FTEST

Microsoft publishes '=FTEST(A2:A6,B2:B6)' with the result 0.64831785. Derived independently in Python at 50 digits, and along a different path from any statistics library's F routines: the two sample variances are computed by hand from the data (sample 1 mean 11.6, sum of squared deviations 159.2, variance 159.2/4 = 39.8; sample 2 mean 31.4, sum of squared deviations 259.2, variance 259.2/4 = 64.8), giving the ratio F = 39.8/64.8 = 0.6141975308641975 on 4 and 4 degrees of freedom. The upper-tail probability is then taken from the REGULARIZED INCOMPLETE BETA function rather than from an F distribution routine -- P(F > f) = I_{d2/(d2+d1*f)}(d2/2, d1/2) = 0.67584107660691275 -- and the two-tailed answer is 2*min(p, 1-p) = 0.64831784678617450366, which rounds to exactly the published 0.64831785. This is the same example data, and the same derived value, that batch C asserted for the modern replacement F.TEST; asserting both is the point, because it checks that an engine's legacy alias really is the same function. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

Not a published example; derived from the documented definition. FTEST "returns the two-tailed probability that the variances in array1 and array2 are not significantly different" -- a statement about the pair of samples with no privileged first argument, so the function must be symmetric. Mechanically: swapping the samples replaces F by 1/F, which swaps the two tails, and 2*min(p, 1-p) is invariant under that swap. Asserted as a difference of exactly zero rather than as two separate values so that the check cannot be passed by an engine that gets both directions equally wrong. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

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, FTEST returns the #DIV/0! error value." C2:C6 is five copies of 7, so its variance is exactly zero and the F ratio's denominator vanishes. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #DIV/0!, the same substitution batch C recorded for this function's modern replacement F.TEST on the identical inputs. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If the number of data points in array1 or array2 is less than 2 ... FTEST returns the #DIV/0! error value." A one-point sample has no n-1 estimator. Asserted separately from the zero-variance case because they are different guards on the same documented error. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #DIV/0!, the same substitution batch C recorded for this function's modern replacement F.TEST on the identical inputs. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft publishes '=FTEST(A2:A6,B2:B6)' with the result 0.64831785. Derived independently in Python at 50 digits, and along a different path from any statistics library's F routines: the two sample variances are computed by hand from the data (sample 1 mean 11.6, sum of squared deviations 159.2, variance 159.2/4 = 39.8; sample 2 mean 31.4, sum of squared deviations 259.2, variance 259.2/4 = 64.8), giving the ratio F = 39.8/64.8 = 0.6141975308641975 on 4 and 4 degrees of freedom. The upper-tail probability is then taken from the REGULARIZED INCOMPLETE BETA function rather than from an F distribution routine -- P(F > f) = I_{d2/(d2+d1*f)}(d2/2, d1/2) = 0.67584107660691275 -- and the two-tailed answer is 2*min(p, 1-p) = 0.64831784678617450366, which rounds to exactly the published 0.64831785. This is the same example data, and the same derived value, that batch C asserted for the modern replacement F.TEST; asserting both is the point, because it checks that an engine's legacy alias really is the same function. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

Not a published example; derived from the documented definition. FTEST "returns the two-tailed probability that the variances in array1 and array2 are not significantly different" -- a statement about the pair of samples with no privileged first argument, so the function must be symmetric. Mechanically: swapping the samples replaces F by 1/F, which swaps the two tails, and 2*min(p, 1-p) is invariant under that swap. Asserted as a difference of exactly zero rather than as two separate values so that the check cannot be passed by an engine that gets both directions equally wrong. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

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, FTEST returns the #DIV/0! error value." C2:C6 is five copies of 7, so its variance is exactly zero and the F ratio's denominator vanishes. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #DIV/0!, the same substitution batch C recorded for this function's modern replacement F.TEST on the identical inputs. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If the number of data points in array1 or array2 is less than 2 ... FTEST returns the #DIV/0! error value." A one-point sample has no n-1 estimator. Asserted separately from the zero-variance case because they are different guards on the same documented error. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #DIV/0!, the same substitution batch C recorded for this function's modern replacement F.TEST on the identical inputs. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

Microsoft publishes '=FTEST(A2:A6,B2:B6)' with the result 0.64831785. Derived independently in Python at 50 digits, and along a different path from any statistics library's F routines: the two sample variances are computed by hand from the data (sample 1 mean 11.6, sum of squared deviations 159.2, variance 159.2/4 = 39.8; sample 2 mean 31.4, sum of squared deviations 259.2, variance 259.2/4 = 64.8), giving the ratio F = 39.8/64.8 = 0.6141975308641975 on 4 and 4 degrees of freedom. The upper-tail probability is then taken from the REGULARIZED INCOMPLETE BETA function rather than from an F distribution routine -- P(F > f) = I_{d2/(d2+d1*f)}(d2/2, d1/2) = 0.67584107660691275 -- and the two-tailed answer is 2*min(p, 1-p) = 0.64831784678617450366, which rounds to exactly the published 0.64831785. This is the same example data, and the same derived value, that batch C asserted for the modern replacement F.TEST; asserting both is the point, because it checks that an engine's legacy alias really is the same function. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

Not a published example; derived from the documented definition. FTEST "returns the two-tailed probability that the variances in array1 and array2 are not significantly different" -- a statement about the pair of samples with no privileged first argument, so the function must be symmetric. Mechanically: swapping the samples replaces F by 1/F, which swaps the two tails, and 2*min(p, 1-p) is invariant under that swap. Asserted as a difference of exactly zero rather than as two separate values so that the check cannot be passed by an engine that gets both directions equally wrong. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

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, FTEST returns the #DIV/0! error value." C2:C6 is five copies of 7, so its variance is exactly zero and the F ratio's denominator vanishes. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #DIV/0!, the same substitution batch C recorded for this function's modern replacement F.TEST on the identical inputs. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.

Excel documents: "If the number of data points in array1 or array2 is less than 2 ... FTEST returns the #DIV/0! error value." A one-point sample has no n-1 estimator. Asserted separately from the zero-variance case because they are different guards on the same documented error. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #VALUE! here instead of the documented #DIV/0!, the same substitution batch C recorded for this function's modern replacement F.TEST on the identical inputs. Set up from Microsoft's own worked-example table for FTEST: the header row Data1 / Data2 in row 1 and the two five-value samples 6, 7, 9, 15, 21 and 20, 28, 31, 38, 40 in A2:A6 and B2:B6, exactly as the page pastes them at A1. Two extra columns this corpus adds for the documented error branches: C2:C6 is five copies of 7 (a sample whose variance is zero) and D2 / E2 are single-cell samples. Column F is untouched because this harness writes the formula under test into cell F1.