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Zoho Sheet CONFIDENCE: Known-Sigma Normal Confidence Intervals

Statistical Intermediate Zoho Sheet

Find normal-theory margins of error in Zoho Sheet CONFIDENCE, build interval endpoints, and avoid confusing a half-width with the full interval.

Verification status: See the evidence and test scope described in this guide. How formula examples are checked

Quick answer. The Zoho Sheet formula =CONFIDENCE(0.05;15;100) is a candidate calculation for a 95% normal-theory confidence-interval half-width using known population standard deviation 15 and sample size 100. The mathematically expected result is about 2.939945977. It is not an entire interval and does not contain the sample mean; a separate mean is needed for lower and upper endpoints. The syntax comes from Zoho’s official reference and the numerical result is independently calculated, not natively tested in Zoho. [Z-CONFIDENCE, M1]

Availability and version history

  • Introduced: The original introduction version and date are not established by the checked sources.
  • Availability: Currently documented in Zoho Sheet’s rolling web-service help; no numbered release or retirement endpoint is established.
  • Scope: English-language web-service documentation. Mobile and offline-client parity is outside the verified scope.
  • Checked: October 14, 2026, against the official CONFIDENCE reference. Documentation check; not a new native test.

The exact Zoho signature and required arguments

CONFIDENCE(α; sd; size)
Position Argument Required Value and meaning Example
1 α Yes Significance level of the two-sided normal interval; confidence level is 1−α. 0.05 gives a 95% confidence level.
2 sd Yes Known population standard deviation of the modeled observations, strictly positive according to Zoho’s argument definition. 15
3 size Yes Sample size, at least 1 according to the official error notes. Use a positive whole-number count for statistically meaningful examples. 100

All three arguments are present in Zoho’s published signature. The order is alpha, standard deviation, sample count. It is easy to accidentally reverse sd and size because both are numbers, but that changes the resulting margin. The semicolon is the argument separator shown by the English-language Zoho Help page; account locale behavior was not independently tested. [Z-CONFIDENCE]

The standard statistical construction assumes the population SD σ is known and the estimator’s normal sampling distribution is justified—classically normal observations or appropriate large-sample conditions. A dataset’s sample standard deviation is not automatically a known population SD. Using an estimated SD for a small sample generally calls for Student’s t methods rather than silently labeling this exact normal margin as an exact result. [M1]

Why the output is a half-width, not both endpoints

For confidence level 1−α and known σ, the conventional two-sided normal confidence interval for the population mean is

sample_mean +/- z_(1 - alpha/2) * population_sd / SQRT(sample_size)

CONFIDENCE represents the nonnegative expression after the plus/minus sign—the margin of error. If the sample mean is 100 and the margin is 2.939945977, the mathematical interval endpoints are approximately 97.060054023 and 102.939945977. The full interval width is twice the margin, about 5.879891954. [M1]

Zoho’s description says it returns a “confidence interval,” but its three-argument formula has no sample mean input and therefore cannot determine an interval’s absolute endpoints. The guide makes this essential semantic distinction explicit. Microsoft’s independently published CONFIDENCE reference likewise describes the range as sample mean ± CONFIDENCE; this is compatibility context, not proof of Zoho’s underlying engine. [Z-CONFIDENCE, MS-CONFIDENCE, M1]

A 95% confidence statement describes a procedure’s long-run coverage under statistical assumptions, not a 95% posterior probability that a particular fixed population mean lies in the already-computed numeric interval. Avoid phrasing that suggests the latter without a separate probabilistic model. [M1]

Reproducible worksheet: change alpha, sigma and sample size

Enter columns A through C as in the following table. The example values are illustrative model parameters, not real study data. Put =CONFIDENCE(A2;B2;C2) in D2 and fill down. [M1]

Row A — alpha B — known population SD C — sample n D — candidate formula Independent expected margin
2 0.05 15 100 =CONFIDENCE(A2;B2;C2) 2.939945977
3 0.10 12 64 =CONFIDENCE(A3;B3;C3) 2.467280440
4 0.01 8 16 =CONFIDENCE(A4;B4;C4) 5.151658607
5 0.05 15 400 =CONFIDENCE(A5;B5;C5) 1.469972988

Check the behavior: increasing sample size from 100 to 400 while holding confidence level and σ fixed halves the margin: 1/sqrt(n) scales inversely with the square root of n. Lowering α from 0.05 to 0.01, on the other hand, requires a larger critical normal z-value and usually creates a wider interval at the same σ and n. [M1]

Independently, the conventional expression can be constructed with Zoho’s separately documented inverse standard-normal function: =NORMSINV(1-A2/2)*B2/SQRT(C2). This should match the normal-theory margin in D2 within rounding if both implement the documented mathematical functions, but no direct worksheet comparison was run. [Z-NORMSINV, M1]

Build an entire interval by adding the sample mean

For a concrete report, enter a sample mean of 100 in F2, alpha 0.05 in G2, known σ 15 in H2, and n = 100 in I2. Place =CONFIDENCE(G2;H2;I2) in J2. The two candidate endpoint formulas are:

