Zoho Sheet CHIDIST: Right-Tail Chi-Square Probabilities

This tutorial follows Zoho Sheet’s English online help reference checked on 2026-10-13. The examples use the help article’s semicolon argument separator and decimal point. In a workbook with another locale, inspect File → Spreadsheet Settings → Locale (language, decimal separator, grouping and regional formats are configurable); use the syntax accepted by your actual spreadsheet rather than guessing from a different product. Zoho locale settings.

These probability calculations assume the mathematical chi-square distribution with the specified positive integer degrees of freedom. A chi-square statistic is generally nonnegative; it is not a raw percentage or a test score. For hypothesis tests, the statistic, degrees of freedom and sampling assumptions must be justified before obtaining a tail probability or cutoff. A low p-value under a model is not the probability that a hypothesis is true, and statistical significance is not an effect size.

Zoho’s current public help article does not identify the function’s earliest-supported product release or establish exact parity across browser, mobile, desktop/offline, editions or account plans. Accordingly, no first-version claim or unsupported platform guarantee is made. No formula was executed in a signed-in Zoho Sheet instance. The values below are independently calculated using a standard chi-square model (SciPy 1.17.0), not screenshots, Zoho output or vendor certification.

=CHIDIST(x; k)

Exactly two arguments are documented. There is no cumulative-mode parameter and no omitted-argument default to select: this function is right-tail only. Zoho’s reference specifically displays CHIDIST(x; k) and lists CHIINV, CHISQDIST, CHISQINV and CHITEST as related. Zoho CHIDIST.

Mathematically, for X ~ χ²(k), the result is P(X ≥ x), sometimes called the survival function 1 − F(x). For values not in a far extreme tail, subtracting a left-tail CDF from one is a useful cross-check. In a very small tail, direct right-tail algorithms may preserve more numerical accuracy than subtracting a number very close to 1; the documentation does not specify Zoho’s numerical algorithm.

Create a blank Zoho Sheet and enter the following table beginning at A1. A and B/C below are plain values; the reference probabilities in D:F were calculated independently for checking and are not outputs of Zoho Sheet:

Format probability cells with 9–12 decimal places when inspecting a calculation. Formatting alone can make two close values look identical; rounding also affects round-trip inverse checks. Formulas belong in a new column G or farther right so you do not overwrite the comparison data. A PDF (probability density) is not the probability that a continuously distributed statistic equals a single exact number: for a continuous variable that point probability is zero.

1. In G1, type Zoho CHIDIST.
2. In G2, enter =CHIDIST(B2;C2). With B2 = 14 and C2 = 5, the independently calculated expected result is 0.015609416100.
3. Fill G2 through G5. Independent expectations are 0.015609416100, 0.045500263896, 0.111610225095 and 0.075235246147.
4. In H2, enter =1-CHISQDIST(B2;C2;TRUE) as a separately documented complement check. The mathematical expected result is 0.015609416100; comparison of G2 and H2 is a proposed Zoho workbook check, not evidence of a native execution.
5. If displaying a percentage, 0.0156094 formats as about 1.56%. Do not mistake it for 0.0156%.

Why five degrees of freedom? They are part of the statistical problem, not an arbitrary input to obtain a desired p-value. In the next example, five mutually exclusive categories with a single fixed-sum count and no fitted parameters lead to 5−1 = 4 degrees of freedom under the standard goodness-of-fit assumptions.

A simplified stock-demand model predicts 20 requests in each of five categories; 100 observed requests arrive as 18, 22, 20, 25 and 15. Create a new worksheet with A1=Category, B1=Observed, C1=Expected, D1=Contribution, enter the five observed counts in B2:B6 and 20 in C2:C6.

In D2 enter =(B2-C2)^2/C2, then fill down to D6. The independent contributions are 0.20, 0.20, 0, 1.25 and 1.25; =SUM(D2:D6) in D8 therefore produces the expected statistic 2.90. Place =CHIDIST(D8;4) in D9; expected right-tail p-value 0.574697205830. This example demonstrates the arithmetic and lookup; it does not assert that the observed requests were independently sampled or that every real business model satisfies chi-square assumptions.

Under the usual complete category set and a fixed, pre-specified distribution, k = 5−1 = 4. If parameters were estimated from the same data, or categories are dependent, that degrees-of-freedom statement can change. Expected counts should be large enough for a chi-square approximation to be appropriate; when sparse, use a suitable exact or resampling test rather than trusting a convenient formula.

