Chi Squared Goodness of Fit Calculator With Sample

Chi-Squared Formula:

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

Chi-Squared Statistic (χ²):

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1. What is Chi-Squared Goodness of Fit Test?

The Chi-Squared Goodness of Fit test determines whether sample data matches a population with a specific distribution. It compares observed counts with expected counts to see if 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 count
\( E \) — Expected count
\( \sum \) — Sum over all categories

Explanation: The test measures how much the observed counts deviate from the expected counts under the null hypothesis.

3. When to Use This Test

Details: Use this test when you have categorical data and want to test whether the observed distribution matches an expected distribution.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of this test?
A: The test assumes random sampling, independent observations, and that expected counts are at least 5 in each category.

Q2: How do I interpret the chi-squared value?
A: Compare your calculated χ² value to a critical value from the chi-squared distribution table with (n-1) degrees of freedom.

Q3: What if my expected counts are less than 5?
A: Consider combining categories or using exact tests like Fisher's exact test.

Q4: Can I use this for continuous data?
A: You need to bin continuous data into categories first.

Q5: What does a significant result mean?
A: It suggests the observed distribution is significantly different from the expected distribution.