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Chi Square Formula:
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The Chi Square (χ²) test is a statistical method used to determine if there's a significant difference between observed and expected frequencies in one or more categories. It's commonly used in hypothesis testing to assess goodness of fit or independence between variables.
The calculator uses the Chi Square formula:
Where:
Explanation: The test compares observed data with data we would expect to obtain according to a specific hypothesis to determine if any observed differences are statistically significant.
Details: The Chi Square test is widely used in research across various fields including biology, medicine, psychology, and social sciences to test relationships between categorical variables and assess how likely any observed difference between sets arose by chance.
Tips: Enter observed and expected values as comma-separated lists. Both lists must have the same number of values. Expected values should not be zero to avoid division errors.
Q1: What is a good chi-square value?
A: There's no "good" or "bad" value. The significance depends on the degrees of freedom and the chosen significance level (typically 0.05). You compare the calculated χ² value to critical values from a chi-square distribution table.
Q2: When should I use a chi-square test?
A: Use it when you have categorical data and want to test hypotheses about distributions or relationships between variables. Common applications include genetics, marketing research, and survey analysis.
Q3: What are the assumptions of the chi-square test?
A: The test assumes random sampling, independence of observations, and that expected frequencies are sufficiently large (typically at least 5 per cell).
Q4: What is the difference between chi-square goodness of fit and test of independence?
A: Goodness of fit tests if sample data matches a population, while test of independence assesses whether two categorical variables are related.
Q5: How do I interpret the p-value from a chi-square test?
A: A p-value less than your significance level (usually 0.05) indicates that the observed data is unlikely under the null hypothesis, suggesting a statistically significant relationship.