p-value from proportion test simulation

Generates single and multi-sample data for proportion tests and return a p-value. Uses binom.test for one-sample applications and prop.test otherwise.

Usage

p_prop.test(
  n,
  h,
  prop = NULL,
  pi = 0.5,
  n.ratios = rep(1, length(prop)),
  two.tailed = TRUE,
  correct = TRUE,
  exact = FALSE,
  gen_fun = gen_prop.test,
  return_analysis = FALSE,
  ...
)

gen_prop.test(
  n,
  h,
  prop = NULL,
  pi = 0.5,
  n.ratios = rep(1, length(prop)),
  ...
)

Arguments

n

sample size per group

h

Cohen's h effect size; only supported for one-sample analysis.

Note that it's important to specify the null value pi when supplying this effect size as the power changes depending on these specific values (see example below).

prop

sample probability/proportions of success. If a vector with two-values or more elements are supplied then a multi-samples test will be used. Matrices are also supported

pi

probability of success to test against (default is .5). Ignored for two-sample tests

n.ratios

allocation ratios reflecting the sample size ratios. Default of 1 sets the groups to be the same size (n * n.ratio)

two.tailed

logical; should a two-tailed or one-tailed test be used?

correct

logical; use Yates' continuity correction?

exact

logical; use fisher's exact test via fisher.test? Use of this flag requires that prop was specified as a matrix

gen_fun

function used to generate the required discrete data. Object returned must be a matrix with two rows and 1 or more columns. Default uses gen_prop.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


# one sample, 50 observations, tested against pi = .5 by default
p_prop.test(50, prop=.65)
#> [1] 0.3222363

# return analysis model
p_prop.test(50, prop=.65, return_analysis = TRUE)
#> 
#> 	Exact binomial test
#> 
#> data:  dat[1, 1] and n
#> number of successes = 29, number of trials = 50, p-value = 0.3222
#> alternative hypothesis: true probability of success is not equal to 0.5
#> 95 percent confidence interval:
#>  0.4320604 0.7181178
#> sample estimates:
#> probability of success 
#>                   0.58 
#> 

# specified using h and pi
h <- pwr::ES.h(.65, .4)
p_prop.test(50, h=h, pi=.4)
#> [1] 0.00024228
p_prop.test(50, h=-h, pi=.65)
#> [1] 0.0004932261

# two-sample test
p_prop.test(50, prop=c(.5, .65))
#> [1] 0.3157569

# two-sample test, unequal ns
p_prop.test(50, prop=c(.5, .65), n.ratios = c(1,2))
#> [1] 0.1648304

# three-sample test, group2 twice as large as others
p_prop.test(50, prop=c(.5, .65, .7), n.ratios=c(1,2,1))
#> [1] 0.2178803

# Fisher exact test
p_prop.test(50, prop=matrix(c(.5, .65, .7, .5), 2, 2))
#> [1] 0.3588457

# \donttest{
    # compare simulated results to pwr package

    # one-sample tests
    (h <- pwr::ES.h(0.5, 0.4))
#> [1] 0.2013579
    pwr::pwr.p.test(h=h, n=60)
#> 
#>      proportion power calculation for binomial distribution (arcsine transformation) 
#> 
#>               h = 0.2013579
#>               n = 60
#>       sig.level = 0.05
#>           power = 0.3447014
#>     alternative = two.sided
#> 

    # uses binom.test (need to specify null location as this matters!)
    Spower(p_prop.test(n=60, h=h, pi=.4))
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 4
#>       n    pi sig.level power
#>   <dbl> <dbl>     <dbl> <lgl>
#> 1    60   0.4      0.05 NA   
#> 
#> Estimate of power: 0.346
#> 95% Confidence Interval: [0.337, 0.356]
#> Execution time (H:M:S): 00:00:03
    Spower(p_prop.test(n=60, prop=.5, pi=.4))
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 5
#>       n  prop    pi sig.level power
#>   <dbl> <dbl> <dbl>     <dbl> <lgl>
#> 1    60   0.5   0.4      0.05 NA   
#> 
#> Estimate of power: 0.336
#> 95% Confidence Interval: [0.327, 0.346]
#> Execution time (H:M:S): 00:00:02

    # compare with switched null
    Spower(p_prop.test(n=60, h=h, pi=.5))
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 4
#>       n    pi sig.level power
#>   <dbl> <dbl>     <dbl> <lgl>
#> 1    60   0.5      0.05 NA   
#> 
#> Estimate of power: 0.253
#> 95% Confidence Interval: [0.244, 0.261]
#> Execution time (H:M:S): 00:00:03
    Spower(p_prop.test(n=60, prop=.4, pi=.5))
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 5
#>       n  prop    pi sig.level power
#>   <dbl> <dbl> <dbl>     <dbl> <lgl>
#> 1    60   0.4   0.5      0.05 NA   
#> 
#> Estimate of power: 0.257
#> 95% Confidence Interval: [0.249, 0.266]
#> Execution time (H:M:S): 00:00:03

    # two-sample test, one-tailed
    (h <- pwr::ES.h(0.67, 0.5))
#> [1] 0.3469169
    pwr::pwr.2p.test(h=h, n=80, alternative="greater")
#> 
#>      Difference of proportion power calculation for binomial distribution (arcsine transformation) 
#> 
#>               h = 0.3469169
#>               n = 80
#>       sig.level = 0.05
#>           power = 0.7085801
#>     alternative = greater
#> 
#> NOTE: same sample sizes
#> 
    p_prop.test(n=80, prop=c(.67, .5), two.tailed=FALSE,
      correct=FALSE) |> Spower()
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 5
#>       n two.tailed correct sig.level power
#>   <dbl> <lgl>      <lgl>       <dbl> <lgl>
#> 1    80 FALSE      FALSE        0.05 NA   
#> 
#> Estimate of power: 0.703
#> 95% Confidence Interval: [0.694, 0.712]
#> Execution time (H:M:S): 00:00:03

    # same as above, but with continuity correction (default)
    p_prop.test(n=80, prop=c(.67, .5), two.tailed=FALSE) |>
      Spower()
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 4
#>       n two.tailed sig.level power
#>   <dbl> <lgl>          <dbl> <lgl>
#> 1    80 FALSE           0.05 NA   
#> 
#> Estimate of power: 0.635
#> 95% Confidence Interval: [0.626, 0.645]
#> Execution time (H:M:S): 00:00:03

    # three-sample joint test, equal n's
    p_prop.test(n=50, prop=c(.6,.4,.7)) |> Spower()
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 3
#>       n sig.level power
#>   <dbl>     <dbl> <lgl>
#> 1    50      0.05 NA   
#> 
#> Estimate of power: 0.797
#> 95% Confidence Interval: [0.789, 0.805]
#> Execution time (H:M:S): 00:00:03

# }

Usage

Arguments

Value

See also

Author

Examples