## Jonckheere-Terpstra test :

The Jonckheere-Terpstra test is a non-parametric statistical test used to determine whether there is a monotonic trend in the median of a dependent variable as a function of an independent variable. A monotonic trend is a pattern in which the values of the dependent variable either consistently increase or consistently decrease as the values of the independent variable increase.

To conduct a Jonckheere-Terpstra test, the data must be ordinal, meaning that the values of the independent variable can be ranked or ordered. For example, if the independent variable is the level of education (with levels ranging from primary school to postgraduate degree), the data can be ordered by the level of education.

To conduct the test, the data are first sorted by the independent variable. The median of the dependent variable is then calculated for each unique value of the independent variable. The difference in the medians for each pair of consecutive values of the independent variable is then calculated. If there is a monotonic trend in the data, the differences in the medians will either consistently be positive or consistently be negative.

To determine whether there is a statistically significant monotonic trend in the data, the Jonckheere-Terpstra test calculates a test statistic and compares it to a critical value from a statistical table. If the test statistic is greater than the critical value, it indicates that there is a statistically significant monotonic trend in the data.

Here are two examples of how the Jonckheere-Terpstra test can be applied:

Examining the relationship between income level and job satisfaction

In this example, the independent variable is income level (ranging from low to high) and the dependent variable is job satisfaction (ranging from low to high). The data is first sorted by income level and the median job satisfaction is calculated for each unique income level. The differences in the medians for each pair of consecutive income levels are then calculated. If there is a monotonic trend in the data, the differences in the medians will either consistently be positive (indicating that job satisfaction increases as income level increases) or consistently be negative (indicating that job satisfaction decreases as income level increases).

The Jonckheere-Terpstra test is then used to determine whether there is a statistically significant monotonic trend in the data. If the test statistic is greater than the critical value, it indicates that there is a statistically significant relationship between income level and job satisfaction.

Evaluating the effectiveness of a training program

In this example, the independent variable is the type of training program (ranging from no training to intensive training) and the dependent variable is the performance improvement of employees (ranging from no improvement to significant improvement). The data is first sorted by the type of training program and the median performance improvement is calculated for each unique training program. The differences in the medians for each pair of consecutive training programs are then calculated. If there is a monotonic trend in the data, the differences in the medians will either consistently be positive (indicating that performance improvement increases as the type of training program increases) or consistently be negative (indicating that performance improvement decreases as the type of training program increases).

The Jonckheere-Terpstra test is then used to determine whether there is a statistically significant monotonic trend in the data. If the test statistic is greater than the critical value, it indicates that there is a statistically significant relationship between the type of training program and the performance improvement of employees.