Reference Validation

ggpower validates core kernels against published reference examples. Direct noncentral t, F, normal, and chi-square procedures use tight tolerances. Exact enumeration is used where the grid is computationally feasible. Approximation-backed procedures report method notes in the result object.

Example 1: One-sample t, a priori

Target: $d = 0.625$, $\alpha = 0.05$ (one-tailed), power $= 0.95$.

Expected: $n = 30$, actual power $\approx 0.955144$, $df = 29$.

r1 <- power_compute("t_one_sample", "a_priori", d = 0.625, alpha = 0.05,
                      power = 0.95, tails = "one")
r1$outputs[c("total_sample_size", "actual_power", "df")]
#> $<NA>
#> NULL
#> 
#> $actual_power
#> [1] 0.9551444
#> 
#> $df
#> [1] 29

Example 2: Multiple regression omnibus, post hoc

$f^2 = 0.1111111$, $\alpha = 0.05$, $N = 95$, 5 predictors.

Expected: $\lambda \approx 10.556$, critical $F \approx 2.317$, $df_2 = 89$, power $\approx 0.674$.

r2 <- power_compute("f_mreg_omnibus", "post_hoc", f2 = 0.1111111,
                      alpha = 0.05, total_n = 95, predictors = 5)
r2$outputs[c("noncentrality_parameter", "critical_f", "denominator_df", "power")]
#> $noncentrality_parameter
#> [1] 10.55555
#> 
#> $critical_f
#> [1] 2.316858
#> 
#> $denominator_df
#> [1] 89
#> 
#> $power
#> [1] 0.6735857

Example 3: ANOVA special, post hoc

$f = 0.2450722$, $N = 108$, $df_1 = 4$, 36 groups.

Expected: $\lambda \approx 6.487$, $df_2 = 72$, power $\approx 0.476$.

r3 <- power_compute("f_anova_special", "post_hoc", f = 0.2450722,
                      alpha = 0.05, total_n = 108, df1 = 4, groups = 36)
r3$outputs[c("noncentrality_parameter", "denominator_df", "power")]
#> $noncentrality_parameter
#> [1] 6.486521
#> 
#> $denominator_df
#> [1] 72
#> 
#> $power
#> [1] 0.4756346

Example 4: Two-sample t, unequal n, post hoc

$d = 0.5$, $n_1 = 4$, $n_2 = 8$, one-tailed $\alpha = 0.05$.

Expected: $\delta \approx 0.816$, $df = 10$, power $\approx 0.189$.

r4 <- power_compute("t_two_sample", "post_hoc", d = 0.5, n1 = 4, n2 = 8,
                      alpha = 0.05, tails = "one")
r4$outputs[c("noncentrality_parameter", "df", "power")]
#> $noncentrality_parameter
#> [1] 0.8164966
#> 
#> $df
#> [1] 10
#> 
#> $power
#> [1] 0.1886663

Recommended tolerances

Kernel type	Tolerance
Direct distribution (t, F, z, $\chi^2$)	$10^{-5}$ to $10^{-4}$
Integer a priori solvers	Sample size exact; actual power $\geq$ target
Approximation-backed	Document method; validate with sensitivity plots

Related

• Support matrix
• Approximation catalog (pkgdown only)
• Formula reference (pkgdown only)