Chi-Square Test Calculator

Chi-Square Test is evaluated from Observed Frequencies and Expected Frequencies. The calculation reports Chi-Square Statistic, Degrees of Freedom and Total Observations.

Results

Thanks — we’ve logged this for review.

About the Chi-Square Test Calculator

Chi-Square Test is treated here as a quantitative relation between Observed Frequencies and Expected Frequencies and Chi-Square Statistic, Degrees of Freedom, Total Observations and Conclusion.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Each category contributes (O - E)^2/E to the sum. Large χ^2 means observed counts differ greatly from expected. Compare to critical value from chi-square distribution table at the chosen α.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Each category contributes (O - E)^2/E to the sum. Large χ^2 means observed counts differ greatly from expected. Compare to critical value from chi-square distribution table at the chosen α.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Dice fairness test (6 faces, 120 rolls)

Inputs

observed: 22, 17, 25, 18, 21, 17 expected: 20, 20, 20, 20, 20, 20
Chi-Square Statistic: 2.6. Degrees of Freedom: 5. Total Observations: 120. Conclusion: Fail to reject H₀ - no significant difference (p >= 0.05)

With Observed Frequencies = 22, 17, 25, 18, 21, 17 and Expected Frequencies = 20, 20, 20, 20, 20, 20 as the stated inputs, the result is Chi-Square Statistic = 2.6, Degrees of Freedom = 5 and Total Observations = 120. Each value corresponds to the declared output fields.

Example 2: Survey: color preference (marketing research)

Inputs

observed: 50, 60, 40, 30 expected: 45, 55, 45, 35
Chi-Square Statistic: 2.2799. Degrees of Freedom: 3. Total Observations: 180. Conclusion: Fail to reject H₀ - no significant difference (p >= 0.05)

With Observed Frequencies = 50, 60, 40, 30 and Expected Frequencies = 45, 55, 45, 35 as the stated inputs, the result is Chi-Square Statistic = 2.2799, Degrees of Freedom = 3 and Total Observations = 180. Each value corresponds to the declared output fields.

Example 3: Political polling: expected vs observed vote shares

Inputs

observed: 320, 280, 100 expected: 300, 300, 100
Chi-Square Statistic: 2.6667. Degrees of Freedom: 2. Total Observations: 700. Conclusion: Fail to reject H₀ - no significant difference (p >= 0.05)

With Observed Frequencies = 320, 280, 100 and Expected Frequencies = 300, 300, 100 as the stated inputs, the result is Chi-Square Statistic = 2.6667, Degrees of Freedom = 2 and Total Observations = 700. Each value corresponds to the declared output fields.

Example 4: Genetics: Mendelian ratio test (pea plants)

Inputs

observed: 705, 224 expected: 698.25, 232.75
Chi-Square Statistic: 0.3942. Degrees of Freedom: 1. Total Observations: 929. Conclusion: Fail to reject H₀ - no significant difference (p >= 0.05)

With Observed Frequencies = 705, 224 and Expected Frequencies = 698.25, 232.75 as the stated inputs, the result is Chi-Square Statistic = 0.3942, Degrees of Freedom = 1 and Total Observations = 929. Each value corresponds to the declared output fields.

Common Use Cases

  • Test if observed frequencies differ from expected
  • Chi-square test of independence for categorical data
  • Goodness-of-fit test for statistics homework