p-value from comparing two or more correlations simulation

Function utilizes cocor to perform correlation comparison for independent, overlapping, and non-overlapping correlation designs. Type type of correlation design is inferred based on which correlations are specified.

Usage

p_2r(
  n,
  r.ab,
  r.ab2 = NULL,
  r.ac,
  r.bc,
  r.ad,
  r.bd,
  r.cd,
  n2_n1 = 1,
  alternative = "two.sided",
  test = NULL,
  gen_fun = gen_2r,
  return_analysis = FALSE,
  ...
)

gen_2r(n, R, ...)

Arguments

n: sample size
r.ab: correlation between variable A and B (for independent groups, this is for sample 1)
r.ab2: (for independent group test only) correlation between variable A and B in sample 2
r.ac: (for overlap/non-overlap) correlation between A and C. This is the correlation used in the overlapping hypothesis test, comparing this input to r.ab
r.bc: (for overlap/non-overlap only) correlation between B and C.
r.ad: (for non-overlap only) correlation between A and D
r.bd: (for non-overlap only) correlation between B and D
r.cd: (for non-overlap only) correlation between C and D. This is the correlation used in the non-overlapping hypothesis test, comparing this input to r.ab
n2_n1: sample size ratio. Only used for independent group test
alternative: character vector passed to alternative analysis function (most commonly, 'two.sided', 'greater', 'less')
test: hypothesis testing method to use. Defaults to 'fisher1925' for the independent groups test and 'steiger1980' for overlap/non-overlap tests
gen_fun: function used to generate the required discrete data. Object returned must be a matrix with n rows. Default uses gen_2r. 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
R: a correlation matrix constructed from the inputs to p_2r

Value

a single p-value

Details

For independent group tests, only r.ab and r.ab2 need to be specified, where the null hypothesis pertains to \(H_0: r_{ab}=r_{ab2}\).

For overlapping correlation tests, r.ab, r.ac, and r.bc need to be specified, where the null hypothesis pertains to \(H_0: r_{ab}=r_{ac}\).

For non-overlapping correlation tests, all correlations expect for r.ab2 must be specified, where the null hypothesis pertains to \(H_0: r_{ab}=r_{cd}\).

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


# independent (same x-y pairing across groups)
p_2r(100, r.ab=.5, r.ab2=.6)
#> [1] 0.9316161

# return cocor object for further analysis
p_2r(100, r.ab=.5, r.ab2=.6, return_analysis = TRUE)
#> 
#>   Results of a comparison of two correlations based on independent groups
#> 
#> Comparison between r1.jk (y, x) = 0.3373 and r2.hm (y, x) = 0.5773
#> Difference: r1.jk - r2.hm = -0.24
#> Data: sample1: j = y, k = x; sample2: h = y, m = x
#> Group sizes: n1 = 100, n2 = 100
#> Null hypothesis: r1.jk is equal to r2.hm
#> Alternative hypothesis: r1.jk is not equal to r2.hm (two-sided)
#> Alpha: 0.05
#> 
#> fisher1925: Fisher's z (1925)
#>   z = -2.1406, p-value = 0.0323
#>   Null hypothesis rejected
#> 

# \donttest{

   # estimate empirical power
   p_2r(n=100, r.ab=.5, r.ab2=.6) |> Spower()
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 5
#>       n  r.ab r.ab2 sig.level power
#>   <dbl> <dbl> <dbl>     <dbl> <lgl>
#> 1   100   0.5   0.6      0.05 NA   
#> 
#> Estimate of power: 0.162
#> 95% Confidence Interval: [0.155, 0.169]
#> Execution time (H:M:S): 00:00:16

   # estimate n required to reach 80% power
   p_2r(n=interval(100, 5000), r.ab=.5, r.ab2=.6) |> Spower(power=.80)
#> 
#> ── Spower Results ──────────────────────────────────────────────────────────────
#> 
#> Design conditions:
#> 
#> # A tibble: 1 × 5
#>       n  r.ab r.ab2 sig.level power
#>   <dbl> <dbl> <dbl>     <dbl> <dbl>
#> 1    NA   0.5   0.6      0.05   0.8
#> 
#> Estimate of n: 770.4
#> 95% Confidence Interval: [764.3, 776.3]
#> Execution time (H:M:S): 00:01:02

# }

# overlap (same y, different xs)
# H0: r.ab = r.bc
p_2r(100, r.ab=.5, r.ac=.3, r.bc=.2)
#> [1] 2.903639e-06

# nonoverlap (different ys, different xs)
# H0: r.ab = r.cd
p_2r(100, r.ab=.5, r.ac=.3, r.bc=.2, r.ad=.2, r.bd=.4, r.cd=.2)
#> [1] 0.3552939