MTMasterTool

Chi-Square Calculator

Calculate chi-square using your data.

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What this tool does

Calculate chi-square using your data. Goodness-of-fit test with independently observed categories and fixed expected totals; not a contingency-table independence test.

How to use the Chi-Square Calculator

  1. Enter or select observed, expected (one category per line).
  2. Enter or select parameters estimated from data.
  3. Read the calculated result; change any measurement to compare alternatives.

Formula

χ²=sum((observed−expected)²/expected); df=categories−1−estimated parameters; p=upper regularized gamma(df/2,χ²/2)
rows
Observed, expected (one category per line)
estimated
Parameters estimated from data

Goodness-of-fit test with independently observed categories and fixed expected totals; not a contingency-table independence test.

Worked example

For chi-square calculator, the following measurements illustrate the exact method: Observed, expected (one category per line): 20,25 30,25 25,25 25,25; Parameters estimated from data: 0.

Inputs

  • Observed, expected (one category per line)20,25 30,25 25,25 25,25
  • Parameters estimated from data0

Result

  • Chi-square statistic2
  • Degrees of freedom3
  • Right-tail p-value0.57

Results explained

Chi-square statistic
Chi-square statistic from the formula above. Goodness-of-fit test with independently observed categories and fixed expected totals; not a contingency-table independence test.
Degrees of freedom
Degrees of freedom from the formula above. Goodness-of-fit test with independently observed categories and fixed expected totals; not a contingency-table independence test.
Right-tail p-value
Right-tail p-value from the formula above. Goodness-of-fit test with independently observed categories and fixed expected totals; not a contingency-table independence test.

Frequently asked questions

χ²=sum((observed−expected)²/expected); df=categories−1−estimated parameters; p=upper regularized gamma(df/2,χ²/2)

Goodness-of-fit test with independently observed categories and fixed expected totals; not a contingency-table independence test.

Enter numbers only, separated as described in the labels. Check sample units and remove missing values rather than substituting zero.

No. Statistical inference depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.

No. Calculations and numerical distribution algorithms run entirely in the browser.