Statistical
F-Test formula: compare two sample variances (precision & spread ratio)
Calculate an oriented variance ratio and compare it with a two-sided F-test threshold under the stated assumptions.
Orient the ratio and its degrees of freedom together
An F-test compares process consistency—for example, whether Machine A produces wider diameter spread than Machine B—by dividing one sample variance VAR.S by the other.
Putting the larger sample variance in the numerator produces F >= 1. For a two-sided test, use an upper alpha/2 threshold with degrees of freedom matching that ordering.
| Metric | Machine A [9.1, 9.7, 10.3, 10.9] | Machine B [9.6, 9.9, 10.2, 10.3] |
|---|---|---|
| Sample Mean | 10.00 mm | 10.00 mm |
| Sample Variance (VAR.S) | 0.60 | 0.10 |
| Oriented F-Statistic | 0.60 / 0.10 = 6.00 | df1 = 3, df2 = 3 |
Upper-tail F-ratio and critical-value check
For df=(3,3), the rounded upper 2.5% critical value is 15.4392. The observed ratio 6 does not exceed it.
=LET(varianceTermA, VAR.S(A2:A5), varianceTermB, VAR.S(B2:B5), ROUND(MAX(varianceTermA, varianceTermB) / MIN(varianceTermA, varianceTermB), 4))Compare F against critical threshold in C2
Flags "Reject equal variance" when F > CriticalF.
=IF(MAX(VAR.S(A2:A5), VAR.S(B2:B5)) / MIN(VAR.S(A2:A5), VAR.S(B2:B5)) > C2, "Reject equal variance", "Fail to reject")Inputs and interpretation
Use independent normal samples with at least two observations and positive variance each. The F-test is sensitive to nonnormality. This two-sided 5% example uses the upper 2.5% threshold. Numerator and denominator degrees of freedom must follow the variance ordering, including when sample sizes differ. Failure to reject does not establish equal variances.
Try the example
Use the original values or change them to test your understanding.