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Power Analysis for One-/Two-Sample and Paired t Tests

Source: R/pwrttest.r
pwrttest.Rd

Computes statistical power, required total sample size, \(\alpha\), or the minimal detectable effect size for a t-test in one of three designs: one-sample, two-sample (independent), or paired/repeated measures.

Usage

pwrttest(
  paired = FALSE,
  onesample = FALSE,
  n_total = NULL,
  alpha = NULL,
  power = NULL,
  delta = NULL,
  cohensf = NULL,
  peta2 = NULL,
  alternative = c("two.sided", "one.sided"),
  nlim = c(2, 10000)
)

Arguments

paired

Logical. FALSE for two-sample (independent; default), TRUE for paired/repeated-measures. Ignored when onesample = TRUE.

onesample

Logical. TRUE for the one-sample t-test; if TRUE, paired is ignored.

n_total

Integer scalar. Total sample size. If NULL, the function solves for n_total.

alpha

Numeric in \((0,1)\). If NULL, it is solved for given the other inputs.

power

Numeric in \((0,1)\). If NULL, it is computed; if n_total is NULL, n_total is solved to attain this power.

delta

Numeric (non-negative). Cohen's \(d\)-type effect size. If NULL, it is derived from cohensf or peta2 when available. If all three effect-size arguments (delta, cohensf, peta2) are NULL, then the effect size is treated as the unknown quantity and is solved for given n_total, alpha, and power. The exact definition depends on the design:

  • One-sample: Cohen's \(d = (\mu - \mu_0)/\sigma\).

  • Paired: Cohen's \(d_z = \bar{d}/s_d\), i.e., the mean of the difference scores divided by their standard deviation.

  • Two-sample (equal allocation): Cohen's \(d\) is defined as the mean difference divided by the pooled standard deviation; internally related to \(f\) via \(d = 2f\).

If NULL, delta is derived from cohensf or peta2 when available.

cohensf

Numeric (non-negative). Cohen's \(f\). If NULL, it can be derived from delta; if delta is supplied, cohensf is ignored. Effect-size relations by design:

  • Two-sample (equal allocation): \(d = 2f\)

  • Paired: \(d_z = f\)

  • One-sample: \(f\) and \(\eta_p^2\) are not supported

peta2

Numeric in \((0,1)\). Partial eta squared. If NULL, it can be derived from cohensf; if delta is supplied, peta2 is ignored. Not defined for one-sample designs.

alternative

Character. Either "two.sided" or "one.sided".

nlim

Integer vector of length 2. Search range of total n when solving sample size.

Value

A one-row data.frame with class "cal_power", "cal_n", "cal_alpha", or "cal_es", depending on the solved quantity. Columns: df, n_total, alpha, power, delta, cohensf, peta2, t_critical, ncp.

Details

  • If multiple effect-size arguments are supplied (delta, cohensf, peta2), precedence is delta \(>\) cohensf \(>\) peta2; the rest are ignored with a warning.

  • For the two-sample design, equal allocation is assumed; n_total must be even when provided, and the solved n_total will be an even number.

  • For the paired design, the effect size is interpreted as \(d_z\).

  • Computations use the central and noncentral t-distributions (stats::qt, stats::pt); root finding uses stats::uniroot() where needed.

  • Results have been validated to match those produced by G*Power for equivalent one-sample, paired, and two-sample t tests.

Examples

# (1) Two-sample (independent), compute power given N and d
pwrttest(paired = FALSE, onesample = FALSE, alternative = "two.sided",
         n_total = 128, delta = 0.50, alpha = 0.05)
#>    df n_total alpha     power delta cohensf      peta2 t_critical      ncp
#> 1 126     128  0.05 0.8014596   0.5    0.25 0.05882353   1.978971 2.828427
#> Power (1 - beta) was calculated based on the total sample size, effect size, and alpha.

# (2) Paired t-test, solve required N for target power
pwrttest(paired = TRUE, onesample = FALSE, alternative = "one.sided",
         n_total = NULL, delta = 0.40, alpha = 0.05, power = 0.90)
#>   df n_total alpha     power delta_z cohensf    peta2 t_critical      ncp
#> 1 54      55  0.05 0.9004524     0.4     0.4 0.137931   1.673565 2.966479
#> The required total sample size was calculated based on the effect size, alpha, and power.
#> Note: 'power' indicates the achieved power rather than the target power.

# (3) One-sample t-test, solve alpha given N and power
pwrttest(onesample = TRUE, alternative = "two.sided",
         n_total = 40, delta = 0.40, alpha = NULL, power = 0.80)
#>   df n_total     alpha power delta cohensf peta2 t_critical      ncp
#> 1 39      40 0.1001708   0.8   0.4      NA    NA   1.683997 2.529822
#> Alpha was calculated based on the total sample size, effect size, and power.

# (4) Two-sample, specify effect via f or partial eta^2 (converted internally)
pwrttest(paired = FALSE, cohensf = 0.25, n_total = NULL, alpha = 0.05, power = 0.80)
#>    df n_total alpha     power delta cohensf      peta2 t_critical      ncp
#> 1 126     128  0.05 0.8014596   0.5    0.25 0.05882353   1.978971 2.828427
#> The required total sample size was calculated based on the effect size, alpha, and power.
#> Note: 'power' indicates the achieved power rather than the target power.