1/15/2013
Categorical Variable
Unit 1 Section 1
Response falls into one or more
categories.
Categorical Data
Examples
Eye Color
Stage of Colon Cancer
Blue
Brown
Green/Hazel
Examples
Examples
I
II
III
IV
Political Party
Democrat
Republican
Independent
Exam
5/5/2013
Data
Models for Matched Data
Two Related Questions
Same Categorical Responses (Yes, No)
Same Respondents for Both Questions
McNemars Test
Data
Probabilities
Q2 = Yes
Q2 = No
Total
Probability of Yes Response
.
.
Compare
If
.
to
.
Marginal Homog
5/5/2013
Variables
Unit 2 Section 6
Categorical Variable
categories
Poisson Regression Analysis of
Multi-Dimensional Contingency
Tables
Data
Random sample of size from
population.
Cross-classify based on responses to
each categorical variable.
= number of
4/3/2013
Space Transportation System (STS)
Unit 2 Section 2
Better known as the Space Shuttle.
NASAs manned spacecraft.
135 missions from 1981 to 2011.
The Special Case of the
Space Shuttle Challenger
STS on Launch Pad
STS on Launch Pad
External Fuel Tank
Technology Guide: Unit 2: Sections 1 - 3
Stat 457
Spring 2013
Below is an explanation of the R commands and functions needed to analysis and fit simple and
multiple logistic regression models. Before starting your data analysis, you should change the
work
1/10/2016
Random Variables
Unit 1 Section 2
Variable whose value is determined
based on random event.
Bernoulli, Binomial and
Multinomial Random Variables
Random Variables
Two Types
Discrete finite or countably infinite
number of possible values.
Continuo
1/10/2016
Categorical Variable
Unit 1 Section 1
Value for variable falls into one or more
categories.
Numerical and Graphical
Summaries of Categorical
Variables
Examples
Eye Color
Blue
Brown
Green
Hazel
Other
Examples
Political Party
Democrat
Republican
I
STATISTICS 457
Technology Guide
Unit 1 - Section 1
Below is an explanation of the R commands and functions needed to analyze categorical variables. Before
starting your data analysis, you should change the working directory in R to the folder containing y
STATISTICS 457
Technology Guide
Unit 1 - Section 2
Below is an explanation of the R commands and functions needed to work with bernoulli, binomial, and
multinomial random variables in R.
Bernoulli Distribution
To work with the Bernoulli Distribution in R
1/27/2016
Outline
Unit 1 Section 5
Confidence Intervals for a
Population Proportion
Binomial Random Variables
Random event with 2 outcomes
2 Outcomes = Success and Failure
Success = Category of Interest
Failure = Not in Category of Interest
Binomial Rando
1/20/2016
Outline
Unit 1 Section 4
Hypothesis Test for
a Population Proportion
Binomial Random Variables
Random event with 2 outcomes
2 Outcomes = Success and Failure
Success = Category of Interest
Failure = Not in Category of Interest
Binomial Random Var
1/20/2016
Binomial Random Variable
Unit 1 Section 3
Random event with 2 outcomes
2 Outcomes = Success and Failure
Sampling Distribution for a
Sample Proportion
Binomial Random Variable
number of successes in
independent and identical trials of
random even
2/3/2016
Multinomial Random Variables
Random event with outcomes
Probability of each Outcome =
Unit 1 Section 6
1
Goodness of Fit Test for
One Categorical Variable
Multinomial Random Variables
number of observations in
outcome in independent and identical
STATISTICS 457
Technology Guide
Unit 1 - Section 3
Below is an explanation of the R commands and functions needed to investigate the sampling distribution
of the sample proportion p.
^
For larger sample sizes, we can use generated values from a binomial d
5/5/2013
Variables
Unit 2 Section 5
Data
categories
Categorical Variable
Poisson Regression Analysis of
Two-Dimensional Contingency Tables
Categorical Variable
categories
Data Example 3x4 Table
Random sample size from population.
Cross-classify data acco
1/22/2013
Categorical Variable
Unit 1 Section 4A
Two Categories
Inference for a Population
Proportion - Hypothesis Tests
Inference for
is a specific value or
*Hypothesis Test for .
If
10 and
1
,
10:
or
proportion of observations
from sample in catego
1/24/2013
Categorical Variable
Unit 1 Section 4B
Two Categories
Inference for a Population
Proportion Confidence Intervals
Inference for
Determine if
population proportion in category
of interest
Data
is a specific value or not.
Hypothesis Test for .
*Est
1/16/2013
Categorical Variable
Unit 1 Section 5
Categorical Variable has categories.
= population proportion of category .
1.
Goodness of Fit Test for
One Categorical Variable
Model for Categorical Variable
,
,
The Data
1
Collect random sample size .
num
1/15/2013
Categorical Variables
Unit #1 Section 2
Variable with categories as values.
Descriptive Statistics for One
Categorical Variable
Numerical Summaries
Gender (Male, Female)
Marital Status (Married, Widowed, Never
Married, Divorced)
Eye Color (Blue,
Whatisyourgender?
67%
BabyPicturesPartI
One of the babies pictured
at right is the daughter of
the mother pictured below.
1.
33%
2.
Male
Female
Whichbabyisthedaughterofthemotherpictured?
37%
26%
32%
5%
1.
2.
3.
4.
BabyA.
BabyB.
BabyC.
BabyD.
1
One of the
2/11/2013
Variables
Unit 1 Section 7b
Response Variable
Categorical with 2 categories.
Testing the Equality of Multiple
Population Proportions
Explanatory Variable (Grouping)
Two Cases
Population Proportions
Population proportion in category
of interest i
1/17/2013
Categorical Variable
Unit 1 Section 3
Two Categories
Category of Interest (Success)
Everything else (Failure)
Models for a Categorical Variable
Population
Data
proportion of population in
category of interest.
1
proportion of population not in
1/31/2013
Variables
Unit 1 Section 6
Cross-classify data according to
categories for response and explanatory
variables.
number of observations in the th
category of explanatory variable and th
category of response variable.
Categorical with
Categorical w
2/11/2013
Variables
Unit 1 Section 9
Random sample size from population.
Gather information about response and
explanatory variables.
Cross-classify data according to
categories of response and explanatory
variables.
Data
Note: The number of observations
2/11/2013
Variables
Unit 1 Section 7a
Response Variable
Categorical with 2 categories.
Testing the Equality of Two
Population Proportions
Explanatory Variable (Grouping)
Two Cases
Population Proportions
Population proportion in category
of interest in gro
2/11/2013
Variables
Unit 1 Section 8
Response Variable
2 categories
Relative Risk and the Odds Ratio
Explanatory Variable (Grouping)
Population Proportions
= population proportion in the
category of interest in group 1.
= population proportion in the
cate
2/20/2013
Measures of Association
Unit 1 Section 10
Measures of Association
Correlation Coefficient
Population Proportions
Response Variable
Correlation Coefficient
Coefficient
Cramers V
Goodman-Kruskal Gamma
Response Variable
2 categories
Explanatory
Cat
4/3/2013
Format
Unit 2 Section 1
Response Variable
2 Categories
Simple Logistic Regression
Explanatory Variable
Motivating Example
Does the temperature at incubation
affect the sex of turtles? Turtle eggs
were taken from nests and randomly
placed in an in
STATISTICS 457
Technology Guide
Unit 1 - Section 4
Below is an explanation of the R commands and functions needed to conduct hypothesis tests for the population proportion p.
Binomial Exact Test
The R function for the binomial exact test for the populati