Syntax
CHISQ.DIST(x, deg_freedom, cumulative)
| Parameter | Description |
|---|---|
| x | Parameter of the CHISQ.DIST function. |
| deg_freedom | Parameter of the CHISQ.DIST function. |
| cumulative | Parameter of the CHISQ.DIST function. |
Examples
Left-tail probability for goodness-of-fit
Formula
=CHISQ.DIST(5.99, 2, TRUE)
Returns ~0.9500. The chi-squared value of 5.99 with 2 df corresponds to the 95th percentile, commonly used as a critical value in 2-df tests.
Cumulative probability of observed chi-sq
Formula
=CHISQ.DIST(10.5, 5, TRUE)
Returns ~0.9375. About 93.8% of the chi-squared distribution with 5 df falls at or below 10.5.
PDF for charting
Formula
=CHISQ.DIST(3, 4, FALSE)
Returns ~0.1353. The density value at x=3 with 4 degrees of freedom, useful for plotting the chi-squared curve.
Common Errors
#NUM!
x must be non-negative and degrees of freedom must be at least 1 (and between 1 and 10^10).
#VALUE!
Occurs when arguments are non-numeric.
Tips
Left-tail CDF
CHISQ.DIST with cumulative=TRUE gives the left-tail probability. For the right-tail (p-value in most chi-squared tests), use CHISQ.DIST.RT or =1 - CHISQ.DIST(x, df, TRUE).
Degrees of freedom matter a lot
The shape of the chi-squared distribution changes dramatically with degrees of freedom. At df=1-2 it is heavily right-skewed; at large df it becomes more symmetric.
For hypothesis testing use the right tail
Most chi-squared tests (goodness-of-fit, independence) reject in the right tail. Use CHISQ.DIST.RT to get the p-value directly.
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