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Chi-Square Formula:
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The Chi-Square Goodness of Fit test is a statistical hypothesis test used to determine whether sample data matches a population distribution. It compares observed frequencies with expected frequencies to assess how well a theoretical distribution fits the observed data.
The calculator uses the Chi-Square formula:
Where:
Explanation: The test measures how much the observed frequencies deviate from the expected frequencies. A larger chi-square value indicates a greater discrepancy between observed and expected values.
Details: The Chi-Square Goodness of Fit test is crucial for determining whether sample data follows a specific distribution, testing hypotheses about population distributions, and validating statistical models in 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 be zero to avoid division errors.
Q1: What is a good chi-square value?
A: There's no "good" or "bad" value - it depends on degrees of freedom and significance level. Compare your calculated χ² value to critical values from chi-square distribution tables.
Q2: When should I use this test?
A: Use when you want to test if your observed data follows an expected distribution pattern, such as testing for normality, uniform distribution, or any other theoretical distribution.
Q3: What are the assumptions of this test?
A: The test assumes that data are randomly sampled, categories are mutually exclusive, and expected frequencies are sufficiently large (typically ≥5 for each category).
Q4: How do I interpret the results?
A: A small chi-square value suggests the observed data fit the expected distribution well. A large value suggests a poor fit between observed and expected data.
Q5: What are the limitations of this test?
A: The test is sensitive to sample size, requires sufficient expected frequencies, and may not be reliable with small sample sizes or when expected frequencies are too low.