r_effect: r-family effect size wrapper

In MOTE: Effect Size and Confidence Interval Calculator

r-family effect size wrapper

Description

This function provides a unified interface for computing r- and variance-based effect sizes (e.g., correlations and coefficients of determination) from different input summaries. It is analogous to the d_effect() wrapper for standardized mean difference effect sizes.

Usage

r_effect(
  d = NULL,
  n1 = NULL,
  n2 = NULL,
  r = NULL,
  n = NULL,
  x2 = NULL,
  c = NULL,
  dfm = NULL,
  dfe = NULL,
  msm = NULL,
  mse = NULL,
  mss = NULL,
  sst = NULL,
  ssm = NULL,
  ssm2 = NULL,
  sss = NULL,
  sse = NULL,
  sse1 = NULL,
  sse2 = NULL,
  sse3 = NULL,
  j = NULL,
  f_value = NULL,
  a = 0.05,
  design,
  ...
)

Arguments

d	Cohen's d value for the contrast of interest (used when 'design = "d_to_r"').
n1	Sample size for group one (used when 'design = "d_to_r"').
n2	Sample size for group two (used when 'design = "d_to_r"').
r	Sample Pearson correlation coefficient (used when 'design = "r_correl"'), or the number of rows in the contingency table (used when 'design = "v_chi_sq"').
n	Sample size for the correlation (used when 'design = "r_correl"'), the total sample size for the chi-square test (used when 'design = "v_chi_sq"'), or the total sample size for the ANOVA (used when 'design = "omega_f"' or 'design = "omega_partial_ss_bn"').
x2	Chi-square test statistic for the contingency table (used when 'design = "v_chi_sq"').
c	Number of columns in the contingency table (used when 'design = "v_chi_sq"').
dfm	Degrees of freedom for the model term (used when 'design = "epsilon_full_ss"', 'design = "eta_f"', 'design = "omega_f"', 'design = "omega_full_ss"', 'design = "omega_partial_ss_bn"', 'design = "eta_full_ss"', 'design = "eta_partial_ss"', 'design = "ges_partial_ss_mix"', 'design = "ges_partial_ss_rm"', 'design = "omega_partial_ss_rm"', or 'design = "omega_g_ss_rm"').
dfe	Degrees of freedom for the error term (used when 'design = "epsilon_full_ss"', 'design = "eta_f"', 'design = "omega_f"', 'design = "omega_full_ss"', 'design = "omega_partial_ss_bn"', 'design = "eta_full_ss"', 'design = "eta_partial_ss"', 'design = "ges_partial_ss_mix"', 'design = "ges_partial_ss_rm"', 'design = "omega_partial_ss_rm"', or 'design = "omega_g_ss_rm"').
msm	Mean square for the model (used when 'design = "epsilon_full_ss"', 'design = "omega_full_ss"', 'design = "omega_partial_ss_bn"', or 'design = "omega_partial_ss_rm"').
mse	Mean square for the error (used when 'design = "epsilon_full_ss"', 'design = "omega_full_ss"', 'design = "omega_partial_ss_bn"', or 'design = "omega_partial_ss_rm"').
mss	Mean square for the subject or between-subjects term (used when 'design = "omega_partial_ss_rm"').
sst	Total sum of squares for the outcome (used when 'design = "epsilon_full_ss"', 'design = "omega_full_ss"', or 'design = "omega_g_ss_rm"').
ssm	Sum of squares for the model term (used when 'design = "eta_full_ss"', 'design = "eta_partial_ss"', 'design = "ges_partial_ss_mix"', 'design = "ges_partial_ss_rm"', 'design = "omega_partial_ss_bn"', 'design = "omega_partial_ss_rm"', or 'design = "omega_g_ss_rm"').
ssm2	Sum of squares for a second model or component term (used when 'design = "omega_g_ss_rm"').
sss	Sum of squares for the subject or between-subjects term (used when 'design = "ges_partial_ss_mix"', 'design = "ges_partial_ss_rm"', or 'design = "omega_partial_ss_rm"').
sse	Sum of squares for the error term (used when 'design = "eta_partial_ss"', 'design = "ges_partial_ss_mix"', or 'design = "omega_partial_ss_rm"').
sse1	Sum of squares for the first error term (used when 'design = "ges_partial_ss_rm"').
sse2	Sum of squares for the second error term (used when 'design = "ges_partial_ss_rm"').
sse3	Sum of squares for the third error term (used when 'design = "ges_partial_ss_rm"').
j	Number of levels for the factor (used when 'design = "omega_g_ss_rm"').
f_value	F statistic for the model term (used when 'design = "eta_f"', 'design = "eta_full_ss"', 'design = "eta_partial_ss"', 'design = "ges_partial_ss_mix"', 'design = "ges_partial_ss_rm"', 'design = "omega_f"', or 'design = "omega_g_ss_rm"').
a	Significance level used for confidence intervals. Defaults to 0.05.
design	Character string indicating which r-family effect size design to use. See **Supported designs**.
...	Additional arguments for future methods (currently unused).

