Determine the necessary per-group sample size to achieve a desired level of statistical power for the test of a single planned (unstandardized) contrast on the adjusted means in a one-way analysis of covariance, or, given a per-group sample size, return the realized statistical power.
ss_power_c_ancova(
psi,
c_weights,
sigma,
rho,
desired_power = 0.85,
alpha_level = 0.05,
n = NULL,
directional = FALSE
)A data.frame with rows for necessary_n_per_group (or
specified_n_per_group), actual_power, and noncentral_t_parm.
The result carries the dmar_ss_power class, so
The population unstandardized contrast effect on the adjusted means, \(\psi = \sum c_j \mu^{(adj)}_j\)
Vector of contrast weights (must sum to zero); use fractional weights so the positive weights sum to 1
Within-group population standard deviation of the response (the same \(\sigma\) as in a one-way ANOVA on the response)
Within-group population correlation between the response and the covariate; must lie in (-1, 1)
Desired statistical power (default 0.85)
Type I error rate (default 0.05)
Per-group sample size (assumed balanced); if specified, returns the realized power
Logical: TRUE for a one-sided test (in the same sign as psi), FALSE (default) for a two-sided test
Ken Kelley [email protected]
This function uses the standard large-sample formulation in which the ANCOVA error variance is \(\sigma^2_{adj} = \sigma^2 (1 - \rho^2)\), the contrast t-statistic has degrees of freedom \(N - J - 1\) (one less than the corresponding ANOVA contrast because of the covariate), and the noncentrality parameter is \(\lambda = \psi / (\sigma \sqrt{1 - \rho^2} \sqrt{\sum c_j^2 / n})\). This assumes the covariate means are equal across groups (the typical assumption under random assignment); for designs with substantial group differences in the covariate, the small-sample correction \(1 + (\bar X_{j} - \bar X_{\cdot})^2 / SS^{(within)}_X\) would slightly inflate the standard error and reduce power, an effect that is negligible for moderate or large \(n\).
Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge.
Lai, K., & Kelley, K. (2012). Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: Sample size planning via narrow confidence intervals. British Journal of Mathematical and Statistical Psychology, 65, 350--370. tools:::Rd_expr_doi("10.1111/j.2044-8317.2011.02029.x")
ss_power_c, ci_c_ancova, ss_aipe_c_ancova
design_consequences for what a chosen design delivers:
power, the Type S (sign) and Type M (exaggeration) errors of the
significance filter, and the expected confidence interval width.
Other sample size for power:
power_fisher_exact(),
ss_aipe_mixed_effects(),
ss_power_R2(),
ss_power_R2_sensitivity(),
ss_power_c(),
ss_power_composite_ancova(),
ss_power_composite_ancova_2group(),
ss_power_composite_anova(),
ss_power_composite_factorial_ancova(),
ss_power_composite_factorial_ancova_het(),
ss_power_composite_factorial_anova(),
ss_power_composite_sem(),
ss_power_contrast(),
ss_power_equivalence_c(),
ss_power_factorial_ancova(),
ss_power_factorial_anova(),
ss_power_indirect_effect(),
ss_power_mixed_effects(),
ss_power_one_way_anova(),
ss_power_pcm(),
ss_power_r(),
ss_power_rc(),
ss_power_reg_coef(),
ss_power_reg_coef_sensitivity(),
ss_power_rm_anova(),
ss_power_sc(),
ss_power_sem(),
ss_power_smd(),
ss_power_split_plot_anova()
# Same population contrast as in the ANOVA example, with rho = 0.5 between
# outcome and covariate; ANCOVA is more efficient than ANOVA here.
ss_power_c_ancova(psi = 0.5, c_weights = c(0.5, 0.5, -0.5, -0.5),
sigma = 1, rho = 0.5, desired_power = 0.80)
# Realized power for n = 30 per group
ss_power_c_ancova(psi = 0.5, c_weights = c(0.5, 0.5, -0.5, -0.5),
sigma = 1, rho = 0.5, n = 30)
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