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DOE中有关MIXED DESIGN的问题

问一个MTB中有关DOE, MIXED DESIGN的问题, 数据结构为

Factor Type Levels Values
Temp fixed 2 100, 135
Op random 2 1, 2
Mach(Op) random 4 1, 2, 3, 4

Mach NESTED WITHIN IN Op

Analysis of Variance for Efficiency, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Temp 1 10.351 10.351 10.351 2.09 0.386
Op 1 40.951 40.951 40.951 3.10 0.337 x
Mach(Op) 2 31.972 31.972 15.986 2.06 0.327
Temp*Op 1 4.961 4.961 4.961 0.64 0.508
TempMach(Op) 2 15.502 15.502 7.751 *
Error 0 *
Total 7 103.739

x Not an exact F-test.
** Denominator of F-test is zero.

在MTB中注明红色部分的F值不是一个标准的F-TEST, 但是3.1这个值是怎么求出来的, 一直没想通 求教
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Description

Why does the ANOVA output include an "x" next to a p-value in the ANOVA table and the label "Not an exact F-test?"
Solution

An exact F-test for a term is one in which the expected value of the numerator mean squares differs from the expected value of the denominator mean squares only by the variance component or the fixed factor of interest. For more details, see Knowledgebase ID 1194.

Sometimes, however, such a mean square cannot be calculated. In this case, MINITAB uses a mean square that results in an approximate F-test and displays an "x" next to the p-value to indicate that the F-test is not exact.

For example, suppose you performed an ANOVA with the fixed factor Supplement and the random factor Lake, and the following output was given for the expected mean squares (EMS):

Expected Mean Squares, using Adjusted SS

Source Expected Mean Square for Each Term
1 Supplement (4) + 1.7500(3) + Q
2 Lake (4) + 1.7143(3) + 5.1429(2)
3 Supplement*Lake (4) + 1.7500(3)
4 Error (4)


The F statistic for Supplement is the mean square for Supplement divided by the mean square for the Supplement*Lake interaction. If the effect for Supplement is very small, the expected value of the numerator equals the expected value of the denominator. This is an example of an exact F test.

Notice, however, that for a very small Lake effect, there are no mean squares such that the expected value of the numerator equals the expected value of the denominator. Therefore, MINITAB uses an approximate F-test. In this example, the mean square for Lake is divided by the mean square for the Supplement*Lake interaction. This results in an expected value of the numerator being approximately equal to that of the denominator if the Lake effect is very small.

Reference: D. C. Montgomery (1997). Design and Analysis of Experiments, Fourth Edition. John Wiley & Sons.

只提到是近似的,没详细说明。(Knowledgebase ID 1194里也没说明。)

http://www.minitab.com/en-CN/s ... D1033

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