Chi Square Calculator For Goodness Of Fit

Chi Square Formula:

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

Chi Square Value (χ²):

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1. What is Chi Square Test For Goodness Of Fit?

The Chi Square test for goodness of fit is a statistical test used to determine whether observed categorical data match expected values from a theoretical distribution. It helps assess how well the observed data fit the expected distribution.

2. How Does the Calculator Work?

The calculator uses the Chi Square formula:

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

Where:

\( O \) — Observed frequency (unitless)
\( E \) — Expected frequency (unitless)
\( \chi^2 \) — Chi square statistic (unitless)

Explanation: The test compares observed frequencies with expected frequencies, with larger chi square values indicating poorer fit between observed and expected distributions.

3. Importance of Chi Square Test

Details: The goodness of fit test is crucial for validating theoretical models, testing hypotheses about distributions, and determining if sample data come from a population with a specific distribution.

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 must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the chi square test?
A: The test assumes categorical data, independence of observations, and expected frequencies of at least 5 in each category.

Q2: How do I interpret the chi square value?
A: Compare the calculated chi square value with critical values from the chi square distribution table based on degrees of freedom and significance level.

Q3: What are degrees of freedom in chi square test?
A: Degrees of freedom = number of categories - 1 - number of parameters estimated from the data.

Q4: When should I use this test?
A: Use when you want to test if observed frequencies match expected frequencies from a theoretical distribution (e.g., normal, uniform, binomial).

Q5: What are the limitations of chi square test?
A: The test requires sufficiently large sample sizes, may not be reliable with small expected frequencies, and is sensitive to sample size.