Statistical Tests
QM-1: Session 15
Inferences About Differences
Inferences About Differences
Paired Data
Many statistical applications use paired data
samples to draw conclusions about the
difference between two population means.
Data pairs occur very n
Statistical Tests
INFERENCES USING
THE CHI-SQUARE DISTRIBUTION
Chi is a Greek letter denoted by the symbol , so chi-square is denoted by
symbol
the
Because the distribution is of chi-square values, the values begin at 0 and
then are all positive.
The gr
Hypothesis Testing
Review of last session
Types of error
Level of significance
Review
Null hypothesis H0
This is the statement that is under investigation or
being tested. Usually the null hypothesis represents a
statement of no effect, no difference, o
Hypothesis
Testing
Hypothesis Testing
Charles Lutwidge Dodgson (18321898) was an English mathematician who loved to
write childrens stories in his free time.
The dialogue between Alice and the Cheshire Cat occurs in the masterpiece Alices
Adventures in Wo
Session 12
Chapter 15
Confidence
Intervals
Point Estimate
An estimate of a population parameter given by a single
number is called a point estimate for that parameter. It will
come as no great surprise that we use (the sample mean) as
the point estimat
Linear regression model
Simple Regression
Simple regression analysis is a statistical tool That
gives us the ability to estimate the mathematical
relationship between a dependent variable (usually
called y) and an independent variable (usually
called x).
Probability
Understanding Random
Situations
Probability
Our goal is to understand uncertain situations, at least to the
greatest extent possible.
Unfortunately, we will probably never be able to say for sure
exactly what will happen in the future.
Howe
Distributions
Binomial Distribution
Poisson Distribution
Normal Distribution
Binomial Distribution
work directly from n and
X = n
X = n(1)
n a
P( X a ) (1 )n a
a
n!
a (1 )n a
a! (n a )!
1 2 3 . n
a (1 ) n a
[1 2 3 . a ][1 2 3 . ( n a )]
Binomia
Session 11
Chapter 13
Samples and
Surveys
Random Sampling
The basis for statistical inference about a population
based on a sample
Example: Build restaurant in Campus?
Population: the collection of items you want to
understand
N items. Example: all peo
Random Variables
(Chapter- 9)
Probability models for Counts
(Chapter- 11)
The Normal Probability Model
(Chapter- 12)
Random Variable
Result from a random experiment
The number is the observation of the random variable
The random variable is the meaning
Types of Data
Data
Categorical
Numerical
Examples:
Marital Status
Political Party
Eye Color
Gender
(Defined categories)
Discrete
Examples:
Number of Children
Defects per hour
(Counted items)
Continuous
Examples:
Weight
Voltage
(Measured characteristics)
C
Freemark Abbey Winery
Grape Variety
Riesling is a white
grape variety
which originated
in the Rhine
region of
Germany.
Riesling is an
aromatic grape
variety displaying
flowery, almost
perfumed,
aromas as well as
high acidity
Riesling
Botrytis cinerea
Summary Statistics
Descriptive Statistics
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Measures of Dispersion
There are two types of measures of dispersion:
1. Absolute measures of d
Chapter 5
Association
between
Categorical
Variables
Example
BUSY WEB SITES LIKE GOOGLE AND YAHOO CHARGE
FOR THE PRIVILEGE OF ADVERTISING ON THEIR
PAGES.
If you are an online retailer, how are you to decide
which locations deliver buyers?
It should come
Probability Tree
Decision tree
Probability Trees (Tree Diagrams)
Graphical depiction of conditional probabilities
(helpful for large problems)
Shows sequence of events as paths that suggest
branches of a tree
Whether or Not Viewer Sees Ad
Probability Tr
Chapter 4
Describing
Numerical Data
Measures of Central Tendency
1. Mathematical averages
(a) Arithmetic mean or mean
Simple
Weighted
(b) Geometric mean
(c) Harmonic mean
2. Positional averages
(a) Median
(b) Mode
(c) Quartiles
(d) Deciles
(e) Percentiles