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The chi-squared (χ²) test statistic for goodness of fit measures how well observed data match expected values from a theoretical distribution. It quantifies the discrepancy between observed and expected frequencies across different categories.
The calculator uses the chi-squared formula:
Where:
Explanation: The formula calculates the sum of squared differences between observed and expected values, normalized by the expected values. A smaller χ² value indicates a better fit between observed and expected distributions.
Details: The goodness of fit test is crucial in statistics for validating theoretical models, testing hypotheses about distributions, and determining whether sample data come from a population with a specific distribution.
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 does a high chi-squared value indicate?
A: A high χ² value suggests a significant discrepancy between observed and expected values, indicating a poor fit between the data and the theoretical model.
Q2: How do I interpret the chi-squared result?
A: Compare your calculated χ² value to critical values from the chi-squared distribution table with appropriate degrees of freedom (categories - 1) to determine statistical significance.
Q3: What are the assumptions of the chi-squared test?
A: The test assumes independence of observations, adequate sample size (expected frequencies ≥5 for most categories), and categorical or frequency data.
Q4: Can I use this test for continuous data?
A: The chi-squared goodness of fit test is designed for categorical data. For continuous data, other tests like Kolmogorov-Smirnov are more appropriate.
Q5: What is the relationship between χ² and p-value?
A: The χ² value is used to calculate a p-value, which indicates the probability of observing the data if the null hypothesis (that the distributions match) is true.