Chi-Square Test Calculator
Calculate the chi-square statistic for categorical data. Get instant step-by-step solutions — completely free, no signup required.
Free Chi-Square Test Calculator Calculator
Enter your problem below to get an instant step-by-step solution.
About Chi-Square Test Calculator
Calculate the chi-square statistic for categorical data. Statistics is the science of collecting, analyzing, and interpreting numerical data. Statistical methods are used in research, business, medicine, and machine learning.
Our Chi-Square Test Calculator calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any chi-square test calculator expression and receive a complete, verified solution with every step shown.
Chi-Square Test Calculator Formula
χ² = Σ (O − E)² / E
The chi-square test compares observed counts (O) with the counts expected (E) under a null hypothesis. A large χ² means the observed data differ from expectation more than chance would explain. Compare the statistic with the critical value for your degrees of freedom.
Worked Example
A die is rolled 60 times: 8, 9, 12, 11, 6, 14. Is it fair?
- Expected count per face: 60 / 6 = 10
- (O − E)²/E: 0.4, 0.1, 0.4, 0.1, 1.6, 1.6
- χ² = 4.2 with df = 6 − 1 = 5
- Critical value at α = 0.05 is 11.07; 4.2 < 11.07
Answer: χ² = 4.2 — no evidence the die is unfair
Common Mistakes to Avoid
- Running the test on percentages or means instead of raw counts.
- Using it when expected counts are below 5.
- Getting the degrees of freedom wrong (categories − 1, or (rows − 1)(cols − 1)).
How to Use the Chi-Square Test Calculator Calculator
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Enter your data values or statistical parameters for Chi-Square Test Calculator
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Press Enter or click the Solve button to run the calculation
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Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Chi-Square Test Calculator formula?
χ² = Σ (O − E)² / E. The chi-square test compares observed counts (O) with the counts expected (E) under a null hypothesis. A large χ² means the observed data differ from expectation more than chance would explain. Compare the statistic with the critical value for your degrees of freedom.
Can you show a worked Chi-Square Test Calculator example?
A die is rolled 60 times: 8, 9, 12, 11, 6, 14. Is it fair?: Expected count per face: 60 / 6 = 10; (O − E)²/E: 0.4, 0.1, 0.4, 0.1, 1.6, 1.6; χ² = 4.2 with df = 6 − 1 = 5; Critical value at α = 0.05 is 11.07; 4.2 < 11.07. Answer: χ² = 4.2 — no evidence the die is unfair.
Is this Chi-Square Test Calculator calculator free to use?
Yes — the Chi-Square Test Calculator calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Chi-Square Test Calculator homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.