Examples of Sign Test Example

Understanding the Sign Test

The Sign Test is a non-parametric statistical method used to determine whether there is a significant difference between the medians of two related groups. It is particularly useful when the data does not meet the assumptions required for parametric tests, such as normality. This test is based on the direction of differences rather than their magnitude, making it suitable for ordinal data or non-normally distributed interval data.

Here are three diverse, practical examples of the Sign Test in action:

Example 1: Evaluating a New Medication’s Effectiveness

In a clinical trial, researchers want to assess the effectiveness of a new medication compared to a placebo. They select a group of patients suffering from a particular condition and measure their symptoms intensity on a scale from 1 to 10 before and after treatment.

The data is summarized as follows:

• Before Treatment: [5, 7, 6, 4, 8]
• After Treatment: [3, 5, 4, 3, 6]

To perform the Sign Test:

1. Calculate the difference for each patient:

• Patient 1: 5 - 3 = 2 (Positive)
• Patient 2: 7 - 5 = 2 (Positive)
• Patient 3: 6 - 4 = 2 (Positive)
• Patient 4: 4 - 3 = 1 (Positive)

• Patient 5: 8 - 6 = 2 (Positive)

  2. Count the number of positive and negative differences:

• Positive: 5, Negative: 0

  3. Since all differences are positive, we can conclude that the new medication significantly reduced symptom intensity compared to the placebo.

Notes: The Sign Test can be conducted using a binomial distribution to determine the significance level, considering the total number of paired observations.

Example 2: Analyzing Customer Satisfaction Before and After Service Changes

A restaurant implements several changes to improve customer satisfaction, such as menu updates and staff training. To evaluate the impact of these changes, they collect customer satisfaction ratings on a scale from 1 to 10 before and after the changes.

The ratings are as follows:

• Before Changes: [7, 6, 8, 5, 4]
• After Changes: [8, 7, 9, 6, 5]

Using the Sign Test:

1. Calculate the differences:

• Customer 1: 7 - 8 = -1 (Negative)
• Customer 2: 6 - 7 = -1 (Negative)
• Customer 3: 8 - 9 = -1 (Negative)
• Customer 4: 5 - 6 = -1 (Negative)

• Customer 5: 4 - 5 = -1 (Negative)

  2. Count the differences:

• Positive: 0, Negative: 5

  3. All customers reported lower satisfaction after the changes, suggesting that the implemented changes did not improve customer satisfaction.

Notes: The Sign Test is particularly useful here, as it allows the restaurant to make evidence-based decisions regarding their service strategies without assuming a normal distribution of ratings.

Example 3: Pre- and Post-Test Scores in an Educational Study

An educator wants to evaluate the effectiveness of a new teaching method. They administer a test to a group of students before and after the method is implemented, recording their scores.

The data is as follows:

• Pre-Test Scores: [78, 82, 75, 90, 85]
• Post-Test Scores: [85, 88, 80, 95, 90]

To apply the Sign Test:

1. Compute the differences:

• Student 1: 78 - 85 = -7 (Negative)
• Student 2: 82 - 88 = -6 (Negative)
• Student 3: 75 - 80 = -5 (Negative)
• Student 4: 90 - 95 = -5 (Negative)

• Student 5: 85 - 90 = -5 (Negative)

  2. Count the differences:

• Positive: 0, Negative: 5

  3. All students scored lower on the pre-test, indicating that the new teaching method has a positive effect on student learning outcomes.

Notes: The Sign Test here demonstrates the effectiveness of a teaching method, allowing educators to assess pedagogical strategies based on student performance data.