Details

Currently, ‘r_effect()' supports effect sizes derived from Cohen’s d, from correlations, and from ANOVA summaries via several designs (see **Supported designs**). These designs call lower-level functions as [d_to_r()], [r_correl()], [epsilon_full_ss()], [eta_f()], [omega_f()], [omega_full_ss()], [eta_full_ss()], [eta_partial_ss()], [ges_partial_ss_mix()], [ges_partial_ss_rm()], [omega_partial_ss_rm()], and [omega_g_ss_rm()] with the appropriate arguments.

Value

A list whose structure depends on the selected design. For 'design = "d_to_r"', the returned object is the same as from [d_to_r()].

Supported designs

- '"d_to_r"' — correlation and R^2 from Cohen's d for independent groups. Supply 'd', 'n1', and 'n2'. In this case, 'r_effect()' will call [d_to_r()] with the same arguments.

- '"r_correl"' — correlation and R^2 from a sample Pearson correlation. Supply 'r' and 'n'. In this case, 'r_effect()' will call [r_correl()] with the same arguments.

- ‘"v_chi_sq"' — Cramer’s V from a chi-square test of association for an r x c contingency table. Supply 'x2', 'n', 'r', and 'c'. In this case, 'r_effect()' will call [v_chi_sq()] with the same arguments.

- '"epsilon_full_ss"' — epsilon-squared (\epsilon^2) from an ANOVA table using model and error mean squares and the total sum of squares. Supply 'dfm', 'dfe', 'msm', 'mse', and 'sst'. In this case, 'r_effect()' will call [epsilon_full_ss()] with the same arguments.

- '"eta_f"' — eta-squared (\eta^2) from an ANOVA F statistic and its associated degrees of freedom. Supply 'dfm', 'dfe', and 'f_value'. In this case, 'r_effect()' will call [eta_f()] with the same arguments.

- '"omega_f"' — omega-squared (\omega^2) from an ANOVA F statistic, its associated degrees of freedom, and the total sample size. Supply 'dfm', 'dfe', 'n', and 'f_value'. In this case, 'r_effect()' will call [omega_f()] with the same arguments.

- '"omega_full_ss"' — omega-squared (\omega^2) from ANOVA sums of squares, using the model mean square, error mean square, and total sum of squares along with the model and error degrees of freedom. Supply 'dfm', 'dfe', 'msm', 'mse', and 'sst'. In this case, 'r_effect()' will call [omega_full_ss()] with the same arguments.

- '"omega_partial_ss_bn"' — partial omega-squared (\omega^2_p) for between-subjects designs, using the model mean square, error mean square, model sum of squares, and total sample size along with the model and error degrees of freedom. Supply 'dfm', 'dfe', 'msm', 'mse', 'ssm', and 'n'. In this case, 'r_effect()' will call [omega_partial_ss_bn()] with the same arguments.

- '"eta_full_ss"' — eta-squared (\eta^2) from ANOVA sums of squares, using the model sum of squares and total sum of squares along with the model and error degrees of freedom. Supply 'dfm', 'dfe', 'ssm', 'sst', and 'f_value'. In this case, 'r_effect()' will call [eta_full_ss()] with the same arguments.

- '"eta_partial_ss"' — partial eta-squared (\eta^2_p) from ANOVA sums of squares, using the model sum of squares and error sum of squares along with the model and error degrees of freedom. Supply 'dfm', 'dfe', 'ssm', 'sse', and 'f_value'. In this case, 'r_effect()' will call [eta_partial_ss()] with the same arguments.

- '"ges_partial_ss_mix"' — partial generalized eta-squared (\eta^2_{G}) for mixed designs, using the model sum of squares, between-subjects sum of squares, and error sum of squares along with the model and error degrees of freedom. Supply 'dfm', 'dfe', 'ssm', 'sss', 'sse', and 'f_value'. In this case, 'r_effect()' will call [ges_partial_ss_mix()] with the same arguments.

