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Power Analysis for Between-, Within-, or Mixed-Factor ANOVA

Source: R/pwranova.r
pwranova.Rd

Computes power, required total sample size, alpha, or minimal detectable effect size for fixed-effects terms in between-/within-/mixed-factor ANOVA designs.

Usage

pwranova(
  nlevels_b = NULL,
  nlevels_w = NULL,
  n_total = NULL,
  alpha = NULL,
  power = NULL,
  cohensf = NULL,
  peta2 = NULL,
  epsilon = 1,
  target = NULL,
  max_nfactor = 6,
  nlim = c(2, 10000)
)

Arguments

nlevels_b

Integer scalar or vector. Numbers of levels for between-subjects factors. Omit or set NULL if there is no between-subjects factor.

nlevels_w

Integer scalar or vector. Numbers of levels for within-subjects factors. Omit or set NULL if there is no within-subjects factor.

n_total

Integer scalar or vector. Total sample size across all groups. If NULL, the function solves for n_total.

alpha

Numeric in \((0,1)\). If NULL, it is solved for.

power

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

cohensf

Numeric (non-negative). Cohen's \(f\). If NULL, it is derived from peta2 when available. If both effect-size arguments (cohensf and peta2) are NULL, the effect size is treated as unknown and solved for given n_total, alpha, and power.

peta2

Numeric in \((0,1)\). Partial eta squared. If NULL, it is derived from cohensf when available.

epsilon

Numeric in \((0,1]\). Nonsphericity parameter applied to within-subjects terms with \(\mathrm{df}_1 \ge 2\). Ignored if there is no within-subjects factor or if all within factors have two levels.

target

Character vector of term labels to compute (e.g., "B1", "W1", "B1:W1", ...). If NULL, all terms are returned.

max_nfactor

Integer. Safety cap for the total number of factors.

nlim

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

Value

A data frame with S3 class:

  • "cal_power" when power is calculated given n_total, alpha, and effect size;

  • "cal_n" or "cal_ns" when n_total is solved;

  • "cal_alpha" or "cal_alphas" when alpha is solved;

  • "cal_es" when minimal detectable effect sizes are solved.

Columns include term, df_num, df_denom, n_total, alpha, power, cohensf, peta2, F_critical, ncp, epsilon.

Details

  • Fixed-effects, balanced designs are assumed. All groups/cells have equal cell sizes and effects are tested with standard fixed-effects ANOVA models.

  • Numerator degrees of freedom for within-subjects terms with \(\mathrm{df}_1 \ge 2\) are adjusted by the nonsphericity parameter epsilon.

  • Denominator degrees of freedom follow standard mixed-ANOVA formulas and are multiplied by the same epsilon for within-subjects terms.

  • Critical values are computed from the central F-distribution; power uses the noncentral F-distribution with noncentrality parameter \(\lambda = f^2 \cdot n_{\mathrm{total}}\).

  • Effect-size inputs can be given as Cohen’s \(f\) or partial eta-squared \(\eta_p^2\) (internally converted via \(f = \sqrt{\eta_p^2/(1-\eta_p^2)}\)). If both are NULL, the minimal detectable effect size is solved for given n_total, alpha, and power.

  • Exactly one of n_total, an effect-size specification (cohensf/peta2), alpha, or power must be NULL; that quantity is then solved.

  • Validation against GPower: For the subset of designs supported by GPower (between-, within-, and mixed-factor ANOVA with equal cell sizes), pwranova() was validated to produce results identical to those of GPower.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

Examples

# One between factor (k = 3), one within factor (m = 4), compute power
pwranova(nlevels_b = 3, nlevels_w = 4, n_total = 60,
         cohensf = 0.25, alpha = 0.05, power = NULL, epsilon = 0.8)
#>    term df_num df_denom n_total alpha     power cohensf      peta2 F_critical
#> 1    B1    2.0     57.0      60  0.05 0.3744311    0.25 0.05882353   3.158843
#> 2    W1    2.4    136.8      60  0.05 0.3592414    0.25 0.05882353   2.876716
#> 3 B1:W1    4.8    136.8      60  0.05 0.2687648    0.25 0.05882353   2.307783
#>    ncp epsilon
#> 1 3.75     1.0
#> 2 3.75     0.8
#> 3 3.75     0.8
#> Power (1 - beta) was calculated based on the total sample size, effect size, and alpha.

# Solve required total N for target power
pwranova(nlevels_b = 2, nlevels_w = NULL, n_total = NULL,
         peta2 = 0.06, alpha = 0.05, power = 0.8)
#>   term df_num df_denom n_total alpha     power   cohensf peta2 F_critical
#> 1   B1      1      124     126  0.05 0.8034337 0.2526456  0.06    3.91755
#>        ncp epsilon
#> 1 8.042553       1
#> 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.