# 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.
• 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
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