- '"ges_partial_ss_rm"' — partial generalized eta-squared (\eta^2_{G}) for repeated-measures designs, using the model sum of squares, between-subjects sum of squares, and multiple error sums of squares (e.g., for each level or effect) along with the model and error degrees of freedom. Supply 'dfm', 'dfe', 'ssm', 'sss', 'sse1', 'sse2', 'sse3', and 'f_value'. In this case, 'r_effect()' will call [ges_partial_ss_rm()] with the same arguments.

- '"omega_partial_ss_rm"' — partial omega-squared (\omega^2_p) for repeated-measures designs, using the model, subject, and error sums of squares and their associated mean squares along with the model and error degrees of freedom. Supply 'dfm', 'dfe', 'msm', 'mse', 'mss', 'ssm', 'sse', and 'sss'. In this case, 'r_effect()' will call [omega_partial_ss_rm()] with the same arguments.

- '"omega_g_ss_rm"' — generalized omega-squared (\omega^2_G) for repeated-measures or mixed designs, using sums of squares for the model, an additional model/component term, and the total sum of squares, along with the mean square for the subject term and the number of levels for the factor. Supply 'dfm', 'dfe', 'ssm', 'ssm2', 'sst', 'mss', 'j', and 'f_value'. In this case, 'r_effect()' will call [omega_g_ss_rm()] with the same arguments.

Examples

# From Cohen's d for independent groups to r and R^2
r_effect(d = -1.88, n1 = 4, n2 = 4, a = .05, design = "d_to_r")
# From a sample correlation to r and R^2
r_effect(r = -0.8676594, n = 32, a = .05, design = "r_correl")
# From a chi-square test of association to Cramer's V
r_effect(x2 = 2.0496, n = 60, r = 3, c = 3, a = .05, design = "v_chi_sq")
# From F and degrees of freedom to eta^2
r_effect(dfm = 2, dfe = 8, f_value = 5.134, a = .05, design = "eta_f")
# From F, degrees of freedom, and N to omega^2
r_effect(dfm = 2, dfe = 8, n = 11, f_value = 5.134,
a = .05, design = "omega_f")
# From sums of squares to omega^2
r_effect(
  dfm   = 2,
  dfe   = 8,
  msm   = 12.621,
  mse   = 2.548,
  sst   = (25.54 + 19.67),
  a     = .05,
  design = "omega_full_ss"
)
# From sums of squares to partial eta^2
r_effect(
  dfm    = 4,
  dfe    = 990,
  ssm    = 338057.9,
  sse    = 32833499,
  f_value = 2.548,
  a      = .05,
  design = "eta_partial_ss"
)
# From mixed-design sums of squares to partial generalized eta^2
r_effect(
  dfm     = 1,
  dfe     = 156,
  ssm     = 71.07608,
  sss     = 30936.498,
  sse     = 8657.094,
  f_value = 1.280784,
  a       = .05,
  design  = "ges_partial_ss_mix"
)

# From repeated-measures sums of squares to partial generalized eta^2
r_effect(
  dfm     = 1,
  dfe     = 157,
  ssm     = 2442.948,
  sss     = 76988.13,
  sse1    = 5402.567,
  sse2    = 8318.75,
  sse3    = 6074.417,
  f_value = 70.9927,
  a       = .05,
  design  = "ges_partial_ss_rm"
)

# From repeated-measures sums of squares to partial omega^2_p
r_effect(
  dfm   = 1,
  dfe   = 157,
  msm   = 2442.948 / 1,
  mse   = 5402.567 / 157,
  mss   = 76988.130 / 157,
  ssm   = 2442.948,
  sss   = 76988.13,
  sse   = 5402.567,
  a     = .05,
  design = "omega_partial_ss_rm"
)

# From repeated-measures sums of squares to generalized omega^2_G
r_effect(
  dfm     = 1,
  dfe     = 156,
  ssm     = 6842.46829,
  ssm2    = 14336.07886,
  sst     = sum(c(30936.498, 6842.46829,
                  14336.07886, 8657.094, 71.07608)),
  mss     = 30936.498 / 156,
  j       = 2,
  f_value = 34.503746,
  a       = .05,
  design  = "omega_g_ss_rm"
)

MOTE documentation built on Dec. 15, 2025, 9:06 a.m.