On the scales of measurement

Let $\text{X}$ = 〈X, ≧, R₁, R₂…〉 be a relational structure, 〈$\text{X, ≧}$〉 be a Dedekind complete, totally ordered set, and n be a nonnegative integer. $\text{X}$ is said to satisfy n-point homogeneity if and only if for each x₁,…, x_n, y₁,…, y_n such that x₁ ? x₂ ? … ? x_n and y₁ ? y₂ … ? y_n, there exists an automorphism α of $\text{X}$ such that α(x₁) = y_i. $\text{X}$ is said to satisfy n-point uniqueness if and only if for all automorphisms β and γ of $\text{X}$, if β and γ agree at n distinct points of $\text{X}$, then β and γ are identical. It is shown that if $\text{X}$ satisfies n-point homogeneity and n-point uniqueness, then n ≦ 2, and for the case n = 1, $\text{X}$ is ratio scalable, and for the case n = 2, interval scalable. This result is very general and may in part provide an explanation of why so few scale types have arisen in science. The cases of 0-point homogeneity and infinite point homogeneity are also discussed.     

Investigating measurement equivalence of visual analogue scales and Likert-type scales in Internet-based personality questionnaires

Visual analogue scales (VASs) have shown superior measurement qualities in comparison to traditional Likert-type response scales in previous studies. The present study expands the comparison of response scales to properties of Internet-based personality scales in a within-subjects design. A sample of 879 participants filled out an online questionnaire measuring Conscientiousness, Excitement Seeking, and Narcissism. The questionnaire contained all instruments in both answer scale versions in a counterbalanced design. Results show comparable reliabilities, means, and SDs for the VAS versions of the original scales, in comparison to Likert-type scales. To assess the validity of the measurements, age and gender were used as criteria, because all three constructs have shown non-zero correlations with age and gender in previous research. Both response scales showed a high overlap and the proposed relationships with age and gender. The associations were largely identical, with the exception of an increase in explained variance when predicting age from the VAS version of Excitement Seeking (B₁₀ =1318.95, ΔR ² =.025). VASs showed similar properties to Likert-type response scales in most cases.     

Visual analogue scales for mode-independent measurement in self-administered questionnaires

Previous research has shown evidence for mode differences between computer-assisted self-administered interviews (CASI) and paper-and-pencil interviews, especially in the case of sensitive questions. Some of these differences are explained by higher degrees of self-disclosure for CASI than for paper-and-pencil interviews, due to the more private situation with CASIs. This analysis examines the existence of different degrees of self-disclosure for CASI versus paper-and-pencil questionnaires and whether these differences can be reduced by the use of a specific response format. Judgments of items on a self-control scale with discrete 5-point (Likert-type) scales are compared with judgments on continuous visual analogue scales (VAS). Because a categorization effect for Likert-type items is assumed when pressure for social desirability is present, it is hypothesized that VAS compared to Likert-type response formats are less sensitive to mode differences.     

Three loneliness scales: an assessment of their measurement properties

In loneliness research, there has not been a consensus concerning either the factorial structure of most loneliness scales or the factorial structure of each of the proposed dimensions of loneliness. We investigated theoretical and operational definitions, as well as the factorial structure, based on gender of three loneliness scales: the University of California at Los Angeles (UCLA) Loneliness Scale, the Loneliness Deprivation Scale, and the Emotional/Social Loneliness Inventory. Unidimensional, best-fit models of the structures of these scales are presented.     

Interval-level measurement with visual analogue scales in Internet-based research: VAS Generator

The present article describes VAS Generator (www.vasgenerator.net), a free Web service for creating a wide range of visual analogue scales that can be used as measurement devices in Web surveys and Web experimentation, as well as for local computerized assessment. A step-by-step example for creating and implementing a visual analogue scale with visual feedback is given. VAS Generator and the scales it generates work independently of platforms and use the underlying languages HTML and JavaScript. Results from a validation study with 355 participants are reported and show that the scales generated with VAS Generator approximate an interval-scale level. In light of previous research on visual analogue versus categorical (e.g., radio button) scales in Internet-based research, we conclude that categorical scales only reach ordinal-scale level, and thus visual analogue scales are to be preferred whenever possible.     