Lower endpoint: =F2-J2
Upper endpoint: =F2+J2
Full width:     =2*J2

The mathematical expectations are 97.060054023, 102.939945977, and 5.879891954, respectively. Keep enough decimal precision in calculation cells so rounding the margin too early does not distort endpoint reports. Displaying a summary with two decimal places is a presentation decision; underlying data should retain more digits. [M2]

The interval interpretation depends on the random sampling and normal-approximation assumptions. A spreadsheet formula does not check for biased sampling, dependence between observations, a mistaken known standard deviation, or outliers. If the inputs come from a time series or repeated measurements on the same individuals, an ordinary independent-observations formula may understate uncertainty. [M2]

Advanced use: plan sample size for a target margin

The margin equation can be rearranged for the minimum nominal sample size needed to achieve a target margin of error E:

n_required = CEILING((z_(1-alpha/2) * sigma / E)^2)

For a 95% interval, known σ = 15 and desired margin E = 3, the independent real-valued sample-size requirement is roughly 96.03647, so the mathematically required integer sample size is 97. A candidate spreadsheet formula that avoids relying on a possibly different documented CEILING signature is =ROUNDUP((NORMSINV(1-0.05/2)*15/3)^2;0); however, this guide does not assert the exact native behavior of that multi-function expression in any particular Zoho account. Its corresponding mathematical derivation and rounding are independently checked. [Z-NORMSINV, M3]

The n formula describes a statistical design under the assumed model. It does not adjust for expected nonresponse, clustering, finite-population correction, or design effects. In a practical collection plan, those might require additional sample size beyond the nominal result. [M3]

Errors, boundary inputs and troubleshooting

Issue Official or statistical explanation Handling guidance
#NUM! from alpha Zoho says alpha outside the interval between 0 and 1 is invalid. Use an interior significance level such as 0.05; boundary α = 0 or 1 is not a useful finite two-sided normal interval.
#NUM! from sd Zoho’s argument text requires sd > 0; its error table explicitly says it errors for sd < 0. Treat zero SD as an unresolved documentation edge; do not promise acceptance or rejection without native testing. Use a justified strictly positive known SD for examples.
#NUM! from size The official page lists sizes below 1 as invalid. Supply a valid positive sample count; whole numbers are statistically appropriate. Fractional sizes are not natively characterized by this research.
#VALUE! Bad argument types, e.g., a cell contains a text label rather than a number. Check all three referenced cells.
#NAME! Misspelled function or undefined name. Type CONFIDENCE, not CONFIDENT, and inspect named references.
#REF! One or more input cells became invalid after deletion/movement. Repair cell references, avoiding silently substituted inputs.
Margin appears far too large SD and n transposed, or alpha entered as 95 rather than 0.05. Read arguments left to right; 0.05 is 5% significance, not 95% confidence expressed as 95.

The generic #N/A! description in Zoho’s help references lookup behavior and should not be treated as a distinct CONFIDENCE-specific validation rule. Numeric boundaries, sample-size rounding of nonintegers, overflow behavior and floating-point precision in different Zoho editions were not tested. [Z-CONFIDENCE]

Evidence-based compatibility and edition notes

Zoho Sheet: the English-language Statistical help page explicitly documents CONFIDENCE(α; sd; size), alpha/SD/sample-size meanings and the enumerated errors. Its embedded live sheet is not a substitute for native testing by this researcher. The reference does not specify the function’s original introduction version or guarantee mobile/offline parity. We make no unverified plan or edition claim. [Z-CONFIDENCE]

Microsoft Excel: Microsoft separately documents CONFIDENCE(alpha, standard_dev, size) with the same conceptual inputs, and explicitly states that Excel truncates a fractional size. That Excel-specific rule is not evidence that Zoho does the same. Microsoft also lists endpoint error conditions; these are only used for comparison, not transplanted into Zoho troubleshooting. [MS-CONFIDENCE]

Other spreadsheet products: No implementation-specific claim is made without their official documentation and a compatibility test. Formula import, argument punctuation, output precision and chart formatting must be checked in the actual target environment. [Z-CONFIDENCE]

For inverse normal quantiles, Zoho documents NORMSINV(p) at https://help.zoho.com/portal/en/kb/sheet/functions/statistical/articles/normsinv. NORMDIST’s cumulative mode is documented at https://help.zoho.com/portal/en/kb/sheet/functions/statistical/articles/normdist. ZTEST is separately documented at https://help.zoho.com/portal/en/kb/sheet/functions/statistical/articles/ztest; a test probability is a different statistical object from a confidence-interval margin. This ledger verifies official target pages, not internal draft URLs on Spreadsheet-Tutorials.com. [Z-NORMSINV, Z-NORMDIST, Z-ZTEST]

Claim-level sources and limitations — October 13, 2026

Validation limitations: First-supported Zoho version, edge-case execution, locale, account permissions and native workbook results are not verified.