TY - JOUR

T1 - Some results of ordering theory for guttman scaling

AU - Bart, William M.

PY - 1976

Y1 - 1976

N2 - Some of the ramifications of the linear order assumption underlying much of measurement theory are discussed. Ordering theory is then described as an alternative deterministic measurement model that does not make the linear order assumption. With this theory which emanates from Guttman's scalogram analysis, one can examine the ordering properties of sets of test items. One finding of ordering theory for Guttman scaling is that the probability of four or more items forming a Guttman scale is very small. Another finding of ordering theory is that the range of Guttman scales possible for a set of n items is between I and either C(n, n/2) if n is even or C(n, n+1/2) if n is odd. A third finding of ordering theory is that Guttman scales can be classified according to a certain matrix decomposition method. © 1976, Sage Publications. All rights reserved.

AB - Some of the ramifications of the linear order assumption underlying much of measurement theory are discussed. Ordering theory is then described as an alternative deterministic measurement model that does not make the linear order assumption. With this theory which emanates from Guttman's scalogram analysis, one can examine the ordering properties of sets of test items. One finding of ordering theory for Guttman scaling is that the probability of four or more items forming a Guttman scale is very small. Another finding of ordering theory is that the range of Guttman scales possible for a set of n items is between I and either C(n, n/2) if n is even or C(n, n+1/2) if n is odd. A third finding of ordering theory is that Guttman scales can be classified according to a certain matrix decomposition method. © 1976, Sage Publications. All rights reserved.

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U2 - 10.1177/001316447603600113

DO - 10.1177/001316447603600113

M3 - Article

SN - 0013-1644

VL - 36

SP - 141

EP - 148

JO - Educational and Psychological Measurement

JF - Educational and Psychological Measurement

IS - 1

ER -