JT_Test: Jonckheere-Terpstra Test for Ordered Alternatives (with Tie...

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

Jonckheere-Terpstra Test for Ordered Alternatives (with Tie Correction)

Description

Performs the Jonckheere-Terpstra test to evaluate the presence of a monotonic trend (increasing or decreasing) across three or more independent ordered groups. This test is non-parametric and is particularly useful when the independent variable is ordinal and the response is continuous or ordinal.

Usage

JT_Test(formula, data)

Arguments

formula	A formula of the type y ~ group, where 'group' is an ordered factor.
data	A data.frame containing the variables in the formula.

Details

The Jonckheere-Terpstra test compares all pairwise combinations of groups and counts the number of times values in higher-ordered groups exceed those in lower-ordered groups. This implementation includes a full correction for ties in the data, which ensures more accurate inference.

Advantages: - Non-parametric: does not assume normality or equal variances. - More powerful than Kruskal-Wallis when there is an a priori ordering of groups. - Tie correction included, improving robustness in real-world data.

Disadvantages: - Requires that the group variable be ordered (ordinal). - Detects overall trend but not specific group differences. - Sensitive to large numbers of ties or very unbalanced group sizes.

Value

An object of class "jonckheere" with:

• J: Total Jonckheere-Terpstra statistic.

• J_pares: Pairwise J statistics between group combinations.

• mu_J: Expected value of J under the null hypothesis.

• var_J: Variance of J (with complete tie correction).

• Z: Standardized test statistic.

• p_value: Two-sided p-value.

• Trend: Detected trend ("increasing", "decreasing", or "none").

• Method: Description of the method.

References

Hollander, M., Wolfe, D. A., & Chicken, E. (2014). Nonparametric statistical methods. p. 202 (3rd ed.). Wiley.

Examples

df <- data.frame(
  group = factor(rep(1:3, each = 6), ordered = TRUE),
  y = c(40,35,38,43,44,41,38,40,47,44,40,42,48,40,45,43,46,44)
)
res <- JT_Test(y ~ group, data = df)

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