3 Examples of Jonckheere-Terpstra Test

Explore practical examples of Jonckheere-Terpstra Test for non-parametric analysis.
By Jamie

Understanding the Jonckheere-Terpstra Test

The Jonckheere-Terpstra Test is a non-parametric statistical test used to determine whether there is a trend in the median values of different groups. This test is particularly useful when you have more than two groups and want to assess whether there is a consistent ordering among them. It is often utilized in scenarios where the assumptions of parametric tests, such as ANOVA, are not met. Below are three diverse examples that illustrate the application of the Jonckheere-Terpstra Test in real-world contexts.

Example 1: Educational Assessment Across Different Grades

Context

A school district wants to evaluate whether students’ test scores show a trend as they progress through different grades (1st to 5th). The goal is to determine if there is a significant increase in the median scores as students move up in grade level.

The Example

  1. Collect test scores from students in grades 1, 2, 3, 4, and 5.

  2. Organize the data:

    • Grade 1: [78, 82, 85, 80, 76]
    • Grade 2: [80, 85, 88, 82, 84]
    • Grade 3: [85, 87, 89, 90, 86]
    • Grade 4: [90, 92, 93, 91, 88]
    • Grade 5: [95, 97, 96, 94, 98]
  3. Perform the Jonckheere-Terpstra Test to assess the trend in median scores across grades.

Notes

  • The null hypothesis states that there is no trend in median scores across the grades.
  • If the p-value obtained from the test is less than the significance level (e.g., 0.05), we reject the null hypothesis, indicating a significant trend in scores.

Example 2: Evaluating Customer Satisfaction Levels Based on Service Types

Context

A restaurant chain wants to analyze customer satisfaction ratings for three different service types: dine-in, takeout, and delivery. They aim to determine if there is a consistent trend in customer satisfaction as the service type changes.

The Example

  1. Gather customer satisfaction ratings on a scale of 1 to 10 for each service type:

    • Dine-in: [8, 9, 7, 8, 6]
    • Takeout: [6, 7, 8, 5, 7]
    • Delivery: [9, 10, 8, 9, 9]
  2. Organize the ratings and apply the Jonckheere-Terpstra Test to see if customer satisfaction trends significantly across the service types.

Notes

  • The null hypothesis posits that there is no difference in median satisfaction ratings across the service types.
  • A significant result would indicate that customers’ satisfaction levels change consistently with the service type.

Example 3: Analyzing Blood Pressure Levels Among Different Age Groups

Context

A health study aims to investigate whether there is a trend in systolic blood pressure levels as individuals age. The researchers collect blood pressure readings from individuals across three age groups: 20-30, 31-40, and 41-50 years.

The Example

  1. Collect data on systolic blood pressure for each age group:

    • Age 20-30: [120, 122, 118, 121, 125]
    • Age 31-40: [130, 132, 134, 129, 131]
    • Age 41-50: [140, 142, 138, 135, 145]
  2. Use the Jonckheere-Terpstra Test to evaluate if there is a trend in median systolic blood pressure as age increases.

Notes

  • The null hypothesis claims there is no trend in blood pressure levels across age groups.
  • A low p-value would suggest that blood pressure tends to increase with age, indicating a significant trend.

By understanding these practical examples of the Jonckheere-Terpstra Test, researchers and analysts can effectively apply this non-parametric method to assess trends across multiple groups.