CHITEST in Zoho Sheet: Chi-Square Independence Test

CHITEST compares a table of observed category counts with a matching table of expected counts and returns a chi-square-related probability, conventionally interpreted as the test’s p-value. It does not return the raw chi-square statistic. The official Zoho Sheet reference documents CHITEST(observed; expected), requires matching row and column counts, and shows a small decimal result rather than a raw test statistic. This guide uses a reproducible two-row, three-column example for testing whether category choices differ between two groups.

Validation scope: The mathematical values below were calculated outside Zoho Sheet; no formula was executed in Zoho Sheet, and no screenshot or compatibility test is claimed. All examples use an English-language function name and the semicolon argument separator shown in Zoho’s documentation. A locale that displays another separator must be checked in its own formula editor.

CHITEST(observed; expected)

No optional arguments or default values are documented. Keep each observed count aligned with its corresponding expected count. Do not swap a table with its transpose or include headings in one range but not the other. Zoho specifically requires equal numbers of rows and columns and at least two values in each argument. Z1

The input should represent frequencies, not percentages, rates, a list of raw customer identifiers, or a table of the individual transactions from which the frequencies were counted. For a standard Pearson chi-square independence analysis, frequencies are nonnegative and expected cells should be positive. Those last statistical requirements govern the model; Zoho’s help page does not list every engine-level invalid-input response.

A survey records three mutually exclusive choices from Group A and Group B. Enter this table in A1:C3. Put the expected counts table in A5:C7, keeping the headings outside each formula range.

Both groups contributed 50 observations. The category totals are Red 37, Green 38 and Blue 25; the overall total is 100. Under independence, the expected count for a cell is row total × column total ÷ grand total. For A6 this is 50 × 37 ÷ 100 = 18.5. You may fill the expected table using the following formula in A6, copied right to C6 and then down to row 7:

=SUM($A2:$C2)*SUM(A$2:A$3)/SUM($A$2:$C$3)

This formula is independently derived arithmetic; it is not a claim of live Zoho execution. Make sure rows 6–7 are populated with positive, unrounded expected values. Enter the test in an unused cell such as E2:

=CHITEST(A2:C3;A6:C7)

Independently calculated mathematical expectation: 0.296771219684 (approximately 0.2968). This is a predicted result for the Pearson chi-square independence model, not a result captured from a Zoho Sheet session. The official reference’s own example uses different hidden embedded-sheet data and reports 0.26796475045188; do not confuse it with the newly created dataset. Z1

Verify the math without trusting a black box

For a conventional Pearson test, sum (observed − expected)^2 ÷ expected over the six cells:

χ² = 2 × (12.25/18.5 + 1/19 + 6.25/12.5)
   = 2.429587482219061

A 2 × 3 independence table has (2−1) × (3−1) = 2 degrees of freedom. The right-tail probability P(χ²₂ ≥ 2.4295874822) is 0.296771219684. For an independent cross-check in a sheet, the previously documented CHIDIST(x; k) calculates the right-tail probability, so the mathematical comparison formula is:

=CHIDIST(2.429587482219061;2)

The official CHIDIST reference establishes its right-tail meaning. Equality of the CHITEST and CHIDIST output for this newly authored data has not been tested in Zoho.

Interpret, rather than overstate, the answer

At a prespecified significance threshold of 0.05, a p-value near 0.297 does not provide strong evidence against the independence model. It does not prove that preferences are identical, that the two groups are equivalent, or that there is a 29.7% probability the null hypothesis is true. A p-value describes the extremeness of the data conditional on the stated null model. Document the sample-selection method and whether observations are independent.

The chi-square analysis considers counts. Multiplying every cell by ten while keeping proportions unchanged changes the sample size and test statistic; it can change significance. That is one reason not to substitute normalized percentages for the original frequency counts.

Suppose two store locations have the following observed counts for choosing a standard or premium delivery option:

The row totals are both 30 and column totals are 27 and 33, so the independence expectations are [13.5, 16.5] in each row. If the observed table is in G2:H3 and the expected table in G6:H7, use:

=CHITEST(G2:H3;G6:H7)

Independently modeled p-value: 0.019517481182; the Pearson statistic is 5.454545454545 with one degree of freedom. At α=0.05 this is evidence against independence if the sampling and expected-count assumptions hold. It is a model example, not a claimed Zoho output. Do not add a Yates continuity adjustment unless your selected statistical method explicitly calls for it; the documentation does not specify a continuity correction for CHITEST.

For a table with r rows and c columns, keep the model’s degrees of freedom as (r−1)(c−1) when both dimensions exceed one. A Pearson residual (observed−expected)/SQRT(expected) can help identify which cells contribute heavily to the overall statistic. For the first Red cell, that quantity is (22−18.5)/SQRT(18.5) ≈ 0.8137. That calculation is for diagnosis; it does not supply a separate post-hoc multiple-comparisons procedure.

A simple effect-size description is Cramér’s V: SQRT(χ²/(N × MIN(r−1;c−1))) as a mathematical formula. For this 2 × 3 table, sqrt(2.429587482219061/100) ≈ 0.155871. Effect size is not a replacement for study design, confidence intervals or practical significance. Do not treat independence tables as paired before/after records unless the chosen test actually models paired data.

If expected counts become very small, the usual chi-square approximation can be inaccurate. Depending on the study design, an exact method (for example Fisher’s exact test for some 2 × 2 layouts) or combining scientifically defensible categories may be appropriate; this guide does not claim Zoho implements every exact-test method.

Do not claim a specific Zoho response for zero expected counts, negative counts, noninteger inputs, unbalanced missing data, or version-specific parser behavior without a native test. The help page does not establish an exhaustive input-validation matrix.

Zoho documents the CHITEST(observed; expected) spelling and semicolon syntax in its English public Sheet knowledge base. Z1 Microsoft documents CHITEST(actual_range,expected_range) as a backward-compatibility Excel function and points to CHISQ.TEST; Microsoft’s statistical explanation gives the chi-square statistic and degrees-of-freedom rules used as independent methodological context here. M1 An Excel function behaving a particular way does not prove identical Zoho parsing, numerical precision or all edge cases. In particular, this guide does not assert that CHISQ.TEST is a built-in Zoho alias.

This research concerns the publicly documented Zoho Sheet service. The help article does not establish the first supported release, parity on every mobile client, behavior of imported Excel workbooks, or locale-specific separator rules. Those remain unverified.

The following are official documentation links:

• CHIDIST: right-tail chi-square probability (use after independently calculating χ² and degrees of freedom).
• CHIINV: right-tail chi-square critical value (critical-value perspective).
• CHISQDIST: left-tail distribution; explicit TRUE for cumulative (not the same default as right-tail CHIDIST).
• CHISQINV: left-tail inverse (different tail convention).
• Microsoft’s CHITEST explanation (comparative statistical method, not Zoho execution evidence).

Official source review date: 2026-10-13 UTC. Official syntax and common errors: research in Z1. Related function semantics: Z2–Z5. Mathematical validation: independently evaluated Pearson cell contributions and chi-square survival probabilities using Python/SciPy (not part of the Zoho engine). Native Zoho execution: not performed. Evidence caveat: Zoho’s webpage describes the function’s purpose succinctly and embeds a workbook that was not executed here; the exact results for our invented tables are modeled expectations awaiting native confirmation.