Chapter 3
Data Distributions
The laymans denition of the term probability indicates the measure of ones
belief in the occurrence of a non-deterministic future event. The concept of probability is necessary in dealing with physical, biological or social sy
Topic 11. Data Distributions: Part VI
Theoretical Quantile-Quantile Plots
Text Reference: Ravishankers Chapter 3
Reading Assignment: Ravishankers Sections 3.7-3.9
1/19
What are Theoretical Q-Q Plots?
A theoretical Q-Q plot (or probability plot) is an impo
Topic 10. Data Distributions: Part V
Continuous Data Models: Normal and Related Distributions
Text Reference: Ravishankers Chapter 3
Reading Assignment: Ravishankers Sections 3.7-3.9
1/37
Standard Normal Distribution
Density and Distribution Function
Let
Topic 9. Data Distributions: Part IV
Continuous Data Models
Text Reference: Ravishankers Chapter 3
Reading Assignment: Ravishankers Sections 3.7-3.9
1/23
Uniform Distribution
Standard Uniform
A random variable Y is uniformly distributed over the unit int
Topic 8. Data Distributions: Part III
Discrete Data Models - Graphical Assessment and Overdispersion
Text Reference: Ravishankers Chapter 3
Reading Assignment: Ravishankers Sections 3.5-3.6
1/26
Graphical Assessment of Discrete Distributions
We may use va
Topic 7. Data Distributions: Part II
Discrete Data Models
Text Reference: Ravishankers Chapter 3
Reading Assignment: Ravishankers Sections 3.5-3.6
September 16-18, 2014
1/1
Bernoulli Distribution
Bernoulli Trial
(i) Two possible outcomes: success or fail
Topic 6. Data Distributions: Part I
Basic concepts of Random Variables and Probability Distributions.
Text Reference: Ravishankers Chapter 3
Reading Assignment: Ravishankers Sections 3.3-3.4
1/1
Sample Space and Events
Sample Space
Sample space, S, is th
Topic 5. Summaries of Data: Part IV
Graphical and Numerical Summaries of Multivariate Data
Text Reference: Ravishankers Chapter 2
Reading Assignment: Ravishankers Sections 3.1-3.2
1/23
Suppose we aim to compare several sets of data, which are not
associat
Topic 4. Summaries of Data: Part III
More Graphical and Numerical Summaries of Quantitative Data
Text Reference: Ravishankers Chapter 2
Reading Assignment: Ravishankers Sections 2.5 - 2.8
1/49
Box-and-Whisker Plots (Boxplots)
The Box-and-Whisker plot (or
Topic 3. Summaries of Data: Part II
Graphical and Numerical Summaries of Univariate Quantitative Data
Text Reference: Ravishankers Chapter 2
Reading Assignment: Ravishankers Sections 2.5 - 2.8
September 2nd, 2014
1/42
Graphical Approaches for Univariate Q
Topic 2. Summaries of Data: Part I
Types of Data & Graphical Summaries of Qualitative Data
Text Reference: Ravishankers Chapter 2
Reading Assignment: Ravishankers Sections 2.5 - 2.8
1/18
Variables and Data
A variable is any characteristic that is being co
Applied Statistics I, Fall 2014
Class:
AUST 344;
Tu Th 3:30pm - 4:45pm
Instructor:
Oce Hours:
Haim Bar
<[email protected]>
AUST 315; Tu 12:00pm-1:30pm or by appointment
TA:
Brian Bader
Syllabus:
Available on course website: http:/learn.uconn.edu
<brian.b
BIST/STAT 5605. Applied Statistics II, Spring 2017
Homework 8
The point value for each problem, should it be selected for grading, is indicated below.
Codes are to be included in your R Markdown source.
1. [15 points] Problem 8.15 on page 337 (343) of the
Topic 12. Multivariate Distribution Models
Text Reference: Ravishankers Chapter 3
Reading Assignment: Ravishankers Sections 4.1-4.1
1/37
Multivariate Random Variables
We dene a k-dimensional random vector Y = (Y1 , Y2 , . . . , Yk ) as a
function from a s
Topic 13. Limiting Theory and Point Estimation
Text Reference: Ravishankers Chapter 4
Reading Assignment: Ravishankers Sections 4.3-4.4
1/1
Weak Law of Large Numbers (WLLN)
Under general conditions, the WLLN states that the sample mean
approaches the popu
Chapter 2
Graphical and Numerical
Summaries of Data
Data is collected by measuring one or more variables of interest on a set of
population or sample units. It is useful to think of observed data as realizations
of a random variable dened with respect to
Applied Statistics I STAT5505-002
Fall 2015: Tu Th 9:30am - 10:45am; AUST 313
Instructor:
Oce Hours:
Grader:
Elizabeth Schifano
<[email protected]>
AUST 317; Tuesday 10:45am-11:45am or by appointment
John (Anthony) Labarga
<[email protected]
1.0
0.6
0.8
We consider two possible values for the
population mean (null and alternative)
a
0.0
0.2
0.4
0
4
2
0
2
4
6
1.0
0.6
0.8
Using the null hypothesis, set up a rejection region (based on
the (null) mean and the confidence level)
The red segment in
Topic 21. Categorical Data Analysis
Text Reference: Ravishankers Chapter 5
Reading Assignment: Ravishankers Sections 5.5
1/73
The measurement scale for a categorical variable consists of a set of
categories.
