Essentials for Measurement

Basic requirements for measuring 1) The reduction of experience to a one dimensional abstraction. 2) More or less comparisons among persons and items. 3) The idea of linear magnitude inherent in positioning objects along a line. 4) A unit determined by a process which can be repeated without modification over the range of the variable.

Let’s consider weight At some point, weight was constructed… why? 1) Is it one dimensional? 2) Can we make comparisons of more and less? 3) Does it have linear magnitude? (1 lb + 1 lb = 2 lbs?) 4) Do we have a process to determine weight which we can repeat without modification over the range of the variable?

Social science measures should follow the same criteria Just like weight, height, time and temperature are measured with “universally” useful instruments, our task is to devise instruments to measure variables in the human sciences. Psychometrics is often more about the “psycho” and less about the “metrics.” Rasch modeling does not replace or supercede statistical analyses; it should precede it.

We start by searching for the possibility of order “Amount” of an attribute in a person vs. “amount” in another person “Amount” in an item vs. “amount” of that attribute in another item Can we level items such that endorsing the next item indicates more of the attribute in the person?

The Rasch model is probabilistic Guttman’s idea: If you endorse an extreme statement, you will endorse ALL less extreme statements. This makes a scale. With Rasch: If you endorse an extreme statement, there is a good probability that you will endorse all less extreme statements.

Objectivity Values should have similar meaning over time and place. The measure (set of items) assigned to the construct must be independent of the person taking these items. Does the weight of 1 pound on a scale depend on what a person is measuring? Should the difficulty of an item depend on the distribution of abilities of persons responding to the item?

Conjoint Additivity To be additive, units must be identical. Are apples additive? 1 Apple + 1 Apple = 2 Apples. But 2 Apples are twice as much as 1 Apple only when the 2 Apples are perfectly identical. Real apples are not! Rasch measurement forms an equal interval linear scale, just like weight.

Conjoint Additivity When any pair of measurements have been made with respect to the same origin on the same scale, the difference between them is obtained merely by subtraction. Rasch measurement creates a single person/item yardstick with person “ability” (B n ) estimated in conjunction with item “difficulty” (D i ). B n -D i > 0, Probability the person will answer “correctly” (P xni )>.05. B n -D i < 0, P xni <.05. B n -D i = 0, P xn =.05.

“Fit” to the model Fit statistics indicate where the principles of probabilistic conjoint measurement have been sufficiently satisfied to justify the claim that results can be used as a scale with interval measurement properties.

Rasch unit for “counting”: a logit Logit: A Log-Odds Unit Transformation of the raw score scale (ordinal) into an interval scale: The raw score percentage is converted into its success- to-failure ratio The logarithm of this score is taken In this way, the bounded outcome of probabilities (ogive) is straightened.

What is a success-to-failure ratio?