“If a thing exists, it exists in some amount; and if it exists in some amount, it can be measured.” –E. L. Thorndike (19

1. “If a thing exists, it exists in some amount; and if it exists in some amount, it can be measured.” –E. L. Thorndike (1914)

2. “If you haven't measured it you don't know what you are talking about.” -Lord Kelvin

3. Today’s Questions • What does it mean to measure a psychological variable? • What is the difference between categorical and continuous variables, and why does the difference matter?

4. Basic Terminology • Variable: a characteristic that can vary or take on different values • Example: height is a variable • Value: a number representing one of many possible “states” of the variable • Example: some possible values of height are 6 feet or 4 feet 2 inches • Score: a specific value for a given person • Example: my score on the variable of height is 6 feet

5. Systematic Observation • In order to systematically observe something, it is critical to have a well-defined or quantitative system of measurement. • Simple example: How tall is Josh?

6. A More Complex Example • What about a question such as “How shy is Josh?” • This seems a bit more tricky because shyness, unlike height, isn’t something that we’re used to measuring with an everyday tool. It is a bit more abstract and elusive.

7. Can Psychological Properties be Measured? • However, there are two points worth considering. • Height isn’t exactly a “thing” in the way that a desk is a thing. Height, however, is an extremely useful abstraction. Is there any reason why shyness should be any more intractable than height? • There is nothing intrinsically concrete about inches, feet, miles, and meters. These are standard (i.e., conventional and agreed upon), but ultimately arbitrary, metrics.

8. Can Psychological Properties be Measured? • Finally, we must address a common complaint: Psychological variables can’t be measured. • We regularly make judgments about who is shy and who isn’t; who is suffering and who isn’t; which marriages are functioning well and which are not

9. Quantitative • Implicit in these statements is the notion that some people are more shy, for example, than others • This kind of statement is inherently quantitative. • Quantitative: subject to numeric qualification.

10. Interim Summary • Shyness, like distance, is a useful abstraction • We use the concept of shyness, like height, in quantitative ways (e.g., greater than, less than) • One goal of psychological measurement is to find standard and useful ways to systematically measure psychological constructs, such as shyness

11. Quantification • An important first-step in measurement is determining whether a variable is categorical or continuous. • Why? This property of a variable determines how we quantify the variable, how we model its statistical behavior, and the way we analyze data regarding that variable.

12. Nominal Scale • With categorical, taxonic, qualitative, or nominal variables, people either belong to a group or they do not • Examples: • country of origin • biological sex (male or female) • animal or non-animal • married vs. single • Quantitative question: How many people belong to each category?

13. Scales of Measurement: Nominal Scale • Sometimes numbers are used to designate category membership • Example: Country of Origin 1 = United States 3 = Canada 2 = Mexico 4 = Other • However, in this case, it is important to keep in mind that the numbers do not have numeric implications; they are simply convenient labels

14. Continuous Variables • With continuous variables, people vary in a graded way with respect to the property of interest • Examples: • age • working memory capacity • marital discord • Quantitative question: How much? or To what extent or degree?

15. Scales of Measurement: Continuous Variables • When we assign numbers to people (i.e., “scale” people) with respect to a continuous variable, those numbers represent something that is more meaningful than those used with nominal variables • Exactly what those numbers mean, and how they should be treated, however depends on the exact metric of the continuous variable...

16. Scales of Measurement: Ordinal • Ordinal: Designates an ordering; quasi-ranking • Does not assume that the intervals between numbers are equal • Example: finishing place in a race (first place, second place) 1st place 2nd place 3rd place 4th place 1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours

17. Scales of Measurement: Interval • Interval: designates an equal-interval ordering • The distance between, for example, a 1 and a 2 is the same as the distance between a 4 and a 5 • Example: Common IQ tests are assumed to use an interval metric

18. Scales of Measurement: Ratio • Ratio: designates an equal-interval ordering with a true zero point (i.e., the zero implies an absence of the thing being measured) • Example: • number of intimate relationships a person has had • 0 quite literally means none • a person who has had 4 relationships has had twice as many as someone who has had 2

19. Scales of Measurement: Additional Comments • In general, most observable behaviors can be measured on a ratio-scale • In general, many unobservable psychological qualities (e.g., extraversion), are measured on interval scales • We will mostly concern ourselves with the simple categorical (nominal) versus continuous distinction (ordinal, interval, ratio) variables categorical continuous ordinal interval ratio