Measurement and Scaling Concepts

Measurement Measurement is the process of describing some property of a phenomenon of interest, usually by assigning numbers in a reliable and valid way. The numbers convey information about the property being measured. When numbers are used the researcher must have a rule for assigning a number to an observation in a way that provides accurate description.

We measure attributes of object. We do not measure objects . What do we measure? We measure attributes of object. We do not measure objects .

A generalized idea that represent something of meaning. Concept A generalized idea that represent something of meaning.

Operational Definition Researchers measure concepts through a process known as operationalization. This process involves identifying scales that correspond to variance in the concept.

Constructs A construct is a term used for concepts that are measured with multiple variables. Constructs are not directly measured. Constructs are measured through indicator variables.

Scale Series of items arranged according to value for the purpose of quantification A continuous spectrum

Levels of Scale Measurement Types of Scales Nominal: classifies/identifies by a quality of the object Ordinal: classifies using a ranking order of objects Interval: quantifies objects in order on a continuum Ratio: classifies by comparison to a standard Categorical: classifies by a specific characteristic

Nominal, Ordinal, Interval, and Ratio Scales Provide Different Information © 2007 Thomson/South-Western. All rights reserved.

Nominal Scale Properties A nominal scale assigns a value for identification or classification purpose only. Sammy Sosa # 21 Barry Bonds # 25

Nominal Scale

Ordinal Scale Properties An ordinal scale is a ranking scale. Class rank of students is determined by using ordinal scale. For example, 1st, 2nd, …, 10th . But we can not compare in terms of marks or GPA. Win, place, & show (Exhibit 13.4)

Ordinal Scale

Interval Scale Properties Interval scales have both nominal and ordinal properties, but they also capture information about differences in quantities of a concept. See Exhibit 13.4

Interval Scale

Ratio Scale Properties Highest form of measurement. Have all properties of interval scales with the additional attribute of representing absolute quantities.

Ratio Scale

Three Criteria for Good Measurement Reliability Validity Sensitivity

Facts About the Four Levels of Scales © 2007 Thomson/South-Western. All rights reserved.

Facts About the Four Levels of Scales (cont’d) © 2007 Thomson/South-Western. All rights reserved.

Three Criteria for Good Measurement Reliability Validity Good Measurement Sensitivity © 2007 Thomson/South-Western. All rights reserved.

Measurement Accuracy: Reliability The degree to which measures are free from random error and therefore yield consistent results. An indicator of a measure’s internal consistency. Internal Consistency Represents a measure’s homogeneity or the extent to which each indicator of a concept converges on some common meaning. Measured by correlating scores on subsets of items making up a scale. © 2007 Thomson/South-Western. All rights reserved.

Methods for Measuring Reliability Test Retest Stability Equivalent Forms Splitting Halves Internal Consistency Reliability © 2007 Thomson/South-Western. All rights reserved.

Methods for Measuring Internal Consistency Split-half Method Assessing internal consistency by checking the results of one-half of a set of scaled items against the results from the other half. Coefficient alpha (α) The most commonly applied estimate of a multiple item scale’s reliability. Represents the average of all possible split-half reliabilities for a construct. © 2007 Thomson/South-Western. All rights reserved.

Measuring Stability Test-retest Method Administering the same scale or measure to the same respondents at two separate points in time to test for stability. Represents a measure’s repeatability. Test-retest Reliability Problems The pre-measure, or first measure, may sensitize the respondents and subsequently influence the results of the second measure. Time effects that produce changes in attitude or other maturation of the subjects. © 2007 Thomson/South-Western. All rights reserved.

Measurement Accuracy: Validity (cont’d) The accuracy of a measure or the extent to which a score truthfully represents a concept. Does a scale to measure what was intended to be measured? Establishing Validity: Is there a consensus that the scale measures what it is supposed to measure? Does the measure correlate with other measures of the same concept? Does the behavior expected from the measure predict actual observed behavior?

Approaches to Establishing Validity Face or Content Validity Concurrent Predictive Criterion Validity Construct Validity Validity © 2007 Thomson/South-Western. All rights reserved.

Measurement Accuracy: Validity (cont’d) Face (content) Validity A scale’s content logically appears to reflect what was intended to be measured. Criterion Validity The ability of a measure to correlate with other standard measures of similar constructs or established criteria. Construct Validity Exists when a measure reliably measures and truthfully represents a unique concept. © 2007 Thomson/South-Western. All rights reserved.

Measurement Accuracy: Validity (cont’d) Convergent Validity Another way of expressing internal consistency; highly reliable scales contain convergent validity. Discriminant Validity Represents how unique or distinct is a measure; a scale should not correlate too highly with a measure of a different construct. © 2007 Thomson/South-Western. All rights reserved.

EXHIBIT 13.7 Reliability and Validity on Target © 2007 Thomson/South-Western. All rights reserved.

Measurement Accuracy: Sensitivity A measurement instrument’s ability to accurately measure variability in stimuli or responses. Composite measures allow for a greater range of possible scores, they are more sensitive than single-item scales. Sensitivity is generally increased by adding more response points or adding scale items. © 2007 Thomson/South-Western. All rights reserved.