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