Test Statistic For Goodness Of Fit Calculator P Value

Chi-Square Goodness of Fit Test:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \] \[ P\text{-value} = 1 - \text{chisqcdf}(\chi^2, df) \]

Chi-Square Statistic (χ²):

Degrees of Freedom (df):

P-value:

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1. What is the Chi-Square Goodness of Fit Test?

The Chi-Square Goodness of Fit Test determines whether observed categorical data matches an expected distribution. It compares observed counts to expected counts under a null hypothesis, calculating a test statistic (χ²) and corresponding p-value.

2. How Does the Calculator Work?

The calculator uses the Chi-Square formula:

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

Where:

\( O \) — Observed count
\( E \) — Expected count under null hypothesis
\( \sum \) — Sum over all categories

The p-value is calculated from the chi-square distribution with degrees of freedom (df) equal to the number of categories minus 1.

3. Interpreting the Results

Chi-Square Statistic: Larger values indicate greater deviation between observed and expected counts.

P-value: Probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. Small p-values (typically <0.05) suggest rejecting the null hypothesis.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: What's the difference between goodness of fit and test of independence?
A: Goodness of fit compares one categorical variable to a distribution, while test of independence examines the relationship between two categorical variables.

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

Q4: How are degrees of freedom determined?
A: For goodness of fit, df = number of categories - 1 - number of estimated parameters.

Q5: Can I use this for continuous data?
A: No, you would need to bin continuous data into categories first.