Thurstone scale

Key takeaways

Thurstone scale belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Thurstone scale to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Thurstone scale from memory before moving on to harder problems.

Reference excerpt

In psychology and sociology, the Thurstone scale was the first formal technique to measure an attitude. It was developed by Louis Leon Thurstone in 1928, originally as a means of measuring attitudes towards religion. Today it is used to measure attitudes towards a wide variety of issues. The technique uses a number of statements about a particular issue, and each statement is given a numerical value indicating how favorable or unfavorable it is judged to be. These numerical values are prepared ahead of time by the researcher and not shown to the test subjects. The subjects then check each of the statements with which they agree, and a mean score of those statements' values is computed, indicating their attitude.

Thurstone scale Thurstone's method of pair comparisons can be considered a prototype of a normal distribution-based method for scaling-dominance matrices. Even though the theory behind this method is quite complex (Thurstone, 1927a), the algorithm itself is straightforward. For the basic Case V, the frequency dominance matrix is translated into proportions and interfaced with the standard scores. The scale is then obtained as a left-adjusted column marginal average of this standard score matrix (Thurstone, 1927b). The underlying rationale for the method and basis for the measurement of the "psychological scale separation between any two stimuli" derives from Thurstone's Law of comparative judgment (Thurstone, 1928). ASU The principal difficulty with this algorithm is its indeterminacy with respect to one-zero proportions, which return z values as plus or minus infinity, respectively. The inability of the pair comparisons algorithm to handle these cases imposes considerable limits on the applicability of the method. The most frequent recourse when the 1.00-0.00 frequencies are encountered is their omission. Thus, e.g., Guilford (1954, p. 163) has recommended not using proportions more extreme than .977 or .023, and Edwards (1957, pp. 41–42) has suggested that "if the number of judges is large, say 200 or more, then we might use pij values of .99 and .01, but with less than 200 judges, it is probably better to disregard all comparative judgments for which pij is greater than .98 or less than .02."’ Since the omission of such extreme values leaves empty cells in the Z matrix, the averaging procedure for arriving at the scale values cannot be applied, and an elaborate procedure for the estimation of unknown parameters is usually employed (Edwards, 1957, pp. 42–46). An alternative solution of this problem was suggested by Krus and Kennedy (1977). With later developments in psychometric theory, it has become possible to employ direct methods of scaling such as application of the Rasch model or unfolding models such as the Hyperbolic Cosine Model (HCM) (Andrich & Luo, 1993). The Rasch model has a close conceptual relationship to Thurstone's law of comparative judgment (Andrich, 1978), the principal difference being that it directly incorporates a person parameter. Also, the Rasch model takes the form of a logistic function rather than a cumulative normal function.

See also Thurstonian model – Stochastic transitivity mathematical model Bogardus scale – Scale measuring a person's willingness to engage with various types of people Guttman scale – Single, ordinal psychometric scale Likert scale – Psychometric measurement scale Semantic differential – Empirical method used in Linguistics Diamond of opposites – Type of plot used in psychodrama groups

References Andrich, D. (1978b) Relationships between the Thurstone and Rasch approaches to item scaling. Applied Psychological Measurement, 2, 449-460. Andrich, D. & Luo, G. (1993) A hyperbolic cosine model for unfolding dichotomous single-stimulus responses. Applied Psychological Measurement, 17, 253-276. Babbie, E., 'The Practice of Social Research', 10th edition, Wadsworth, Thomson Learning Inc., ISBN 0-534-62029-9 Edwards, A. L. Techniques of attitude scale construction. New York: Appleton-Century- Crofts, 1957. Guilford, J. P. Psychometric methods. New York: McGraw-Hill, 1954. Krus, D.J., & Kennedy, P.H. (1977) Normal scaling of dominance matrices: The domain-referenced model. Educational and Psychological Measurement, 37, 189-193 (Request reprint). Krus, D.J., Sherman, J.L., & Kennedy, P.H. (1977) Changing values over the last half-century: the story of Thurstone's crime scales. Psychological Reports, 40, 207-211 (Request reprint). Thurstone, L. L. (1927a) A Law of comparative judgment. Psychological Review, 34, 273-286. Thurstone, L. L. (1927b) The method of paired comparisons for social values. Journal of Abnormal and Social Psychology, 21, 384-400. Thurstone, L. L. (1928). Attitudes can be measured. American Journal of Sociology, 33, 529-54.

Worked examples

Example 1 — a first encounter with Thurstone scale

Start with the simplest possible case. Write down what Thurstone scale claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Thurstone scale before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Thurstone scale ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Thurstone scale

In research: Thurstone scale appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Thurstone scale in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Thurstone scale is common in secondary-school and first-year university syllabi. It links to neighbouring topics Rating scales, so understanding it makes those chapters shorter.
In everyday life: Look for Thurstone scale outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Thurstone scale in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Thurstone scale means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Thurstone scale out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Thurstone scale in simple terms?

In psychology and sociology, the Thurstone scale was the first formal technique to measure an attitude. It was developed by Louis Leon Thurstone in 1928, originally as a means of measuring attitudes towards religion.

Why does Thurstone scale matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Thurstone scale?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Thurstone scale.