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“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?

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“If a thing exists, it exists in some amount; and if it exists in some amount, it can be measured.”

–E. L. Thorndike (1914)

Today’s Questions talking about.”

• What does it mean to measure a psychological variable?

• What is the difference between categorical and continuous variables, and why does the difference matter?

Basic Terminology talking about.”

• 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 talking about.”

• 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?

A More Complex Example talking about.”

• 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.

Can Psychological Properties be Measured? talking about.”

• 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? talking about.”

• 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 talking about.”

• 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 talking about.”

• 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 talking about.”

• 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 talking about.”

• 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 talking about.”

• 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

Continuous Variables talking about.”

• 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 talking about.”

• 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 talking about.”

• 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

Scales of Measurement: Interval talking about.”

• 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 talking about.”

• 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 talking about.”

• 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