Categorical data are usually represented in tab
Topic 20. Pearson Chi-Square Goodness of Fit
Test
1/8
Pearson Chi-Square Goodness-of-t Test
Pearsons chi-squared test is used to assess two types of comparison:
tests of independence/association (in the notes on Categorical Data
Analysis)
tests of goodnes
Topic 19. Nonparametric Inference Procedures
Text Reference: Ravishankers Chapter 4
Reading Assignment: Ravishankers Sections 5.1-5.3
1/51
Nonparametric methods are used for inference when there is no specied
mathematical model that is assumed to describe
The Bootstrap Procedure
B. Efron (1979)
To construct condence intervals for parameters of interest, or
to perform hypothesis testing, one has to obtain the
distributional properties of the estimator (for example, its
variance, quantiles, etc.).
In many si
Topic 17. Hypothesis Tests II
Likelihood Ratio Tests, CI and Testing Relationship, p-values,
One- and Two- Sample Problems from Normal Populations
Text Reference: Ravishankers Chapter 4
Reading Assignment: Ravishankers Sections 4.5-4.7
1/50
Likelihood Rat
Topic 16. Hypothesis Tests I
Text Reference: Ravishankers Chapter 4
Reading Assignment: Ravishankers Sections 4.4
1/38
In the classical framework, with point and interval estimation there was
no supposition about the actual value of the parameter prior to
Supplement to Topic 15 (Example 15.6 in more detail):
Suppose Y1 , Y2 , . . . , Yn is a random sample from a Bernoulli(p) distribution. Derive a
95% approximate condence interval (CI) for p.
Solution: We consider here three ways to do this based on statis
Topic 14. Methods of Point Estimation
Text Reference: Ravishankers Chapter 4
Reading Assignment: Ravishankers Sections 4.3-4.4
1/37
Point estimates for an unknown parameter () are based on a sample
from the population.
Common Methods:
Method of Moments (M
BIST/STAT 5605. Applied Statistics II, Spring 2017
Homework 6
The point value for each problem, should it be selected for grading, is indicated below.
Please include all your code in your R Markdown source.
1. Problem 10.9, Parts a-c, e, and g, on page 41
BIST/STAT 5605. Applied Statistics II, Spring 2017
Homework 9: due 11:59pm, Sunday, April 9, 2017
The point value for each problem, should it be selected for grading, is indicated below.
Submit all code for all relevant problems in a separate file.
1. (20
Topic 11. Data Distributions: Part VI
Theoretical Quantile-Quantile Plots
Text Reference: Ravishankers Chapter 3
Reading Assignment: Ravishankers Sections 3.7-3.9
1/19
What are Theoretical Q-Q Plots?
A theoretical Q-Q plot (or probability plot) is an impo
BIST/STAT 5605. Applied Statistics II, Spring 2017
Homework 7
The point value for each problem, should it be selected for grading, is indicated below.
Codes are to be included in your R Markdown source.
1. Re-analyze the Solid Waste Data (Example 6) from
BIST/STAT 5605. Applied Statistics II, Spring 2017
Homework 10: due 11:59pm, Saturday, April 29, 2017
The point value for each problem, should it be selected for grading, is indicated below.
Submit all code for all relevant problems in a separate file.
1.
BIST/STAT 5605. Applied Statistics II, Spring 2017
Homework 2
The point value for each problem, should it be selected for grading, is indicated below.
1. The least squares regression line for a given set of data with a sample size of n = 20
is Y = 42 + 0.
BIST/STAT 5605. Applied Statistics II, Spring 2017
Homework 5
The point value for each problem, should it be selected for grading, is indicated below.
Please include all your code in the R Markdown source.
1. Problem 7.24 on page 291 (297) of the textbook
BIST/STAT 5605. Applied Statistics II, Spring 2017
Homework 4
The point value for each problem, should it be selected for grading, is indicated below.
Submit include all your code in the R Markdown source.
1. Problem 7.3 on page 289 (295) of the textbook.