Chi-Square Calculator
Calculate the chi-square statistic and p-value for your observed and expected values.
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Table of Contents
Chi-Square Formula
The chi-square test is used to determine if there is a significant difference between the expected and observed frequencies in one or more categories.
Where:
- χ² is the chi-square statistic
- O is the observed value
- E is the expected value
- Σ is the sum of all categories
How to Calculate Chi-Square
To calculate chi-square, follow these steps:
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1Collect observed and expected values for each category
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2Calculate (O - E)² / E for each category
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3Sum all the values to get the chi-square statistic
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4Calculate the p-value using the chi-square distribution
Interpreting Chi-Square Results
Understanding what the chi-square test tells you about your data:
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1Small Chi-Square Value:
Indicates that observed values are close to expected values.
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2Large Chi-Square Value:
Indicates significant difference between observed and expected values.
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3P-Value Interpretation:
P-value < 0.05 suggests rejecting the null hypothesis.
Practical Examples
Example 1 Genetic Cross
Observed: 30, 20, 20, 30
Expected: 25, 25, 25, 25
Chi-Square = 4.0
P-Value = 0.2615
The results are not statistically significant.
Example 2 Survey Results
Observed: 40, 60, 30, 70
Expected: 50, 50, 50, 50
Chi-Square = 20.0
P-Value = 0.0002
The results are statistically significant.
Example 3 Dice Roll
Observed: 18, 17, 16, 19, 15, 15
Expected: 17, 17, 17, 17, 17, 17
Chi-Square = 0.941
P-Value = 0.967
The die appears to be fair.