ASTM E1325-02
(Terminology)Standard Terminology Relating to Design of Experiments
Standard Terminology Relating to Design of Experiments
SCOPE
1.1 This standard includes those statistical items related to the area of design of experiments for which standard definitions appears desirable.
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An American National Standard
Designation:E1325–02
Standard Terminology Relating to
1
Design of Experiments
This standard is issued under the fixed designation E1325; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope occurs together in the same number, l, of blocks from the b
blocks.
1.1 This standard includes those statistical items related to
the area of design of experiments for which standard defini-
DISCUSSION—The design implies that every version of the principal
tions appears desirable.
factor appears the same number of times r in the experiment and that
the following relations hold true: bk = tr and r (k−1)= l(t − 1).
2. Referenced Documents
For randomization, arrange the blocks and versions within each
blockindependentlyatrandom.Sinceeachletterintheaboveequations
2.1 ASTM Standards:
represents an integer, it is clear that only a restricted set of combina-
2
E456 Terminology related to Quality and Statistics
tions (t, k, b, r, l) is possible for constructing balanced incomplete
block designs. For example, t =7, k =4, b =7, l=2.Versions of the
3. Significance and Use
principal factor:
3.1 This standard is a subsidiary to Terminology E456.
Block1 1236
3.2 It provides definitions, descriptions, discussion, and 2 2347
3 3451
comparison of terms.
4 4562
5 5673
4. Terminology
6 6714
7 7125
aliases,n—inafractionalfactorialdesign,twoormoreeffects
which are estimated by the same contrast and which,
completely randomized design, n—a design in which the
therefore, cannot be estimated separately.
treatments are assigned at random to the full set of experi-
n
DISCUSSION—(1) The determination of which effects in a 2 factorial
mental units.
are aliasedcanbemadeoncethe defining contrast(inthecaseofahalf
1
DISCUSSION—No block factors are involved in a completely random-
replicate) or defining contrasts (for a fraction smaller than ⁄2) are
ized design.
stated. The defining contrast is that effect (or effects), usually thought
tobeofnoconsequence,aboutwhichallinformationmaybesacrificed
completely randomized factorial design, n—a factorial ex-
fortheexperiment.Anidentity, I,isequatedtothe defining contrast(or
2 2 2
periment (including all replications) run in a completely
defining contrasts) and, using the conversion that A = B = C = I, the
randomized design.
multiplication of the letters on both sides of the equation shows the
aliases.Intheexampleunderfractionalfactorialdesign,I =ABCD.So composite design, n—a design developed specifically for
2 2 2
that: A = A BCD = BCD, and AB = A B CD=CD.
fitting second order response surfaces to study curvature,
constructed by adding further selected treatments to those
( 2) With a large number of factors (and factorial treatment n
obtained from a 2 factorial (or its fraction).
1 1
combinations) the size of the experiment can be reduced to ⁄4 , ⁄8,or
k n-k
1
in general to ⁄2 to form a 2 fractional factorial.
DISCUSSION—If the coded levels of each factor are−1 and+1 in the
n
2 factorial(seenotation2underdiscussionfor factorial experiment),
(3) There exist generalizations of the above to factorials having
the(2n +1)additionalcombinationsforacentralcompositedesignare
more than 2 levels.
(0, 0, ., 0), (6a, 0, 0, ., 0) 0, 6a, 0, ., 0) ., (0, 0, ., 6 a). The
n
minimum total number of treatments to be tested is (2 +2n +1) for a
balanced incomplete block design (BIB), n—an incomplete n
2 factorial. Frequently more than one center point will be run. For n
block design in which each block contains the same number
=2, 3 and 4 the experiment requires, 9, 15, and 25 units respectively,
k of different versions from the t versions of a single although additional replicate runs of the center point are usual, as
n
compared with 9, 27, and 81 in the 3 factorial. The reduction in
principal factor arranged so that every pair of versions
experiment size results in confounding, and thereby sacrificing, all
information about curvature interactions.The value of a can be chosen
1 to make the coefficients in the quadratic polynomials as orthogonal as
ThisterminologyisunderthejurisdictionofASTMCommitteeE11onQuality
possibletooneanotherortominimizethebiasthatiscreatedifthetrue
and Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling.
form of response surface is not quadratic.
The definitions in this standard were extracted from E456–89c.
Current edition approved Oct. 10, 2002. Published December 2002. Originally
confounded factorial design, n—a factorial experiment in
published as E1325–90. Last previous edition E1325–91(1997)
2
Annual Book of ASTM Standards, Vol 14.02. whi
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