Definitions and Measurement Scales

Definitions

  • 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

Definitions

  • 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.

Measurement

“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

Questions

  • What does it mean to measure a psychological variable?
  • What are the different types of measurement scales and why does the difference matter?

Measurement

  • 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

Quantitative

  • 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.

Quantification

  • 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