F.TEST

Microsoft's page publishes '=F.TEST(A2:A6,B2:B6)' over the data 6/7/9/15/21 and 20/28/31/38/40 with the result 0.64831785. Re-derived independently: the sample variances are 39.8 and 64.8, so the F statistic is 64.8/39.8 = 1.6281407035175879846 with 4 and 4 degrees of freedom; its upper tail computed from the regularized incomplete beta function with mpmath at 50 digits is 0.32415892339308724265, and the documented "two-tailed probability" is twice that, 0.64831784678617448529, i.e. exactly the published 0.64831785 at 8 dp.

A deliberate duplicate of the documented example under a different setup, kept because Microsoft documents that "If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included", and the page's own worksheet has the text headers Data1 and Data2 sitting directly above the two ranges. An engine with an off-by-one range read picks up a header and diverges here while passing nothing else differently.

Excel documents: "If the number of data points in array1 or array2 is less than 2, or if the variance of array1 or array2 is zero, F.TEST returns the #DIV/0! error value." D2:D6 holds five copies of the value 5, so its variance is exactly zero. EXECUTED RESULT: all four LibreOffice builds return #VALUE! where the page documents #DIV/0! -- the #VALUE!-substitution pattern reaching a documented #DIV/0! rather than the usual #NUM!, the same shape batch B recorded for CHISQ.TEST's documented #N/A.

Excel documents the same rule for size as for zero variance: "If the number of data points in array1 or array2 is less than 2 ... F.TEST returns the #DIV/0! error value." E2:E3 is a two-cell range holding the number 3 and the text "n/a", and Microsoft documents on the same page that "If an array or reference argument contains text, logical values, or empty cells, those values are ignored" -- so the range contributes exactly ONE data point, one short of the documented minimum. The two conditions the sentence joins are asserted separately (see F.TEST_zero_variance_div0) so a single #DIV/0! cannot stand in for both. EXECUTED RESULT: all four LibreOffice builds return #VALUE! where the page documents #DIV/0!, the same substitution as F.TEST_zero_variance_div0.

Microsoft's page publishes '=F.TEST(A2:A6,B2:B6)' over the data 6/7/9/15/21 and 20/28/31/38/40 with the result 0.64831785. Re-derived independently: the sample variances are 39.8 and 64.8, so the F statistic is 64.8/39.8 = 1.6281407035175879846 with 4 and 4 degrees of freedom; its upper tail computed from the regularized incomplete beta function with mpmath at 50 digits is 0.32415892339308724265, and the documented "two-tailed probability" is twice that, 0.64831784678617448529, i.e. exactly the published 0.64831785 at 8 dp.

A deliberate duplicate of the documented example under a different setup, kept because Microsoft documents that "If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included", and the page's own worksheet has the text headers Data1 and Data2 sitting directly above the two ranges. An engine with an off-by-one range read picks up a header and diverges here while passing nothing else differently.

Excel documents: "If the number of data points in array1 or array2 is less than 2, or if the variance of array1 or array2 is zero, F.TEST returns the #DIV/0! error value." D2:D6 holds five copies of the value 5, so its variance is exactly zero. EXECUTED RESULT: all four LibreOffice builds return #VALUE! where the page documents #DIV/0! -- the #VALUE!-substitution pattern reaching a documented #DIV/0! rather than the usual #NUM!, the same shape batch B recorded for CHISQ.TEST's documented #N/A.

Excel documents the same rule for size as for zero variance: "If the number of data points in array1 or array2 is less than 2 ... F.TEST returns the #DIV/0! error value." E2:E3 is a two-cell range holding the number 3 and the text "n/a", and Microsoft documents on the same page that "If an array or reference argument contains text, logical values, or empty cells, those values are ignored" -- so the range contributes exactly ONE data point, one short of the documented minimum. The two conditions the sentence joins are asserted separately (see F.TEST_zero_variance_div0) so a single #DIV/0! cannot stand in for both. EXECUTED RESULT: all four LibreOffice builds return #VALUE! where the page documents #DIV/0!, the same substitution as F.TEST_zero_variance_div0.

Microsoft's page publishes '=F.TEST(A2:A6,B2:B6)' over the data 6/7/9/15/21 and 20/28/31/38/40 with the result 0.64831785. Re-derived independently: the sample variances are 39.8 and 64.8, so the F statistic is 64.8/39.8 = 1.6281407035175879846 with 4 and 4 degrees of freedom; its upper tail computed from the regularized incomplete beta function with mpmath at 50 digits is 0.32415892339308724265, and the documented "two-tailed probability" is twice that, 0.64831784678617448529, i.e. exactly the published 0.64831785 at 8 dp.

A deliberate duplicate of the documented example under a different setup, kept because Microsoft documents that "If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included", and the page's own worksheet has the text headers Data1 and Data2 sitting directly above the two ranges. An engine with an off-by-one range read picks up a header and diverges here while passing nothing else differently.

Excel documents: "If the number of data points in array1 or array2 is less than 2, or if the variance of array1 or array2 is zero, F.TEST returns the #DIV/0! error value." D2:D6 holds five copies of the value 5, so its variance is exactly zero. EXECUTED RESULT: all four LibreOffice builds return #VALUE! where the page documents #DIV/0! -- the #VALUE!-substitution pattern reaching a documented #DIV/0! rather than the usual #NUM!, the same shape batch B recorded for CHISQ.TEST's documented #N/A.

Excel documents the same rule for size as for zero variance: "If the number of data points in array1 or array2 is less than 2 ... F.TEST returns the #DIV/0! error value." E2:E3 is a two-cell range holding the number 3 and the text "n/a", and Microsoft documents on the same page that "If an array or reference argument contains text, logical values, or empty cells, those values are ignored" -- so the range contributes exactly ONE data point, one short of the documented minimum. The two conditions the sentence joins are asserted separately (see F.TEST_zero_variance_div0) so a single #DIV/0! cannot stand in for both. EXECUTED RESULT: all four LibreOffice builds return #VALUE! where the page documents #DIV/0!, the same substitution as F.TEST_zero_variance_div0.