Statistics. Summary numbers, or indices, that result from an analysis of data (numbers) – pg. 2 All the procedures and tools used to organize and interpret facts, events, and observations that can be expressed numerically – pg. 2. Imaginary World. Snap. Crackle. Imaginary World #2. Snap.
Q: Why is little Sally afraid of dogs?
A: What are the variables, and how do they vary together?
(the presence or absence of dogs, Sally’s emotional state, Sally’s neural structure as it relates to these other events, Sally’s history and how it relates to the above elements, etc.)
Q: Why does my roommate drink my milk and leave the empty jug in the refrigerator?
Break it down:
Design Trumps Analysis
Variability ≠ Randomness
Randomness is an Illusion
Every person or object in a group (past, present, future, often infinite)
Part of the population
Summary Measure = Parameter
Ex: μ = pop. mean
σ2 = pop. variance
σ = pop. standard deviation
Summary Measure = Statistic
Ex: X = sample mean
s2 = sample variance
s = sample standard deviation
Notice: Greek symbols are used for parameters, Roman symbols for statistics
We want to make inferences about the population.
Definition: a conclusion reached on the basis of evidence [in our case, sample data] and reasoning [in our case, statistical analysis]
Inferential Statistics: using statistical methods to make inferences about the population given sample data
Ex: How likely is it that my depression intervention results (from my sample) will generalize to the population?
Descriptive Statistics: using statistical methods to describe a set of data
Ex: What is the mean depression score on the Hamilton Rating Scale for clients I am working with?
Sampling error: the error caused by observing a sample instead of the population.
1. Random Sampling
2. Large Samples
3. Multiple Samples
Ex: Total pig population (16 pigs):
You think the color of the pig might be an important variable, but you can only afford to do the study with half of the pigs. How many black and how many pink pigs would you include in your study?
That’s right! Six pink pigs and two black pigs.
What should your
look like if your
total sample size is
People age 16-65
living in the U. A. E.
U. A. E.
I wrote the number of females as a fraction of the total population, and put my unknown over my sample size on the other side.
Here’s how I solved it:
So, your sample should look like this:
Then I solved for X.
Definition: the assignment of numbers or labels to objects or events
Labels? How is that measurement?
Ordinal scales give us limited data.
Note: We will treat them as interval scales in this course, but only for convenience.