Google Sheets CHISQ.DIST.RT Function: Syntax, Examples & Tips

What Is CHISQ.DIST.RT?

CHISQ.DIST.RT returns the probability that a chi-square random variable is greater than a given value. In hypothesis testing, this right-tail area is the p-value for a chi-square statistic: the chance of seeing a result at least as extreme as yours if the null hypothesis were true.

The chi-square distribution describes the sum of squares of independent standard normal variables. It only takes non-negative values, is skewed to the right, and has one parameter: degrees of freedom. With few degrees of freedom the curve is bunched near zero with a long right tail; as degrees of freedom grow, it shifts right and becomes more symmetric. Its mean equals the degrees of freedom.

In practice you meet it most often in hypothesis tests: goodness-of-fit tests (does observed data match an expected pattern?), tests of independence in contingency tables (are two categories related?), and tests about a variance.

CHISQ.DIST.RT is the modern replacement for CHIDIST. Both take the same two arguments and return the same result.

How CHISQ.DIST.RT Works

You pass the test statistic x and its degrees of freedom. The function returns the area under the curve to the right of x. Larger statistics produce smaller probabilities. It is equivalent to 1 - CHISQ.DIST(x, degrees_freedom, TRUE).

Basic Examples

p-value for a statistic

=CHISQ.DIST.RT(3.841, 1)

Returns about 0.05.

An exact check

=CHISQ.DIST.RT(4, 2)

Returns about 0.1353. With 2 degrees of freedom the right tail equals e^(−x/2), so this is e^(−2).

From a statistic you computed

=CHISQ.DIST.RT(F10, (ROWS(B2:D4)-1)*(COLUMNS(B2:D4)-1))

If F10 holds the chi-square statistic for a 3×3 contingency table, this computes degrees of freedom as (rows − 1) × (columns − 1) and returns the p-value.

Make a decision

=IF(CHISQ.DIST.RT(F10, 4) < 0.05, "Significant", "Not significant")

Computing the Statistic Yourself

If you have observed counts in B2:B6 and expected counts in C2:C6, the goodness-of-fit statistic is:

=SUMPRODUCT((B2:B6-C2:C6)^2/C2:C6)

Pass it to CHISQ.DIST.RT with 4 degrees of freedom (categories − 1). If you only need the p-value, CHISQ.TEST skips this step.

Reference Critical Values

A statistic above the 5% critical value gives a p-value below 0.05.

Common Use Cases

• Goodness-of-fit: do website visits split evenly across weekdays?
• Independence tests: is product preference related to age group?
• Survey analysis: do response patterns differ between regions?
• Model checks: likelihood-ratio statistics compared against chi-square

Common Errors

• #NUM!: x is negative or degrees_freedom is below 1.
• #VALUE!: An argument is text.
• Wrong degrees of freedom: Goodness-of-fit uses categories − 1; independence tests use (rows − 1) × (columns − 1). A wrong value changes the p-value substantially.
• Small expected counts: The chi-square approximation is unreliable when expected counts are small (a common rule of thumb is below 5).

Tips and Best Practices

• Report the statistic, degrees of freedom, and p-value together.
• Use CHISQ.INV.RT to get the critical value for a chosen significance level.
• Round p-values with ROUND or display them with a fixed number of decimals.

Related Functions

• CHISQ.DIST: left-tailed probability or density
• CHISQ.INV.RT: critical value from a right-tail probability
• CHISQ.TEST: p-value of a test from observed and expected tables
• CHIDIST: legacy right-tailed probability
• IF: turn a p-value into a decision