Analitica (version 2.2.0)

BonferroniTest: Bonferroni-Corrected Pairwise t-Tests v2.0

Description

Performs pairwise t-tests with Bonferroni adjustment for multiple comparisons. This method controls the family-wise error rate by dividing the alpha level by the number of comparisons.

Usage

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

Value

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

• Resultados: a data.frame with columns Comparacion, Diferencia, SE, t_value, p_value (unadjusted), p_ajustada (Bonferroni), 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: "Bonferroni-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.

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

Advantages: - Very simple and easy to implement. - Strong control of Type I error. - Applicable to any set of independent comparisons.

Disadvantages: - Highly conservative, especially with many groups. - Can lead to low statistical power (increased Type II error). - Does not adjust test statistics, only p-values.

References

Dunn, O. J. (1964). Multiple Comparisons Using Rank Sums. Technometrics, 6(3), 241–252. tools:::Rd_expr_doi("10.1080/00401706.1964.10490181")

Wilcoxon, F. (1945). Individual Comparisons by Ranking Methods. Biometrics Bulletin, 1(6), 80–83. tools:::Rd_expr_doi("10.2307/3001968")

Examples

#DCA
data(d_e, package = "Analitica")
mod1 <- aov(Sueldo_actual ~ as.factor(labor), data = d_e)
summary(mod1)
resultado <- BonferroniTest(mod1)
summary(resultado)

DBA: y ~ tratamiento + bloque
mod2 <- aov(Sueldo_actual ~ as.factor(labor) + Sexo, data = d_e)
res <- BonferroniTest(mod2, comparar = "as.factor(labor)")
summary(res); plot(res)

# DFactorial: y ~ A * B
mod2 <- aov(Sueldo_actual ~ as.factor(labor) * Sexo, data = d_e)
resAB <- BonferroniTest(mod2, comparar = c("as.factor(labor)","Sexo"))  # compara celdas A:B
summary(resAB, n = Inf); plot(resAB, horizontal = TRUE)