Definitions and Measurement Scales


  • Statistics: A Branch of mathematics that involves techniques for dealing with sets of numbers
    • Summarizing them
    • Describing them
    • Figuring out what they mean

2 Types Of Statistics

  1. Descriptive statistics: Used to describe and summarize (Example: The average height of people in this class is 5’5”)
  2. Inferential statistics: Used to figure out what the numbers mean. More specifically, to make inferences from samples to populations


  • Inference: To draw a conclusion (Example: when you see smoke, you infer that there’s a fire)
  • Population: The entire group of interest (Example: Every mongoose on the island of Hawaii)
  • Sample: A subset of the population (Example: A group of 100 mongooses that I’m studying in Pahoa)
  • Variable: A characteristic that varies from person to person (Example: height, IQ, hair color, shyness)
  • 2 types of variables
    • Independent Variable (IV): A variable that is manipulated by the researcher (Example: I assign you to drink either 1)coffee with caffeine or 2) decaf)
    • Dependent Variable (DV): The variable that is measured to see if the independent variable had an effect (Example: I measure how alert you are after you drink the coffee)
  • Data: Information (usually in statistics we use numerical information)
    • Note: the word data is plural!
    • One piece of data is called a datum.


“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 are the different types of measurement scales and why does the difference matter?


  • Measurement is the application of mathematics to things or events.
  • A system of measurement is a crucial component of psychological research
  • A simple example: How tall is Jane?
  • More complex example: How shy is Jane?

Can Psychological Properties be Measured?

  • A common complaint: Psychological variables can’t be measured.
  • But we make judgments about:
    • who is shy and who isn’t
    • who is angry or happy and who isn’t
    • which relationships are functioning well and which are not


  • This implies that some people are more shy, for example than others.
  • This kind of statement is inherently quantitative.
    • Quantitative: subject to numeric qualification.

Interim Summary

  • One goal of psychological measurement is to find standard and useful ways to measure psychological attributes, such as shyness.
  • This allows for communication.


  • What are the four different types of measurement scales and why does the difference matter?
  • Measurement properties of variables determine
    • how we quantify the variable
    • how we graph the variable
    • how we analyze the variable

Scales of Measurement: Nominal Scale

  • Nominal: Not a measure of quantity. Measures identity and difference. People either belong to a group or they do not
  • a.k.a. categorical, taxonic, qualitative
  • Examples:
    • Eye color: blue, brown, green, etc.
    • Biological sex (male or female)
    • Democrat, republican, green, libertarian, etc.
    • Married, single, divorced, widowed

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
  • Here, the numbers do not have numeric implications; they are simply convenient labels.

Scales of Measurement:

Ordinal Scale

  • Ordinal: Designates an ordering: greater than, less than.
  • Does not assume that the intervals between numbers are equal
  • Example:
    • finishing place in a race (first place, second place)
  • The ranking is also ordinal
  • Example: Rank your food preference where 1 = favorite food and 5 = least favorite
    • _ sushi
    • _ hamburger
    • _ lau lau
    • _ chocolate
    • _ papaya

Interval Scale

  • Interval: designates an equal-interval ordering
  • The difference in temperature between 20 degrees F and 25 degrees F is the same as the difference between 76 degrees F and 81 degrees F
  • Examples: Temperature in Fahrenheit or Celsius is the interval. Common IQ tests are assumed to use an interval metric.
  • Likert scale: For each question below….
  • 1 = Strongly Disagree
  • 2 = Uncharacteristic
  • 3 = Neutral
  • 4 = Characteristic
  • 5 = Strongly Agree
  • Likert scale: How do you feel about Stats?
  • 1 = I’m totally dreading this class!
  • 2 = I’d rather not take this class.
  • 3 = I feel neutral about this class
  • 4 = I’m interested in this class.
  • 5 = I’m SO excited to take this class!

Ratio Scale

  • Ratio: designates an equal-interval ordering with a true zero point (i.e., the zero implies an absence of the thing being measured)
  • Examples:
    • The temperature in Kelvin (Zero is the absence of heat. Can’t get colder).
    • Measurements of heights of students in this class (Zero means complete lack of height).
    • Someone 6 ft tall is twice as tall as someone 3 feet tall.

Discrete vs. Continuous

  • Discrete variables are made up of distinct or separate units or categories. It can’t have a value between the units.
    • Examples: number of children in a family, number of heads or tails, income.
  • Continuous variables can take on an infinite number of values.
    • Examples: height, temperature, amount of water.

Summary of Measurement Scales

  • Measurement scales differ by how many of these attributes they have:
    • Order
    • Equal intervals between adjacent units
    • Absolute zero-point
  • Nominal: none
  • Ordinal: order
  • Interval: order + equal intervals
  • Ratio: order + equal intervals + true zero