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

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

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?

[exercise on class composition]

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

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 Mike Marks?

A More Complex Example What about a question such as “How shy is Tim Miura?” 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.

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.

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

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.

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

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.

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?

Scales of Measurement: Nominal Scale Sometimes numbers are used to designate category membership Example: Country of Origin 1 = United States3 = Canada 2 = Mexico4 = 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

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?

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...

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) 1 hour2 hours3 hours4 hours5 hours6 hours7 hours8 hours 1st place2nd place3rd place4th place

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

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

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) categoricalcontinuous ordinal interval ratio variables