Design conditions: 
#> 
#> # A tibble: 1 × 3
#>       n sig.level power
#>   <dbl>     <dbl> <lgl>
#> 1   100      0.05 NA   
#> 
#> Estimate of power: 0.887
#> 95% Confidence Interval: [0.885, 0.889]
    p_chisq.test(n=100, P0=P0, P=P) |> Spower(replications=100000)
#> 
#> Execution time (H:M:S): 00:00:17
#> Design conditions: 
#> 
#> # A tibble: 1 × 3
#>       n sig.level power
#>   <dbl>     <dbl> <lgl>
#> 1   100      0.05 NA   
#> 
#> Estimate of power: 0.887
#> 95% Confidence Interval: [0.885, 0.889]

    # slightly differ (latter more conservative due to finite sampling behaviour)
    pwr::pwr.chisq.test(w=w, df=df, power=.8, sig.level=0.05)
#> 
#>      Chi squared power calculation 
#> 
#>               w = 0.3535534
#>               N = 77.07751
#>              df = 2
#>       sig.level = 0.05
#>           power = 0.8
#> 
#> NOTE: N is the number of observations
#> 
    p_chisq.test(n=interval(50, 200), w=w, df=df) |> Spower(power=.80)
#> 
#> Execution time (H:M:S): 00:00:17
#> Design conditions: 
#> 
#> # A tibble: 1 × 3
#>       n sig.level power
#>   <dbl>     <dbl> <dbl>
#> 1    NA      0.05   0.8
#> 
#> Estimate of n: 79.3
#> 95% Predicted Confidence Interval: [79.0, 79.7]
    p_chisq.test(n=interval(50, 200), w=w, df=df, correct=FALSE) |>
      Spower(power=.80)
#> 
#> Execution time (H:M:S): 00:00:20
#> Design conditions: 
#> 
#> # A tibble: 1 × 4
#>       n correct sig.level power
#>   <dbl> <lgl>       <dbl> <dbl>
#> 1    NA FALSE        0.05   0.8
#> 
#> Estimate of n: 79.7
#> 95% Predicted Confidence Interval: [79.1, 80.4]

    # Spower slightly more conservative even with larger N
    pwr::pwr.chisq.test(w=.1, df=df, power=.95, sig.level=0.05)
#> 
#>      Chi squared power calculation 
#> 
#>               w = 0.1
#>               N = 1544.324
#>              df = 2
#>       sig.level = 0.05
#>           power = 0.95
#> 
#> NOTE: N is the number of observations
#> 
    p_chisq.test(n=interval(1000, 2000), w=.1, df=df) |> Spower(power=.95)
#> 
#> Execution time (H:M:S): 00:00:07
#> Design conditions: 
#> 
#> # A tibble: 1 × 4
#>       n     w sig.level power
#>   <dbl> <dbl>     <dbl> <dbl>
#> 1    NA   0.1      0.05  0.95
#> 
#> Estimate of n: 1584.8
#> 95% Predicted Confidence Interval: [1560.0, 1610.0]
    p_chisq.test(n=interval(1000, 2000), w=.1, df=df, correct=FALSE) |>
           Spower(power=.95)
#> 
#> Execution time (H:M:S): 00:00:06
#> Design conditions: 
#> 
#> # A tibble: 1 × 5
#>       n     w correct sig.level power
#>   <dbl> <dbl> <lgl>       <dbl> <dbl>
#> 1    NA   0.1 FALSE        0.05  0.95
#> 
#> Estimate of n: 1571.3
#> 95% Predicted Confidence Interval: [1549.4, 1594.5]

# }

Usage

Arguments

Value

See also

Author

Examples