Scaling and Index Construction Chapter: Ten Scaling and Index Construction

LEVELS OF MEASUREMENT Nominal level variables – classify or categorize – no numerical or ordered meaning, i.e., demographic variables – crime type, race. Ordinal level variables – have characteristics of nominal level; ranking or order, i.e., attitude scales. High to low or first, second, and third, however, does not indicate the magnitude of differences between numbers. Interval level variables – have characteristics of nominal and ordinal level scores and indicate the exact distance between the scores. Uses constant units of measurement, (i.e., inches, pounds, degrees) that yield equal intervals between points on a scale. (Ordinal level variables can sometimes be treated as interval level variables). Ratio level variables – contain characteristics of nominal, ordinal, and interval variables but there is also a presence of an absolute zero (thus, no negative values), i.e., age or pounds – there is no such thing as -2 years of age. Often referred to as interval / ratio measures.

Scaling By using the different levels of measurement, we can make connections between concepts and numbers. Scaling procedures attempt to increase the level of complexity (nominal to ordinal to interval/ratio) to build more complex and composite indicators of phenomena. Scaling enables the use of replication of previously developed scales but with different populations. Existing scales should be consulted before developing new scales because of their established track record.

Arbitrary Scales Arbitrary scales are a rough estimate based on face validity. An example is the Uniform Crime Report crime index. The problem is that this type of index fails to control for seriousness, or in other words, does not weight the categories.

Attitude Scales (Three Major Types) Thurstone scales – makes use of a series of judges to decide the appropriate scale. (Q Sort methodology). Equal appearing intervals. Likert Scales – a simple summation of a five-point bipolar response (from Strong Agree to Strongly Disagree), i.e., attitudinal research. This method uses both reversal items to eliminate response sets and item analysis to eliminate nondiscriminating items. Guttman Scales – unidimensionality; only one dimension or concept should be measured by a particular scale. Provides the opportunity to predict exact patterns of responses. * There are many varieties of these scales, i.e., Q sort, semantic differential, Sellin-Wolfgang Index, crime seriousness scales (rating scales and magnitude scales).

Crime Seriousness Scales (Severity Scales) Crime seriousness scales attempt to assign weight to crimes in terms of their relative severity. There are two types: Simple rating scales: These scales ask respondents to rate crime (usually) on a scale ranging from 1 (not serious) to 9 (extremely serious). These ordinal scales are unable to account for the magnitude of differences between scale scores. Magnitude scales: Measure public rankings of the degrees of relative seriousness of various crimes, i.e., Sellin-Wolfgang index and the National Survey of Crime Severity.

Prediction Scales Assigns scores that attempt to predict the likelihood of certain behaviors, i.e., committing crime, success or failure on parole. The Salient Factor Score – U.S. Parole Commission, i.e., likelihood of prisoner recidivism. Greenwood’s Rand Seven-Factor Index – selective incapacitation (individualized sentences), i.e., likelihood to commit a serious crime. Career Criminals, i.e., ROP (Repeat Offender Program)

Advantages of Scaling Provide more composite and exact measurement. Lend themselves to longitudinal assessment and replication. Force more rigorous thinking on the part of the researcher.

Disadvantages Artificiality – can a person’s true attitude or behavior be measured on a five or seven-point scale? Artificiality leads to “error of measurement.” Scaling is not a substitute for good theoretical and substantive knowledge of the subject under investigation.