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Chi Square Formula:
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The Chi Square test is a statistical method used to determine if there is a significant association between categorical variables. It compares observed frequencies with expected frequencies to assess how well the observed data fit the expected distribution.
The calculator uses the Chi Square formula:
Where:
Explanation: The test calculates the sum of squared differences between observed and expected values, divided by expected values. A larger chi-square value indicates a greater discrepancy between observed and expected results.
Details: The Chi Square test is widely used in research for testing hypotheses about categorical data, including goodness-of-fit tests, tests of independence, and tests of homogeneity.
Tips: Enter observed and expected values as comma-separated lists. Both lists must have the same number of values. Expected values should be greater than zero for accurate results.
Q1: When should I use a Chi Square test?
A: Use it when you have categorical data and want to test whether observed frequencies differ significantly from expected frequencies.
Q2: What are the assumptions of the Chi Square test?
A: The test assumes independence of observations, adequate sample size, and expected frequencies of at least 5 in each category.
Q3: How do I interpret the chi-square value?
A: Compare the calculated chi-square value to a critical value from the chi-square distribution table based on your degrees of freedom and significance level.
Q4: What are degrees of freedom in chi-square tests?
A: For a goodness-of-fit test, degrees of freedom = number of categories - 1. For tests of independence, degrees of freedom = (rows - 1) × (columns - 1).
Q5: Can I use chi-square for small sample sizes?
A: For small sample sizes or when expected frequencies are less than 5, consider using Fisher's exact test instead.