Compute 2D p-value curve for a fixed sample size

Computes the p-value as a function of effect size (Cohen's d) for a single, fixed sample size. This is the 2D analogue of p_surface and is provided for comparison with existing 2D visualization packages such as pvaluefunctions.

Usage

p_curve_2d(d, n, alpha = 0.05)

Arguments

d

Numeric vector of effect sizes (Cohen's d).

n

Single sample size. Must be >= 2.

alpha

Significance level. Default: 0.05.

Value

A data frame with columns:

d

Effect sizes.

p

Two-sided p-values.

significant

Logical; whether p < alpha.

Details

The p-value is computed as: $$p(d) = 2 \left[ 1 - F_{t(n-1)}(d \sqrt{n}) \right]$$

Examples

# 2D curve for n = 30
curve_30 <- p_curve_2d(d = seq(-2, 2, 0.1), n = 30)
head(curve_30)
#>      d            p significant
#> 1 -2.0 8.021139e-12        TRUE
#> 2 -1.9 2.650857e-11        TRUE
#> 3 -1.8 9.099432e-11        TRUE
#> 4 -1.7 3.247269e-10        TRUE
#> 5 -1.6 1.205427e-09        TRUE
#> 6 -1.5 4.654771e-09        TRUE

# Compare with 3D surface
surface <- p_surface(d = seq(-2, 2, 0.1), n = c(10, 30, 100))