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

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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)

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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

- What does it mean to measure a psychological variable?
- What is the difference between categorical and continuous variables, and why does the difference matter?

- 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

- 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?

- 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.

- 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.

- 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

- 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.

- 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

- 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.

- 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?

- 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

- 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?

- 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...

- 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 hour2 hours3 hours4 hours5 hours6 hours7 hours8 hours

- 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

- 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

- number of intimate relationships a person has had

- 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