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Sign Test (S) Calculator

Non-parametric test for difference between two related groups.

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Overview

The Sign Test is a non-parametric statistical test used to determine the significance of differences between paired observations in a repeated measures design. It ignores the magnitude of differences and focuses exclusively on the direction of change, making it highly resistant to outliers.

Symbols

Variables

S = Sign Statistic, n_+ = Plus Signs, n_- = Minus Signs

Sign Statistic
Plus Signs
Minus Signs

Apply it well

When To Use

When to use: Use the Sign Test when analyzing ordinal data or non-normally distributed interval data within a related-samples design. It is ideal for small sample sizes or situations where the only reliable information is the direction of a change rather than its specific value.

Why it matters: In psychological research, it provides a simple yet robust method to verify if a treatment or intervention consistently affects participants. It is often used as a preliminary analysis to determine if a trend exists before applying more complex parametric tests.

Avoid these traps

Common Mistakes

  • Counting the most frequent sign instead of the least.

One free problem

Practice Problem

A clinical psychologist observes 15 patients after a new therapy session. 12 patients reported a decrease in anxiety levels (negative signs) while 3 reported an increase (positive signs). Calculate the Sign Test statistic S.

Plus Signs3
Minus Signs12

Solve for:

Hint: The test statistic S is the minimum value between the count of positive and negative changes.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Sign test
  2. Discovering Statistics Using IBM SPSS Statistics (Andy Field)
  3. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE Publications.
  4. Aron, A., Aron, E. N., & Coups, E. J. (2013). Statistics for Psychology (6th ed.). Pearson.
  5. Gravetter and Wallnau Statistics for the Behavioral Sciences
  6. Field Discovering Statistics Using IBM SPSS Statistics
  7. A-Level Psychology — Research Methods / Statistics