original observations. (For example, a respondent's scale score of 2 implies that that respondent responded positively to questions 1 and 2 and negatively to questions 3, 4, and 5.) Guttman scale, if supported by data, is useful for efficiently assessing subjects (respondents, testees or any collection of investigated objects) on a one-dimensional scale with respect to the specified attribute. Typically, Guttman scales are found with respect to attributes that are narrowly defined. While other scaling techniques (e.g., Likert scale) produce a single scale by summing up respondents' scores—a procedure that assumes, often without justification, that all observed variables have equal weights — Guttman scale avoids weighting the observed variables; thus 'respecting' data for what they are. If a Guttman scale is confirmed, the measurement of the attribute is intrinsically one-dimensional; the unidimensionality is not forced by summation or averaging. This feature renders it appropriate for the construction of replicable scientific theories and meaningful measurements, as explicated in facet theory. Ordinal variables Given a data set of N subjects observed with respect to n ordinal variables, each having any finite number (≥2) of numerical categories ordered by increasing strength of a pre-specified attribute, let aij be the score obtained by subject i on variable j, and define the list of scores that subject i obtained on the n variables, ai=ai1…ain , to be the profile of subject i. (The number of categories may be different in different variables; and the order of the variables in the profiles is not important but should be fixed). Define: Two profiles, as and at are equal, denoted as=at, iff asj=atj for all j=1…n Profile as is greater than Profile at, denoted as>at, iff asj ≥ atj for all j=1…n and asj' > atj' for at least one variable, j. Profiles as and at are comparable, denoted asSat, iff as=at; or as>at; or at>as Profiles as and at are incomparable, denoted as$at, if they are not comparable (that is, for at least one variable, j, asj' > atj' and for at least one other variable, j'', atj'' > asj''. For data sets where the categories of all variables are similarly ordered numerically (from high to low or from low to high) with respect to a given attribute, Guttman scale is defined simply thus: Definition: Guttman scale is a data set in which all profile-pairs are comparable. Example: Non-dichotomous variables Consider the following four variables that assess