Central tendency locates middle of distribution
How are scores distributed around that point?
Low variability vs. high variability
Ways to measure variability
Sum of squares
& Scale Types
Different statistics for different variables
Statistics simplify a large set of data to a single
If there's an effect, how big is it?
How different is from 0, or A from B, etc.?
Separate from reliability
Inferential statistics measure effect relative to standard error
Tiny effects can be reliable, with enough power
Analysis of Variance
Comparing Several Groups
M 12-2 T 9-11
W 8-10 R 9-11
Exam 1 Mean:
Do the group means differ?
Independent-samples t-tests of all pairs
Each test doesn't use all data Less
Some measurements are just types or categories
Favorite color, college major, political affiliation, how
you get to school, where youre from
Minimal mathematical structure, but we can still
Shape of a distribution
The set of values present in a sample or population
Which values occur
Starting point for stati
Psychological Science I:
Professor Matt Jones
Cumulative hard to recover if you get behind
M = 14
-41 M = -36.3
Often interested in whether two groups have same mean
Experimental vs. control conditions
Comparing learning procedures, with vs. without drug, lesions, etc.
Correlation can tell how to predict one variable from
What about multiple predictor variables?
Explaining Y using X1, X2, Xm
Income based on age, education
Memory based on pre-test, IQ
Social behavior based on personality d
Goals of Statistics
Populations and samples
Parameters vs. statistics
Types of statistics
Populations and Samples
Set of subjects, items, or events we want to learn about
Generally very large or infinite
All people, all men/wome
Probability and Estimation
Probability and Statistics
Know the population
Will sample n members at random
What can we say about probability of sample statistics?
p(M = x) for some value x
p(M1 > M2)
Where Am I?
Wake up after a rough night in unfamiliar surroundings
Still in Boulder?
Expected if in Boulder
Surprising but not impossible Couldnt happen IF in Boulder
(likelihood near zero)
Multiple measurements for each subject
Different stimulus types, conditions, times, etc.
All measurements are of the same variable, but in different
Generalizes paired-samples design
Parametric vs. Non-parametric Statistics
Most common type of inferential statistics
r, t, F
Make strong assumptions about the population
Mathematically fully described, except for a few unknown parameters
Three Views of
What are we doing?
In science, we run lots of experiments
In some cases, there's an "effect; in others there's not
Some manipulations have an impact; some don't
Some drugs work; some don't
Goal: Tell these situations
Introduction to Hypothesis Testing:
The Binomial Test
Your friend claims he can predict the future
You flip a coin 5 times, and hes right on 4
Is your friend psychic?
A theory about how the world works
Proposed as an ex
Components of scientific studies
Types of scientific studies
Independent and dependent variables
Confounds, random assignment
Components of Scientific Studies
Scientific study: Basi
Multiple Independent Variables
Simple (one-way) ANOVA tells whether groups differ
Compares levels of a single independent variable
Sometimes we have multiple IVs
Subjects divided in multiple ways
Training type & testing type
Hypothesis Test for Population Mean
Goal: Infer from M
Null hypothesis (H0): = 0
Sometimes another value, e.g. from larger population
Memory improvement, weight loss, etc.
Sub-population within known, large
How good (high, low, etc.) is a given value?
How does it compare to other scores?
below) the mean
Same Thought Experiment
Sample n members
Compute some statistic
What is probability distribution of the statistic?
Doing exactly the same experiment but with a new sample
Sampling variability means eac
Some studies measure multiple variables
Any paired-sample experiment
Training & testing performance; personality variables;
Continuous independent variables
How are these va