A p-value around 0.575 does not provide evidence to reject that stipulated distribution at a conventional 5% threshold. It does not prove the distribution is correct. The threshold is a choice made before inspecting the results; it cannot be deduced from Zoho’s formula.

Use the same statistic in D8 and a user-defined threshold 0.05 in E8. Enter the proposed decision formula in F8:

=IF(CHIDIST(D8;4)<E8;"Review discrepancy";"No threshold crossing")

For the example D8=2.9, the independently expected label is No threshold crossing. The IF text is a workflow illustration, not a claim that the compound formula was run. If many categories or many tests are evaluated, account for multiple testing before claiming that one small p-value indicates a reliable finding.

Alternatively compare D8 with =CHIINV(0.05;4). The independently expected 5% right-tail critical statistic is 9.487729037. Since 2.9 is smaller, the same test does not cross the threshold. This provides an interpretable inverse cross-check; it is not a second independent hypothesis test.

Zoho expressly lists a #NUM condition if x < 0, k < 1 or k > 10^10. Its wording also says k must be a positive integer. If your degrees of freedom have a fractional value such as 4.5, correct the statistical design or input rather than assuming the system truncates or rounds it: Zoho’s reference does not spell out fractional-input coercion. A blank cell, an imported numeral stored as text, and an output rounded to zero are different issues; check each before diagnosing the function.

A small right-tail probability might indicate that the observed statistic is unusually large under its null distribution. A large p-value is not the probability that the null is correct. This function alone cannot select a test, tell you whether expected counts are valid, or establish independence.

The function-specific help page lists generic errors alongside specific #NUM conditions. A generic entry does not mean every such error necessarily occurs for every input. Neither floating-point accuracy guarantees nor boundary outcomes not explicitly documented by Zoho are asserted here. Large degrees of freedom, noninteger degrees of freedom, probability endpoints, blank inputs, logical values and high-precision tails remain native validation cases; do not infer their treatment from Excel or another calculator.

• CHIDIST(x;k) is the right-tail probability P(X ≥ x).
• CHIINV(p;k) is the right-tail cutoff whose right-tail probability is p.
• CHISQDIST(x;k;TRUE) is the left-tail probability P(X ≤ x).
• CHISQDIST(x;k;FALSE) is the probability density, not a tail probability.
• CHISQINV(p;k) is the left-tail cutoff whose left-tail probability is p.

They serve different purposes and must not be substituted just because the names resemble one another. For x=14 and k=5, the right-tail 0.015609416100 and left-tail 0.984390583900 add to 1 within numerical precision, while density is 0.006352131663. That identity follows probability theory; Zoho’s numerical precision remains untested.

Zoho’s help article supplies the behavior described in the syntax section. Modern Excel separately documents CHISQ.DIST(x,deg_freedom,cumulative) where its third argument is required, whereas the Zoho CHISQDIST help page documents an optional flag that defaults to FALSE. Microsoft’s Excel documentation is evidence for Excel only; it does not prove that Zoho has identical numeric coercions, aliases, error names or version availability. Legacy CHI... names in Excel or Google Sheets should be mapped by tail and function type rather than by visual similarity alone.

For porting a model, explicitly specify tails and cumulative modes, preserve degrees of freedom, and test representative cases in the target spreadsheet. A right-tail probability and a left-tail probability are complements for a continuous chi-square statistic, but the corresponding inverse functions receive different probability inputs for the same cutoff.

• Zoho Sheet CHIDIST tutorial
• Zoho Sheet CHIINV tutorial
• Zoho Sheet CHISQDIST tutorial
• Zoho Sheet CHISQINV tutorial

Official Zoho sources, opened and checked on 2026-10-13 (each item supports the stated syntax, direction, related function or the locale setting; none establishes first release):

• Zoho Sheet — this function reference
• CHIDIST in Zoho Sheet
• CHIINV in Zoho Sheet
• CHISQDIST in Zoho Sheet
• CHISQINV in Zoho Sheet
• CHITEST in Zoho Sheet
• Zoho Sheet — spreadsheet locale settings
• Microsoft Excel — CHISQ.DIST behavior (Excel comparison only)

Validation: Official documentation checked on 2026-10-13; worked numbers independently recalculated. Native Zoho executions: 0. Screenshots: 0. Runtime edge cases remain unverified.