2/10/2014
Random variables and discrete
probability distributions
1
Random Variables
Recall the Jewel Wasp, or the Luray
Caverns examples
We talked about the probability of a
randomly selected car driving into the
caverns being an RV or having Canadian
pl
4/2/2014
Tests of 2 means
2 sample tests
In many cases we are going to want to
compare two groups to determine if they
are different
We have discussed how to compare two
groups when the data are proportions
What about other types of data?
1
4/2/2014
2 sam
4/7/2014
Paired comparisons of means
Paired Comparisons
Does a patient weigh more before or
after hospitalization?
Does a particular brand of sunscreen work
better when applied to the same person?
What is the effect of smoking on the
blood pressure of peo
4/16/2014
Assumption testing 2:
Equality of variance
2 sample tests
3 situations we will be concerned with:
1. Equal variances
s
2. Unequal variances
3. Paired observations
Remembering that we have 2 situations when
comparing means where equality of varia
4/14/2014
Testing Normality
Two sample tests on means
As we have seen, there will be many cases
where you will want to compare values
from two groups to see if they differ in a
significant way.
1
4/14/2014
Two sample tests on means
Virtually every statist
5/7/2014
ANOVA Part II:
Post-hoc comparisons and
Experimental design
ANOVA procedure
AmongMS 21339.12
F
4.30
WithinMS
4960.81
Ftable = 2.76, = 0.05 and df = 4,25
Reject H0
Recall that to conduct an ANOVA, we determined how
much error was present in our s
5/5/2014
ANOVA INTRO
ANOVA
So far we have discussed comparison
tests for two samples
H0 : 1=2
We now need to expand our repertoire to
include the comparison of three, four, or
more independent samples taken from
normal populations
H0 :1=2=3 . i
1
5/5/2014
4/28/2014
Linear Regression
Linear Regression
There will be many occasions where we
will be interested in investigating the
relationship between two variables that
come from one sample
What is the response of some variable to
manipulation of the other?
1
4/30/2014
Regression 2
Model Testing
To use the least squares trend line for
predictive purposes, two conditions are
necessary:
1. The straight line model fits the data
2.The straight line being fitted is not
horizontal (i.e., 0). In other words, the
regr
3/5/2014
Comparing 2 Proportions
Comparing 2 proportions
In the last class, we talked about how to
calculate binomial probabilities and to
determine if a single proportion is
different from one stated for the
population in a null hypothesis
1
3/5/2014
Tes
3/31/2014
Tests of Means
So far, weve dealt with what could
thought of as categorical data (in a
very loose sense)
Success vs. failure
Contingency tables
True categorical data
Proportions
Now we are going to move into methods
for analyzing continuous data
3/12/2014
Contingency Analysis:
association between categorical
variables
or
Are these 2 things
independent?
Contingency Analysis
There will be times where we will want to relate two
variables that are categorical.
For example:
1. Do bright and drab butte
2/3/2014
Probability
1
Data
All statistical experiments yield a set of
data
All of the data you collect in an
experiment or study makes up the sample
space S
S is made up of all the sample points that
the study can yield
2
1
2/3/2014
Sample Space
If we fl
1/29/2014
Descriptive Statistics
Descriptive statistics and
EDA
Sometimes you just need to get a picture
of whats going on
Descriptive Statistics are methods for
organizing and summarizing information
Includes the construction of graphs,
charts, and table
2/17/2014
Statistical Inference:
Hypothesis Testing
Hypothesis Testing
Thus far weve talked about some ways to
describe data (central tendency and
variation, graphing)
How to determine the probability of
outcomes
The concept of random variables
1
2/17/201
2/5/2014
Conditional probability,
Dependent Events, and Bayes
Rule
1
Conditional Probability
If we want to know the chance of an
event, we need to take account all
existing information that might affect its
outcome
If we want to know the probability of
se
2/26/2014
Hypothesis testing part II
1
Rejecting Null Hypotheses
1
2/26/2014
Rejecting Null Hypotheses
Rejecting null hypotheses will follow a general pattern:
Calculate a test statistic based on your
sample data
Determine the probability of finding that
1/26/2014
STA 301: Applied Statistics
Introduction
1
Class Goal
Aw, people can come up with
statistics to prove anything,
Kent. Forfty percent of all
people know that
Statistics
To provide you with an overview of the
statistical tools and procedures requi
3/10/2014
Goodness of Fit
1
3/10/2014
Goodness of fit
A company that rents moving trucks owns 65
small trucks, 150 medium trucks, 100 large
trucks, and 50 extra large trucks. Does the
proportion of trucks that they own in each size
matches customers reque
3/3/2014
The binomial distribution
and tests of one proportion
Distributions Recap
The frequency distribution describes the
number of times each value occurs in a
sample.
The distribution of a variable in the
population is called the probability
distribut
STA301: Which Test Do I Use?
Well,
whats my
data?
Do I have one sample, or more?
Am I testing
how my data
are distributed
in categories
One Sample
More than 1
sample
Is my data
binary
(success/failure
Is the data
continuous?
Is known?
Binomial
Test
Yes
No