What is the difference between chi-square independence and goodness of fit?

The goodness-of-fit test checks whether observed frequencies match an expected distribution for a single categorical variable. The test of independence checks whether two categorical variables are associated using a contingency table.

What is the expected frequency requirement?

For the chi-square test to be valid, all expected cell frequencies should ideally be 5 or more. If many expected frequencies are below 5, consider combining categories or using Fisher's exact test.

How do I interpret the result?

If the p-value is less than your significance level (typically 0.05), reject the null hypothesis and conclude that the variables are not independent — there is a statistically significant association between them.

Chi-Square Independence Test Calculator

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About Chi-Square Test of Independence

Enter a contingency table of observed frequencies and test whether the two categorical variables are independent. The calculator computes expected frequencies, the chi-square statistic, degrees of freedom, and the p-value with every step explained.

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FAQ

Is this statistics calculator free?

Yes! The Statistics Calculator provides free step-by-step solutions for descriptive statistics, z-scores, probability distributions, and hypothesis tests. No account required.

What types of statistics problems can it calculate?

It covers descriptive statistics (mean, median, mode, standard deviation, quartiles), z-score calculations with probability lookups, normal and t-distributions, and hypothesis tests including z-tests, t-tests, and proportion tests.

How are the step-by-step solutions generated?

Solutions are generated using scipy.stats and precise mathematical formulas. Unlike AI chatbots, every calculation is deterministic and mathematically guaranteed to be correct.

Can I see graphs and distribution curves?

Yes! Solutions include visual bell curves with shaded probability regions, making it easy to understand z-scores, p-values, and distribution areas at a glance.

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