FTEST in Zoho Sheet: Comparing Two Sample Variances

FTEST examines whether two numeric samples have substantially different amounts of variability. It returns an F-test result described by Zoho Sheet’s official reference as a probability related to the hypothesis of equal variances. The function takes two arrays or ranges, can accept unequal sample sizes, and differs conceptually from a test comparing two means. The example below compares two processes whose averages are similar but whose spreads are very different.

Evidence status: The formulas and argument order come from Zoho’s public English help page. Calculations described as modeled expectations are independent statistical calculations using sample variances and an F distribution, not captured Zoho Sheet results. No account, sheet, mobile app or version was exercised.

FTEST(data1; data2)

Neither argument is optional; Zoho documents no tails, alpha or type parameter and no default values. Its examples include unequal-length ranges such as A2:A6 and B2:B4, so the sample counts need not match. Z1 Do not insert a third argument to control the tail, assume data must be paired, or treat the function name as a request for the F-statistic alone.

A sample is a series of individual observations, not a list of already calculated subgroup standard deviations or averages. Keep data in comparable units: comparing dollar amounts with minutes would be meaningless even if the formula accepted them. Blank cells, text values and error cells should be reviewed before interpreting any statistical result. The general Zoho error table identifies invalid data types, but its FTEST article does not fully specify how all nonnumeric items are ignored or coerced.

Suppose two independent production lines report processing times for eight randomly sampled jobs each, measured in minutes. Enter the numbers in columns A and B with headings in row 1:

Put the formula into a free cell such as D2:

=FTEST(A2:A9;B2:B9)

The sample means are 11.5 minutes for Line Stable and 12.5 minutes for Line Variable. The means are close; however, sample variance is 1.428571428571 and 30.857142857143 square minutes, respectively. This difference in spread is what a variance test studies.

Independent calculation and predicted result

For an ordinary two-sample normal-theory F test, the sample variances are computed as Σ(x−mean)²/(n−1). Their ratio in the displayed order is:

F = 1.428571428571 / 30.857142857143
  = 0.0462962962963

numerator df = 8−1 = 7
denominator df = 8−1 = 7

For a two-sided variance-comparison model, calculate 2 × min(F_CDF(F;7;7), 1−F_CDF(F;7;7)). The resulting independent mathematical value is 0.000622003221437. That is the modeled two-sided p-value, not a result returned from a live Zoho Sheet formula. Microsoft’s official F.TEST reference explicitly describes a two-tailed probability for the corresponding Excel calculation. Zoho’s FTEST page says it computes a likelihood of equal variance but does not independently spell out the tail convention, so an native check is needed before presenting 0.000622003221437 as an exact Zoho return value.

You can independently inspect the F ratio using the separate Zoho VAR function, which documents sample variance:

=VAR(A2:A9)
=VAR(B2:B9)
=VAR(A2:A9)/VAR(B2:B9)

For additional diagnostics, Zoho’s FDIST function is documented as a right-tail F probability, and FINV is its right-tail inverse. A conceptual two-tail check is 2 × MIN(right_tail, 1−right_tail) when using the correctly ordered degrees of freedom and a continuous F model. Do not silently treat right-tail FDIST as an identical replacement for a two-tail FTEST.

How to interpret

If the model returns a two-sided p-value near 0.00062 and your threshold was α=0.05, this is evidence of different variances under the standard independent-normal-samples assumptions. It does not say the lines have different average speeds; their averages address another question. A small p-value also does not directly quantify how much line-to-line spread matters operationally. The sample standard deviations (square roots of sample variances) are approximately 1.19523 and 5.55492 minutes—use these alongside a practical tolerance.

A p-value is not the probability that the variances are equal, and a nonsignificant test is not proof of equal variances. Consider confidence intervals, sample sizes and process context rather than thresholding a single number.

Zoho’s help page demonstrates that the second range can be shorter than the first. Z1 For example, if a second team only completed five comparable independent jobs, keep A2:A9 with eight observations but use a five-number second range such as B2:B6:

=FTEST(A2:A9;B2:B6)

This changes both the sample variance estimated from B and its degrees of freedom: A uses 7, B uses 4. Reusing the eight-by-eight modeled p-value is incorrect. A range of five cells that happens to contain three blanks is also not automatically a five-observation sample: record the numeric count, not only the address span. The official article establishes that unequal range lengths are permitted, but does not supply the exact return value for our invented shortened dataset.

Check assumptions first. The classical F variance test is particularly sensitive to non-normal distributions and strong outliers. Eight observations from each line do not establish approximate normality. Histograms or quantile plots, a documented measurement procedure and independent sampling strengthen interpretation. If outliers or strong skew are prominent, a robust alternative such as a Levene or Brown–Forsythe test may be more appropriate; do not assume Zoho provides those tests as built-in functions merely because they are well known elsewhere.

Design matters. For paired repeated measurements of the same items, the independence model underlying the ordinary two-sample F statistic is not automatically suitable. For single-factor quality monitoring, raw individual observations and control-chart methods may answer a more useful question than a one-off p-value.

Direction matters. The F ratio changes from approximately 0.04630 to 21.6 if you exchange its numerator and denominator. With corresponding degrees of freedom exchanged, a properly constructed two-sided test has the same p-value. A one-sided claim—“Line B is more variable”—requires an explicitly defined alternative and appropriate tail computation; the two-argument Zoho FTEST page does not describe a configurable one-sided option.

Reporting. A useful results note includes both sample sizes, both unbiased sample variances, the statistic and degrees of freedom, which tail convention was used, the significance threshold selected before looking at data, and the limitations of the sampling process.

The official source also contains broad template entries for #N/A!; their inclusion does not mean every missing-value or alias condition has been natively reproduced for FTEST. No first-release version, exhaustive limits or named result for a zero-variance input has been verified. Microsoft’s F.TEST help mentions a zero-variance error for Excel, which does not establish Zoho’s response. M1

Zoho documents FTEST(data1; data2); Microsoft documents modern Excel F.TEST(array1,array2) and explicitly calls its return a two-tailed probability. Z1 M1 Those two pages support a narrow functional comparison—both are variance comparison functions accepting two ranges. They do not prove that Zoho accepts the dotted Excel name F.TEST, that import/export preserves formulas without changes, or that floating-point precision and text coercion are identical. Do not write F.TEST(...) as if it were a verified Zoho alias.

This page covers the current public English Zoho Sheet cloud documentation reviewed on October 13, 2026 UTC. The page supplies no definitive first-supported release, tenant-plan constraints, or mobile/desktop parity matrix. The example’s semicolons follow the documented notation; alternate locale separators are not tested.

• Zoho VAR — sample variance used in the independent F-ratio calculation.
• Zoho FDIST — a one-sided right-tail F distribution probability, not automatically FTEST’s p-value.
• Zoho FINV — inverse right-tail distribution, useful for critical-value work.
• Zoho TTEST — difference in means, not variance; the intended inferential question determines which to use.
• Microsoft F.TEST — comparative Excel documentation only.

Documentation facts Z1: syntax, two required ranges, unequal-range examples, the specifically stated #DIV/0! for fewer than two points, and common errors. Mathematical model: independent sample-variance calculations and F-distribution tail probability, cross-checked in SciPy. Not validated: actual Zoho result for invented input; the exact two-sided convention, coercion, hidden blanks, account features or version matrix. The modeled result must not be presented as an observed Zoho output without a native test.