16.881 – Robust System Design
Solution to Quiz #5
Analysis of Variance
1)
In Taguchi methods, the F value for a factor effect is defined as
a)
The probability that the we reject the hypothesis that the factor effect equals zero.
b)
The sum of squares due to a factor divided by the error variance.
c)
The mean square due to a factor divided by the error variance.
d)
The sum of squares due to a factor divided by the DOF for the factor.
C is the correct answer.
It is very simply the definition of the F value in Taguchi
methods. Note that in traditional oneway ANOVA, the F test statistic is defined
differently
dfB
F
SSB
dfW
SSW
Where SSB is the sum of squares within treatments and SSW is the sum of squares within
treatments.
A is incorrect.
To compute a probability from an F test statistic, you need to integrate
the F distribution over the critical region. This can be done in Mathcad with the pF
function or in excel with the FDIST function. F statistics are not normally used to
compute probabilities in robust design.
B is incorrect.
The sum of squares due to a factor divided by the DOF of the factor is
the mean square due to a factor. This is the key difference. You should note the similarity
in form between the F as defined in one way ANOVA and the Taguchi use of ANOVA.
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 Fall '03
 lDavidMiller
 Statistics, Normal Distribution, error variance

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