Title:	Power Analysis of Flexible ANOVA Designs and Related Tests
Version:	1.0.2
Description:	Provides functions for conducting power analysis in ANOVA designs, including between-, within-, and mixed-factor designs, with full support for both main effects and interactions. The package allows calculation of statistical power, required total sample size, significance level, and minimal detectable effect sizes expressed as partial eta squared or Cohen's f for ANOVA terms and planned contrasts. In addition, complementary functions are included for common related tests such as t-tests and correlation tests, making the package a convenient toolkit for power analysis in experimental psychology and related fields.
License:	GPL-3
Encoding:	UTF-8
URL:	https://github.com/mutopsy/pwranova, https://mutopsy.github.io/pwranova/
BugReports:	https://github.com/mutopsy/pwranova/issues
RoxygenNote:	7.3.2
Depends:	R (≥ 4.1.0)
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2025-10-01 04:59:07 UTC; owner
Author:	Hiroyuki Muto [aut, cre]
Maintainer:	Hiroyuki Muto <mutopsy@omu.ac.jp>
Repository:	CRAN
Date/Publication:	2025-10-07 18:30:09 UTC

Convert Cohen's f to Partial Eta Squared

Description

Converts Cohen's f to partial eta squared (\eta_p^2) using the standard definition in Cohen (1988).

Usage

cohensf_to_peta2(f)

Arguments

Details

The conversion is defined as:

\eta_p^2 = \frac{f^2}{1 + f^2}

This follows from the relationship: f = \sqrt{\eta_p^2 / (1 - \eta_p^2)}

Value

A numeric vector of partial eta squared values.

References

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

See Also

peta2_to_cohensf

Examples

# Convert a single Cohen's f value
cohensf_to_peta2(0.25)

# Convert multiple values
cohensf_to_peta2(c(0.1, 0.25, 0.4))

Convert Partial Eta Squared to Cohen's f

Description

Converts partial eta squared (\eta_p^2) to Cohen's f using the standard definition in Cohen (1988).

Usage

peta2_to_cohensf(peta2)

Arguments

Details

The conversion is defined as:

f = \sqrt{\eta_p^2 / (1 - \eta_p^2)}

This follows from the inverse relationship:

\eta_p^2 = \frac{f^2}{1 + f^2}

Value

A numeric vector of Cohen's f values.

References

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

See Also

cohensf_to_peta2

Examples

# Convert a single partial eta squared value
peta2_to_cohensf(0.06)

# Convert multiple values
peta2_to_cohensf(c(0.01, 0.06, 0.14))

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

Description

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

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.

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.

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)

# 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)

Power Analysis for Planned Contrast in Between- or Within-Factor ANOVA

Description

Computes power, required total sample size, alpha, or minimal detectable effect size for a single planned contrast (1 df) in between-participants or paired/repeated-measures settings.

Usage

pwrcontrast(
  weight = NULL,
  paired = FALSE,
  n_total = NULL,
  cohensf = NULL,
  peta2 = NULL,
  alpha = NULL,
  power = NULL,
  nlim = c(2, 10000)
)

Arguments

Details

For a contrast with weights w_1, \dots, w_K that sum to zero, the numerator df is 1. The denominator df is n - K for between-subjects (unpaired) designs and (n - 1)(K - 1) for paired/repeated-measures designs. Power uses the noncentral F-with \lambda = f^2 \cdot n_{\mathrm{total}}.

• Contrast weights (weight) are not centered internally; only the zero-sum condition is enforced (up to numerical tolerance).

• When paired = FALSE, the total sample size n_total must be a multiple of the number of contrast groups K.

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

• Critical values are computed from the central F-distribution; power is based on 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.

Value

A one-row data frame with class:

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

• "cal_n" when n_total is solved;

• "cal_alpha" when alpha is solved;

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

Columns: term (always "contrast"), weight (comma-separated string), df_num, df_denom, n_total, alpha, power, cohensf, peta2, F_critical, ncp.

References

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

Examples

# Two-group contrast (1, -1), between-subjects: compute power
pwrcontrast(weight = c(1, -1), paired = FALSE,
            n_total = 40, cohensf = 0.25, alpha = 0.05)

# Four-level contrast (e.g., Helmert-like), solve required N for target power
pwrcontrast(weight = c(3, -1, -1, -1), paired = FALSE,
            n_total = NULL, peta2 = 0.06, alpha = 0.05, power = 0.80)

# Paired contrast across K=3 conditions
pwrcontrast(weight = c(1, 0, -1), paired = TRUE,
            n_total = NULL, cohensf = 0.2, alpha = 0.05, power = 0.9)

Power Analysis for Pearson Correlation

Description

Computes statistical power, required total sample size, \alpha, or the minimal detectable correlation coefficient for a Pearson correlation test. Two computational methods are supported: exact noncentral t (method = "t") and Fisher's z-transformation with normal approximation (method = "z").

Usage

pwrcortest(
  alternative = c("two.sided", "one.sided"),
  n_total = NULL,
  alpha = NULL,
  power = NULL,
  rho = NULL,
  method = c("t", "z"),
  bias_correction = FALSE,
  nlim = c(2, 10000)
)

Arguments

Details

• Exactly one of n_total, rho, alpha, or power must be NULL; that quantity is then solved.

• For method = "t", computations are based on the noncentral t-distribution with noncentrality parameter \lambda = \tfrac{\rho}{\sqrt{1-\rho^2}} \sqrt{n}.

• For method = "z", computations use Fisher's z transformation of the population correlation, z_\rho = \operatorname{atanh}(\rho). Let W = \sqrt{n-3}\, z. Under the alternative hypothesis, W \sim \mathrm{Normal}(\mu,\,1) with \mu = \sqrt{n-3}\, z_\rho. If bias_correction = TRUE, \rho is first bias-corrected before applying Fisher's transform. Critical values are taken from the central normal distribution under H_0:\rho=0 (i.e., W \sim \mathrm{Normal}(0,1) under the null). The returned ncp equals \mu.

• Validation against GPower: Results have been confirmed to match those produced by GPower for equivalent correlation tests using the noncentral t-distribution.

• Note: Results from method = "z" will not exactly match pwr::pwr.r.test, because pwr uses a hybrid approach combining the Fisher-z approximation with a t-based critical value.

Value

A one-row data.frame with class "cal_power", "cal_n", "cal_alpha", or "cal_es", depending on the solved quantity. Columns:

• df (only for method = "t")

• n_total, alpha, power

• rho, t_critical or z_critical

• ncp (noncentrality parameter or mean under the alternative: see Details)

Examples

# (1) Compute power for rho = 0.3, N = 50, two-sided test
pwrcortest(alternative = "two.sided", n_total = 50, rho = 0.3, alpha = 0.05)

# (2) Solve required N for target power, using Fisher-z method
pwrcortest(method = "z", rho = 0.2, alpha = 0.05, power = 0.8)

# (3) Solve minimal detectable correlation
pwrcortest(n_total = 60, alpha = 0.05, power = 0.9, rho = NULL)

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

Description

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

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.

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.

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)

# (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)

# (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)

# (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)