Definition:Jonckheere-Terpstra Test

Definition

The Jonckheere-Terpstra test is a non-parametric test where:

the null hypothesis $H_0$ is that three or more independent samples all come from the same population

the alternative hypothesis $H_1$ is that their means $\mu_i$ taken in order show a monotonic trend.

That is:

$H_0$: that $\mu_1 = \mu_2 = \cdots = \mu_k$

against:

$H_1$: that either:

$\mu_1 \le \mu_2 \le \cdots \le \mu_k$

or:

$\mu_1 \ge \mu_2 \ge \cdots \ge \mu_k$

in which at least one of the inequalities is strict.

Also known as

The Jonckheere-Terpstra test is also known as the Jonckheere trend test.

Also see

• Results about the Jonckheere-Terpstra test can be found here.

Source of Name

This entry was named for Aimable Robert Jonckheere and T.J. Terpstra.

Historical Note

The Jonckheere-Terpstra test was devised in $1952$ by T.J. Terpstra, and again independently in $1954$ by Aimable Robert Jonckheere.

Sources

• 1952: T.J. Terpstra: The asymptotic normality and consistency of Kendall's test against trend, when ties are present in one ranking (Indag. Math. Vol. 14: pp. 327 – 333)
• 1954: A.R. Jonckheere: A distribution-free k-sample test against ordered alternatives (Biometrika Vol. 41: pp. 133 – 145)  www.jstor.org/stable/2333011

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Jonckheere-Terpstra test