Statistical Techniques I
EXST7005
Multiple Regression
Multiple Regression
Multiple Regression s The objectives are the same. Testing hypotheses about potential relationships (correlations), fitting and documenting relationships, and estimating parameters

Statistical Techniques I
EXST7005
Sample Size Calculation
The sample size formula
s
The Z-test and t-test use a similar formula.
Z=
Y 0
n
2
The sample size formula
(continued)
Lets suppose we know everything in the formul
except n. Do we really? Maybe not

Statistical Techniques I
EXST7005
The t distribution
Still here
The t-test of Hypotheses
the t distribution is used the same as Z
distribution, except it is used where sigma () ,i
unknown (or whereY is used instead of to
calculate deviations)
s
ti = ( Yi

Statistical Techniques I
EXST7005
Review
Objectives
Develop an understanding and appreciation of
Statistical Inference - particularly Hypothesis
testing concepts.
s
Understand the role of Statistics in decision
making processes
s
Develop procedures of bas

Statistical Techniques I
EXST7005
Power and Types of Errors
Lets go
Hypothesis testing Concepts
s
Logic of Test of Hypothesis is based on the
selected probability, (significance level) for the
test statistic (Z) which determines the range of
what would be

Statistical Techniques I
EXST7005
Testing Hypotheses
Here we go!
TEST OF HYPOTHESIS
s
HYPOTHESIS - a contention based on preliminary evidence of what appears to be fact (an educated guess), which may or may not be true.
- The second step in the scientific

Statistical Techniques I
EXST7005
Measures of Dispersion
Start here
Course Progression
s
Objective - Hypothesis testing Background
We will test primarily means, but also variances
Testing means requires a measure of the
variability in the data set
MEASURE

Statistical Techniques I
EXST7005
Measures of Central Tendency
Start here
Course Progression
s
Objective - Hypothesis testing Background
We will test primarily means, but also variances
Means and other measures of central tendency
will be discussed
SUMMAT

Statistical Techniques I
EXST7005
Frequency Tables
Start here
Course Progression
s
Objective - Hypothesis testing Background
A probability will be involved - we need to cover
frequency distributions in general and probability
distributions in particular
A

EXST7015 Matrix (Part 1)
Matrix Algebra Introduction & Simple Linear Regression
Geaghan Page 1
A. MATRIX STRUCTURE AND NOTATION 1) A matrix is a rectangular arrangement of numbers. The matrix is usually denoted by a capital letter.
A=
LM1 3OP N7 9 Q
A is

EXST7015 : Statistical Techniques II Split-plot and Repeated measures designs
SAS example
Geaghan Page 1
Some of the covariance structures available in SAS proc mixed. From SAS Institute Inc., SAS/STAT software changes and enhancements through release 6.1

EXST7015 : Statistical Techniques II Split-plot and Repeated measures designs
SAS example
Geaghan Page 1
1 *; 2 * Example of a Repeated Measures Design *; 3 * From Snedecor & Cochran, 1960 (pg 379) with modifications *; 4 *; 5 OPTIONS PS=256 LS=121 NOCENT

Statistical Techniques I
EXST7005
The F distribution
The F test
s
This test can be used to either,
test the equality of population variances - our
present topic test the equality of population means (this will be discussed later under ANOVA)
s
The F test

Statistical Techniques I
EXST7005
Probability distribution interrelationships
s
mabtedcs~`
s
Probability Distribution
interrelationships
s
The probability tables we have been
examining are interrelated. One of these
interrelationships is actually pretty

Statistical Techniques I
EXST7005
Simple Linear Regression
Simple Linear Regression
s
Measuring & describing a relationship between
two variables
Simple Linear Regression allows a measure of the
rate of change of one variable relative to another
variable.

Statistical Techniques I
EXST7005
Miscellaneous ANOVA Topics & Summary
LSMeans calculation
The calculations of LSMeans is different. For a
balanced design, the results will be the same.
However, for unbalanced designs the results wi
often differ.
s
The ME

Statistical Techniques I
EXST7005
Factorial Treatments & Interactions
The Factorial Treatment
Arrangement
s
Also known as "two-way" ANOVA
This analysis has two (or more) Treatments, for
example treatment A with two levels (a1 and a2)
and treatment B with

Statistical Techniques I
EXST7005
Linear Combinations
Linear combinations
This is a function of random variables of the form
aiYi where ai is a constant and Yi is a variable.
s
Generic Example: We want to create a score we
can use to evaluate students app

Statistical Techniques I
EXST7005
Confidence Intervals
Confidence intervals
An expression of what we believe to be a range
of values that is likely to contain the true value o
some parameter is called a confidence interval.
s
We can calculate confidence i

Statistical Techniques I
EXST7005
Exam 1 Coverage
Range of Coverage
s
Material covered will be from,
Introduction, including the Scientific Method and
definition of terms, through T-tests of hypothesis and use of the formula for calculating sample size. I

Statistical Techniques I
EXST7005
Distribution of Sample Means
OBJECTIVES
s
Usually we will be testing
hypotheses about means. We will
need some additional information
about the nature of means of
samples in order to do hypothesis
tests.
Distribution of S

Statistical Techniques I
EXST7005
The Z distribution
You are still here
Objective
s
The first statistical distribution we will use and
develop for hypothesis testing is the Z
distribution.
This will require an understanding of the
distribution,
Of how to

Statistical Techniques I
EXST7005
Probability distributions
You are here
Probability
s
PROBABILITY - a measure of the likelihood of
the occurrence of some event
An
event can be any outcome (e.g. verbal,
mathematical, graphical)
Some rules of Probability

Statistical Techniques I
EXST7005
Other topics - Linear models and
Transformations
Course Progression
s
Objective - Hypothesis testing Background
Transformation Many
applications in statistics require modifyin
an existing distribution to a recognized stat

Statistical Techniques I
EXST7005
Introduction
Start here
Internet connection
s
http:/nt1.stat.lsu.edu/EXSTWeb/faculty/geaghan/jpghome.html
s
http:/www.stat.lsu.edu
COURSE OBJECTIVES
Develop an understanding and
appreciation of Statistical Inference
parti

Statistical Techniques I
EXST7005
Two-sample t-tests
Two-sample t-tests
Recall the derived population of sample
means.
s
Imagine you had two of these derived
populations, as we had for variances when
we developed the F-test.
s
Equality of Population Means

Statistical Techniques II
EXST7015
Extra SS
07b_Extra Sum of Squares 1
Multiple regression
Multiple regression involves two or more independent variables (Xi), but still only a single dependent variable (Yi). There is an analysis for multiple dependent va