PSYC 6130
Lecture 17: Multiple Comparisons
Lecture 17 Summary
Why do multiple comparisons
The problem with multiple comparisons
Familywise and per-comparison alpha
Exploratory data analysis
Fishers protected t tests
Tukeys HSD test
Dunnetts Test
REGWQ Tes
Even More Alternatives to the
Two Independent Samples t
Summary of Available Procedures
(up to now)
Equal variances, normal distributions:
Two independent samples t
Even better would be the Welch two-sample t
Unequal variances, normal distributions
W
Testing for Mean Differences
Under Nonnormality
Normality Assumption
In computing Students t, we need to assume
that the populations from which our groups were
sampled are normal in form
When the distributions are not normal
empirical Type I and Type II
Final exam notes
Partitioning the
Variability
In a one-way design we
partitioned the variability
into: SStotal = SSbetween + SSwithin
1
2
3
In a two-way design: SStotal =
SS + SS + SS+ SSwithin
4
Where: SS = nb j (j. - .)2 ,
df = a-1
5
SS = na k (.k - .)2
Midterm exam notes
Partitioning the Variability
In a one-way design we partitioned the
variability into: SStotal = SSbetween + SSwithin
1
2
3
In a two-way design: SStotal = SS + SS +
SS+ SSwithin
4
Where: SS = nb j (j. - .)2 , df = a-1
5
6
7
8
SS = na k (
PSYC 6130 - UNIVARIATE ANALYSIS
Lab Exercise #12
1) A researcher is interested in attitudes towards socialized medicine before and after a
pro-socialized medicine talk. Specifically, the researcher would like to know if attitudes towards
socialized medici
Simple Correlation &
Regression
Review of Correlation and
Regression
A large proportion of psychological research
explores relationships among variables, as
opposed to exploring mean differences in
variables
Example: Effects of Self-Esteem on GPA
It is
Simple Linear Regression
Linear Regression
Predicting Y from X
Recall that the equation for a straight line is:
Y = a + bX
We can also write the prediction equation as:
Y = a + bX
Where:
Y is the predicted value of Y
a is the Y intercept (the value
Univariate Statistics
A Review of Preliminary Concepts
Population/Sample
Population: the entire set of events (e.g.,
university students) to which you are
interested
Sample: a subset of the population that is
used to make inferences regarding the
popula
Standard Assumptions
When we think of traditional parametric tests for
independent groups designs, the following
assumptions are required:
Normal distributions in each of the populations
Equal variances across the populations
Independence of the obser
PSYC 6130 - UNIVARIATE ANALYSIS
ASSIGNMENT #1
Due Date: October 22, 2013 (11:59 pm)
[Submit by hardcopy or email to both Phil and Rob]
Use R Markdown for questions 2 and 3 and submit the html file. Answers to question 1 can
be submitted in any format.
Dat
PSYC 6130 - Univariate Analysis
Class Assignment #4
Question 1:
Dr. Smith believes that she can reduce statistics anxiety in a Department of Psychology
Introductory Statistics course by spending time in each class discussing the importance of
statistics w
Comparisons/Contrasts of
Group Means
Introduction
Ho: 1= 2 = . = k can be tested using a oneway ANOVA and tests the null hypothesis of no
difference between ANY means
However:
Researchers are usually more interested in
precisely what differences exist
Factorial Designs
Introduction to Two-Way
Independent Groups Models
Part 2
Should we Always Analyze
Interactions in Factorial Models
The issue of not including interaction terms in
models arises when we suspect that there may
not be a significant interac
Factorial Designs
Introduction to Two-Way
Independent Groups Models
Introduction
Dr. Black would like to determine if the sex of
a subject, or the size of the community in which
the subject was raised (small, medium, large),
will relate to the amount of
Multiple Regression
Multiple Regression
Multiple regression extends linear regression to allow for
2 or more independent variables.
There is still only one dependent (criterion) variable.
We can think of the independent variables as predictors
of the d
Linear Correlation
Perfect Correlation
2 variables x and y are perfectly correlated if they are
related by an affine transform
y = ax + b
The correlation is positive if a>0 and negative if a<0.
By corollary, 2 variables are perfectly positively
correla
Probability, Bayes Theorem
and the Monty Hall Problem
Probability Distributions
A random variable is a variable whose value is uncertain.
For example, the height of a randomly selected person in this class
is a random variable I wont know its value until
PSYC 6130
One-Way Independent ANOVA
Generalizing t-Tests
t-Tests allow us to test hypotheses about differences
between two groups or conditions (e.g., treatment and
control).
What do we do if we wish to compare multiple groups or
conditions simultaneous
Two-Way (Independent) ANOVA
Two-Way ANOVA
Two-Way means groups are defined by 2 independent
variables.
These IVs are typically called factors.
An experiment in which any combination of values for
the 2 factors can occur is called a completely crossed
f
Introduction to Hypothesis Testing
The One-Sample z Test
The One-Sample z Test
Conditions of Applicability:
One group of subjects
Comparing to population with known mean and variance.
Note: this is not a common situation in Psychology!
PSYC 6130, PROF
Beyond Null Hypothesis Testing
Supplementary Statistical Techniques
Limitations of NHT
Criticisms of NHT date from the 1930s.
Null hypothesis is rarely true.
The real question is not about the existence of an effect, but
about the nature of the effect:
(One-Way) Repeated Measures ANOVA
One-Way Repeated Measures ANOVA
Generalization of repeated-measures t-test to
independent variable with more than 2 levels.
Each subject has a score for each level of the
independent variable.
May be used for repeated
t-Tests
Interval Estimation and the t Distribution
Large Sample z-Test
Sometimes we have reason to test hypotheses involving specific
values for the mean.
Example 1. Claim: On average, people sleep less than the often
recommended eight hours per night.
STUDY GUIDE FOR THE COURSE
Partitioning the
Variability
In a one-way design we
partitioned the variability
into: SStotal = SSbetween + SSwithin
1
2
3
In a two-way design: SStotal =
SS + SS + SS+ SSwithin
4
Where: SS = nb j (j. - .)2 ,
df = a-1
5
SS = na k
An extension of ANOVA in which the effects
of the IV on the DV are assessed after the DV
has been adjusted for by the DVs
relationship with one or more covariates
A covariate is a variable that is related to the
DV, which you cant manipulate, but you wan
PSYC 6130 - UNIVARIATE ANALYSIS
Lab Exercise #15
Two researchers, one from Canada, and one from the US, were interested in exploring the
relationship between level of repentance and level of forgiveness in University students. The
Canadian researchers als
PSYC 6130 - Univariate Analysis
Class Assignment #3
Question 1
Dr. Dermott is interested in determining how the sex and grade of elementary school children
relate to confidence in math ability and reading ability. Male and female children in Kindergarten,