Page 307 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 287

Two-Sided Example
95% Bonferroni confidence intervals for standard deviations
Sample N Lower SD Upper
1 50 2.03691 2.5 3.22022
2 25 1.35868 1.8 2.63474

F Test (Normal Distribution)
Test statistic = 1.93, p value = 0.083.

Conclude: Fail to reject null (p > 0.05); Variances may be equal.

One-Sided Example
Calculate p = (reported p)/2 = 0.083/2 = 0.0415.
Conclude: Reject null; variances are not equal.

Excel

Reports one-sided case; calculate p as
Two-sided: 2*FDIST(F ,ν ,ν )
0
2
1
One-sided: FDIST(F ,ν ,ν )
0 1 2
Two-Sided Example

=2*FDIST(1.93,49,24); p = 0.083; fail to reject; variances may be equal.

One-Sided Example
=FDIST(1.93,49,24); p = 0.042; reject null; variances are not equal.

Interpretation

The result of the test is to compare the calculated statistics with a test statistic. If
the calculated statistic exceeds the critical value of the test statistic (based on the
α level chosen), then we reject the null hypothesis. If not, then we fail to reject