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Chi-Squared Formula:
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The Chi-Squared (χ²) goodness of fit test is a statistical method used to determine how well observed data fit an expected distribution. It compares observed frequencies with expected frequencies to assess whether any differences are statistically significant.
The calculator uses the Chi-Squared formula:
Where:
Explanation: The formula calculates the sum of squared differences between observed and expected values, divided by the expected values. A higher χ² value indicates a poorer fit between observed and expected data.
Details: The Chi-Squared goodness of fit test is crucial for validating statistical models, testing hypotheses about distributions, and determining whether sample data match theoretical expectations across various research fields.
Tips: Enter observed and expected values as comma-separated lists. Both lists must have the same number of values. Expected values should not contain zeros to avoid division errors.
Q1: What does a high chi-squared value indicate?
A: A high χ² value suggests that the observed data significantly deviate from the expected distribution, indicating a poor fit between the two.
Q2: How do I interpret the chi-squared result?
A: Compare the calculated χ² value with critical values from chi-squared distribution tables at your desired significance level (usually 0.05) with appropriate degrees of freedom.
Q3: What are degrees of freedom in chi-squared test?
A: For goodness of fit, degrees of freedom = number of categories - 1 - number of estimated parameters from the data.
Q4: When should I use this test?
A: Use when you want to test whether your observed data follow a specific theoretical distribution (normal, binomial, Poisson, etc.) or expected proportions.
Q5: What are the assumptions of chi-squared test?
A: The test assumes independent observations, adequate sample size (expected frequency ≥5 in each category), and categorical data.