SidakTest: Sidak Test for Multiple Comparisons v2.0

In Analitica: Exploratory Data Analysis, Group Comparison Tools, and Other Procedures

Sidak Test for Multiple Comparisons v2.0

Description

Performs pairwise comparisons using the Sidak correction to adjust p-values and control the family-wise error rate in multiple testing scenarios. This method assumes independence between comparisons and is slightly less conservative than Bonferroni.

Usage

SidakTest(modelo, comparar = NULL, alpha = 0.05)

Arguments

modelo	An aov or lm object (full model: includes blocks, factors, etc.).
comparar	Character vector with the name(s) of the factor(s) to compare: - One name: main effect (e.g., "treatment" or "A") - Several names: interaction (e.g., c("A","B") for A:B) If omitted, it uses the first factor in modelo$xlevels.
alpha	Significance level (default 0.05).

Details

The Sidak procedure adjusts the significance level to maintain an overall alpha across all pairwise tests, providing an effective post hoc tool following ANOVA or similar global tests.

Advantages: - Controls the family-wise error rate under independence assumption. - Slightly more powerful than Bonferroni. - Simple to compute and interpret.

Disadvantages: - Assumes independence of tests (may not hold in correlated data). - Less robust when variances are unequal or data are non-normal.

Value

An object of class "sidak" and "comparaciones" containing:

• Resultados: a data.frame with columns Comparacion, Diferencia, SE, t_value, p_value (unadjusted), p_ajustada (Sidak), Valor_Critico (critical difference), and Significancia.

• Promedios: a named vector of group means as defined by comparar.

• Orden_Medias: group names ordered from highest to lowest mean.

• Metodo: "Sidak-adjusted t-test".

• Termino: the term being compared (e.g., "A", "B", or "A:B").

• MSerror, df_error, N: useful for plots with error bars.

References

Sidak, Z. (1967). "Rectangular confidence regions for the means of multivariate normal distributions." Journal of the American Statistical Association, 62(318), 626–633.

Examples

data(d_e, package = "Analitica")
mod <- aov(Sueldo_actual ~ as.factor(labor), data = d_e)
resultado <- SidakTest(mod)
summary(resultado)
plot(resultado)

# RCBD
mod <- aov(Sueldo_actual ~ as.factor(labor) + Sexo, data = d_e)
res <- SidakTest(mod, comparar = "as.factor(labor)")
summary(res); plot(res)                      # plot usara p_value

# Factorial
mod2 <- aov(Sueldo_actual ~ as.factor(labor) * Sexo, data = d_e)
resAB <- SidakTest(mod2, comparar = c("as.factor(labor)","Sexo"))
summary(resAB, n = Inf); plot(resAB, horizontal = TRUE)

Analitica documentation built on Nov. 5, 2025, 5:13 p.m.