χ²cdf Calculator (Chi-Square CDF)
Compute χ²cdf(lower, upper, df) exactly as a TI-83 or TI-84 does: the area under the chi-square curve between two values. With the upper bound left open, the result is the p-value of a chi-square test.
Need the critical value instead? See the chi-square table or the critical value calculator.
Part of the TI-84 statistics functions guide, which shows when to use χ²cdf and every other DISTR-menu function.
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Chi-Square Table (χ² Critical Values)
Look up chi-square critical values for degrees of freedom 1 to 100 across ten common tail areas.
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What χ²cdf Does
χ²cdf is the cumulative distribution function of the chi-square distribution. Chi-square tests — goodness of fit, independence, and homogeneity — reject the null hypothesis for large statistics, so the p-value is always the right-tail area above the observed χ².
χ²cdf(a, b, df) = P(a ≤ χ² ≤ b)
p-value of a chi-square test → χ²cdf(χ², 1E99, df)
Goodness of fit: df = categories − 1
Independence: df = (rows − 1) × (columns − 1)
How to Use χ²cdf on a TI-84
- Press 2nd then VARS (DISTR).
- Scroll to 8:χ²cdf( and press ENTER.
- Enter the test statistic as the lower bound, 1E99 as the upper bound, and df.
- Select Paste and press ENTER twice.
In Excel or Google Sheets, =CHISQ.DIST.RT(χ², df) returns the same right-tail p-value.
Worked Example: Goodness-of-Fit p-Value
A store claims customers are spread evenly across its 5 branches. A sample of visits gives a goodness-of-fit statistic of χ² = 7.2. Is the claim contradicted at α = 0.05?
- df = 5 categories − 1 = 4.
- p-value = χ²cdf(7.2, 1E99, 4) = 0.125689.
- 0.1257 > 0.05, so the data do not give significant evidence against an even spread.
Equivalently, the 5% critical value for df = 4 is 9.488, and 7.2 falls short of it. To run the whole test from observed and expected counts, use the chi-square test calculator.
Frequently Asked Questions
How do I get a p-value from a chi-square statistic?
Use the right tail: χ²cdf(χ², 1E99, df). Chi-square tests are always right-tailed because larger statistics mean bigger departures from the null hypothesis. Here, just enter the statistic as the lower bound and leave the upper bound blank.
Where is χ²cdf on the TI-84?
Press 2nd, VARS to open DISTR, and choose 8:χ²cdf( (the exact number can vary slightly by OS version). It takes lower bound, upper bound, and degrees of freedom.
Why is the lower bound 0 by default?
A chi-square statistic is a sum of squared terms and can never be negative, so the distribution starts at 0. χ²cdf(0, x, df) is the full left-tail area P(χ² ≤ x).
What degrees of freedom do I use?
For goodness of fit, the number of categories minus 1 (minus any parameters estimated from the data). For a two-way table test of independence or homogeneity, (rows − 1) × (columns − 1).
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