Analitica (version 2.2.0)

T2Test: Tamhane's T2 Post Hoc Test v2.2.0

Description

Performs the Tamhane T2 test for pairwise comparisons after an ANOVA model, assuming unequal variances and/or unequal sample sizes. This test is appropriate when the assumption of homogeneity of variances is violated, such as when Levene's test or Bartlett's test is significant.

Usage

T2Test(modelo, comparar = NULL, alpha = 0.05)

Value

An object of class "tamhanet2" and "comparaciones", containing:

• Resultados: A data frame with pairwise comparisons, mean differences, t_value, gl, p_value, and significance codes.

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

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

• Metodo: A character string indicating the method used ("Tamhane T2").

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

Arguments

modelo

An object of class aov or lm (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 is 0.05).

Details

The test uses a modified t-test with Welch-Satterthwaite degrees of freedom and a conservative approach to control for multiple comparisons.

Advantages: - Controls Type I error under heteroscedasticity. - No assumption of equal sample sizes.

Disadvantages: - Conservative; may reduce power. - Not as powerful as Games-Howell in some contexts.

References

Tamhane, A. C. (1977). "Multiple comparisons in model I one-way ANOVA with unequal variances." Communications in Statistics - Theory and Methods, 6(1), 15–32. <https://doi.org/10.1080/03610927708827524>

Examples

data(d_e, package = "Analitica")
mod <- aov(Sueldo_actual ~ as.factor(labor), data = d_e)
resultado <- T2Test(mod)
summary(resultado)
plot(resultado)

# Con bloques, comparando solo el factor de interés
mod2 <- aov(Sueldo_actual ~ as.factor(labor) + Sexo, data = d_e)
res2 <- T2Test(mod2, comparar = "as.factor(labor)")
summary(res2)
plot(res2)

# Modelo con interacción
mod3 <- aov(Sueldo_actual ~ as.factor(labor) * Sexo, data = d_e)
res3 <- T2Test(mod3, comparar = c("as.factor(labor)", "Sexo"))
summary(res3)
plot(res3)