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Chi-Square Formula:
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The Chi-Square (χ²) Goodness of Fit Test is a statistical test used to determine whether observed categorical data match expected values under a specific hypothesis. It compares observed frequencies to expected frequencies to assess how well a theoretical distribution fits the empirical data.
The calculator uses the Chi-Square formula:
Where:
Explanation: The test calculates a chi-square statistic by summing the squared differences between observed and expected counts, divided by the expected counts for each category.
Details: The goodness-of-fit test is widely used in research to test hypotheses about distributions of categorical variables, such as genetic inheritance patterns, survey response distributions, or quality control in manufacturing.
Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values. Expected counts should typically be ≥5 for each category for valid results.
Q1: What are the assumptions of the chi-square test?
A: The test assumes: 1) Random sampling, 2) Independent observations, 3) Adequate sample size (typically all expected counts ≥5).
Q2: How do I interpret the chi-square statistic?
A: Higher values indicate greater discrepancy between observed and expected. Compare to critical values from chi-square distribution tables based on degrees of freedom.
Q3: What are degrees of freedom in this test?
A: df = number of categories - 1 - number of estimated parameters (if any). For simple goodness-of-fit, it's typically (n-1) where n is number of categories.
Q4: When should I use Yates' correction?
A: Yates' correction is typically used for 2×2 contingency tables with small sample sizes, not for goodness-of-fit tests.
Q5: What alternatives exist if expected counts are too small?
A: For small expected counts, consider Fisher's exact test or combining categories (if theoretically justified).