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Chi-Square Test (X²) Calculator

Difference between observed and expected frequencies.

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Chi-Square

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Overview

The Chi-Square test is a non-parametric statistical method used to evaluate the significance of the difference between observed frequencies and expected frequencies in categorical data. In psychology, it is a foundational tool for determining if the distribution of certain behaviors or traits deviates significantly from a theoretical or null hypothesis distribution.

Symbols

Variables

\chi^2 = Chi-Square, O = Observed, E = Expected

Chi-Square
Observed
Expected

Apply it well

When To Use

When to use: Apply this test when analyzing nominal or ordinal data where you need to compare actual counts against a predicted model. It assumes that observations are independent and that the expected frequency in each category is at least 5 for the results to be statistically valid.

Why it matters: It allows psychologists to conclude whether experimental results, such as the preference for a specific therapy, are due to chance or a genuine underlying effect. This helps in validating theories regarding social behavior, personality distributions, and survey results in diverse populations.

Avoid these traps

Common Mistakes

  • Using percentages instead of raw frequencies.
  • Incorrectly calculating degrees of freedom.

One free problem

Practice Problem

A clinical psychologist expects 10 patients to select a specific coping mechanism based on a baseline study. If 15 patients actually select that mechanism, what is the Chi-Square contribution (X²) for this specific category?

Observed15
Expected10

Solve for:

Hint: Subtract the expected value from the observed value, square the result, and then divide by the expected value.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the Behavioral Sciences (10th ed.). Cengage Learning.
  2. Wikipedia: Chi-squared test
  3. Discovering Statistics Using IBM SPSS Statistics (Field, A.)
  4. Statistics for Psychology (Aron, A., Aron, E., Coups, E.)
  5. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE Publications.
  6. A-Level Psychology — Research Methods / Statistics