Sex Biases in Comparable Worth Analyses

Remunerating jobs according to their comparable worth has been suggested as one way to reduce sex inequities in wages. To implement such a policy, it is necessary to obtain unbiased ratings of a job's worth. The present study investigated whether such ratings would be biased by the incumbent's sex, the sex composition of the occupation, or the job analyst's sex. A second purpose was to ascertain what job characteristics are viewed as worthy of financial compensation. Business school undergraduates viewed videotapes of a male enacting a low prestige, anchor job and either males or females enacting a moderate and a high prestige job. Ratings of the moderate and high prestige jobs relative to the anchor revealed that both male and female analysts perceived the jobs as higher in responsibility, in persuasive ability requirements, and in monetary worth when enacted by males than by females. The occupation's sex composition had no effect on any job ratings, a finding attributed to subjects' failure to recall the sex composition information provided. Regression analyses revealed that the only significant predictors of a job's monetary worth relative to the anchor were its perceived salary, its desirability, the training it required, and the gender of the incumbent. It was concluded that sex biases in comparable worth analyses may yield an underestimation of the wages that women's work is worth.     

Factor structure and measurement invariance of the Wisconsin Schizotypy scales across gender and age

The Wisconsin Schizotypy Scales are among the most widely used instruments for the assessment of psychosis proneness. The main goal of the present work was to study the dimensional structure underlying the Revised Physical Anhedonia Scale (RPhA), the Revised Social Anhedonia Scale (RSAS), the Magical Ideation Scale (MIS) and the Perceptual Aberration Scale (PAS). It was also explored whether the dimensions underlying these scales were invariant across gender and age. The sample was made up of 710 university students with a mean age of 19.8 years (SD = 1.9). The results showed that the dimensional structure of the Wisconsin scales was similar to that found in previous studies, displaying a Positive dimension and a Negative dimension, the Social Anhedonia Scale being related to both dimensions. Moreover, the factor structure of the schizotypy scales was found to be invariant across participants' gender and age.     

Family measurement techniques: The family health scales (fhs): Review and critique

Abstract

Kinston, Loader and Miller (1987) have developed the Family Health Scale (FHS), a research instrument designed to assess a family's level of overall functioning based upon the clinical observation of family interaction. The authors state that the FHS is primarily a research tool, allowing its users to test hypotheses about family dysfunction, to examine changes in the family longitudinally, and to categorize families by “degree of disturbance.” While not its principal use, the scale is also thought to have teaching utility.     

An inaccurate-timing filter for reaction time measurement by JAVA applets implementing Internet-based experiments

JAVA applets are not accurate enough to measure reaction time unless precautions are taken. A response-filtering technique is introduced that identifies inaccurate measurements by testing whether the client-side JAVA implementation produces false measurements of a time interval of known length during the measured reaction time. Reaction times that indicate such inaccuracy are discarded to increase the reliability of the remaining data. Three studies provide illustrative data on the effectiveness of the new technique, using 11 different computer systems. Study 1 showed differences in the accuracy of different clients and higher variability of the obtained means with applets than with native programs. Study 2 showed sharply increased variability when additional loads were imposed on the clients during reaction time measurement. The response-filtering technique diminishes this variability. Study 3 indicated more accurate measurement, with the new technique being able to reveal even smaller differences in difficult technical conditions.     

Estimating major sources of measurement error in individual intelligences scales: Taking our heads out of the sand

Four ubiquitous major sources of measurement error for individual intelligence scales were identified and discussed. It was argued that where these sources cannot be directly investigated, they should be estimated rather than ignored. The typical magnitude of error arising from each of content sampling, time sampling, scoring, and administration was estimated; their composite was found to produce a far larger standard error of measurement than manuals of individual intelligence tests typically report. Implications for practitioners are discussed.