Zoho Sheet CHIINV: Right-Tail Chi-Square Critical Values

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.

=CHIINV(p; k)

There are two required arguments and no documented optional arguments or defaults. Zoho calls this the inverse of the right-tailed chi-square probability, with the p argument first and degrees of freedom second. Zoho CHIINV. In probability notation the output q satisfies P(X ≥ q) = p for X ~ χ²(k). This differs from the usual left-tail percentile P(X ≤ q) = p.

For example, a 95th left-tail percentile uses CHIINV(0.05;k), not CHIINV(0.95;k). This transformation is mathematically justified, but any spreadsheet round-off is platform-dependent. The upper-tail inverse is mainly useful for critical-value checks and for converting known right-tail probabilities back into chi-square statistics.

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, write Recovered chi-square x.
2. In G2, type =CHIINV(D2;C2). D2 is the right-tail probability independently computed from statistic 14 with k=5; its full precision is 0.01560941610026691. Expected output is about 14.0.
3. Fill G2 through G5. The corresponding independent expected values are about 14, 4, 6 and 10. Because reference values are displayed/rounded, do not expect exact bit-for-bit round trips from only 12 digits.
4. In H2, enter =CHIDIST(G2;C2). The mathematical expectation is the input probability in D2, within floating-point rounding.
5. Treat =CHIINV(0.05;5) as a separate direct example: expected 11.070497694; =CHIDIST(11.070497694;5) is expected to return approximately 0.05.

If D2 was accidentally entered as 1.56 rather than 0.0156, it is a probability above 1 and should not be interpreted as a percentage automatically. Enter probabilities on a 0-to-1 scale (5% as a properly formatted numerical 0.05 is fine); verify the underlying value before invoking the inverse.

Choose a right-tail significance threshold before examining the data. With 4 degrees of freedom, use =CHIINV(0.05;4); the independently calculated cutoff is 9.487729037. A right-tail statistic of 2.9 has independent p-value 0.574697205830 according to CHIDIST(2.9;4) and therefore falls below this critical statistic. A statistic of 14 exceeds the cutoff, with independent right-tail area CHIDIST(14;4) around 0.0073; this would cross the same nominal threshold if the reference distribution assumptions hold.

For a simple reproducible threshold table, enter the following in a clean area:

Smaller right-tail areas correspond to larger critical statistics. A common failure is reversing that monotonic relationship when importing from a left-tail percentile function.

For an independent normal population sample with n=16 observations, a hypothetical reference variance sigma0_squared=4 and a sample variance of s_squared=9, the chi-square test statistic is (n−1)*s_squared/sigma0_squared = (15*9)/4 = 33.75, with k=n−1=15. Independently, its right-tail area is 0.003691475316. The matching 5% upper critical statistic is =CHIINV(0.05;15) with expected result 24.995790140. On these assumptions 33.75 exceeds the cutoff.

This is not a generic test of variability: validity depends on independent samples, suitable normality assumptions and the specified null variance. Sample variance computation and the reference null are inputs from the scientific design; neither is established by CHIINV. If testing many hypotheses, choose and document a multiplicity strategy.

Zoho’s help lists #NUM for p outside 0–1 and for k < 1. Its text does not establish the behavior of exactly p=0 or p=1, which mathematically map to an unbounded/zero cutoff in some formulations; test those endpoints directly rather than promising a particular error or infinity. It also describes k as a positive integer but does not fully specify coercion of k=2.5, very large k, or a formatted numeric-looking string. Validate input data and avoid inventing rounding conventions from Excel.

With a very small p, the upper cutoff may be sensitive to the precision of the input. An output of 11.07 rather than 11.070497694 can be a display-format difference; calculate any subsequent p-values from underlying values, not hand-rounded output.

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.

CHIINV(0.05;5) and CHISQINV(0.95;5) represent the same upper cutoff mathematically, about 11.070497694, because the first takes right-tail 0.05 and the second takes left-tail 0.95. By contrast CHISQINV(0.05;5) gives the lower 5th percentile, about 1.145476226. Similarly CHIDIST(14;5) gives right-tail 0.015609416100, while CHISQDIST(14;5;TRUE) gives left-tail 0.984390583900. Use the correct tail explicitly, even if a result seems plausible.

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.