- 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
- Descriptive statistics: Used to describe and summarize (Example: The average height of people in this class is 5’5”)
- 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.
- 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
- 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: Designates an ordering: greater than, less than.
- Does not assume that the intervals between numbers are equal
- 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: 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: designates an equal-interval ordering with a true zero point (i.e., the zero implies an absence of the thing being measured)
- 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:
- Equal intervals between adjacent units
- Absolute zero-point
- Nominal: none
- Ordinal: order
- Interval: order + equal intervals
- Ratio: order + equal intervals + true zero