Goodness Of Fit Test Calculator

Chi-Squared Formula:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Chi-Squared Value (χ²):

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1. What is the Goodness Of Fit Test?

The Goodness of Fit Test (Chi-Squared Test) determines how well observed data fit an expected distribution. It compares observed frequencies with expected frequencies to assess whether any differences are statistically significant.

2. How Does the Calculator Work?

The calculator uses the Chi-Squared formula:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Where:

\( O \) — Observed values (unitless)
\( E \) — Expected values (unitless)
\( \chi^2 \) — Chi-squared value (unitless)

Explanation: The test calculates the sum of squared differences between observed and expected values, divided by expected values. A higher chi-squared value indicates a poorer fit between observed and expected distributions.

3. Importance of Chi-Squared Test

Details: The Goodness of Fit Test is crucial for validating statistical models, testing hypotheses about distributions, and determining whether sample data match theoretical expectations in various research fields.

4. Using the Calculator

Tips: Enter observed and expected values as comma-separated lists. Both lists must have the same number of values. Expected values cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a good chi-squared value?
A: There's no single "good" value. The significance depends on degrees of freedom and the chosen significance level (typically compared against critical values from chi-squared distribution tables).

Q2: 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 pattern.

Q3: What are the assumptions of this test?
A: The test assumes independent observations, categorical data, and that expected frequencies are sufficiently large (typically at least 5 per category).

Q4: How do I interpret the results?
A: Compare the calculated chi-squared value with critical values from chi-squared distribution tables. If calculated value exceeds critical value, reject the null hypothesis that distributions match.

Q5: Are there alternatives to this test?
A: Yes, alternatives include Kolmogorov-Smirnov test, Anderson-Darling test, and Shapiro-Wilk test, depending on the specific distribution being tested.