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Statistics 528  Lecture 22
1
Statistics 528  Lecture 22
Prof. Kate Calder
1
Intro. to Hypothesis Tests
Two of the most common types of statistical inference:
1. Confidence intervals
Goal is to estimate (and communicate uncertainty in our estimate of) a
population parameter.
2. Tests of Significance
Goal is to assess the evidence provided by the data about some claim
concerning the population.
Statistics 528  Lecture 22
Prof. Kate Calder
2
Basic Idea of Tests of Significance
Example:
Each day Tom and Heather decide who pays for lunch based
on a toss of Tom’s favorite quarter.
Heads  Tom pays
Tails  Heather pays
•
Tom claims that heads and tails are equally likely outcomes for this
quarter.
•
Heather thinks she pays more often.
Statistics 528  Lecture 22
Prof. Kate Calder
3
Heather steals the quarter, tosses it 10 times, and gets 7 tails (70% tails).
She is furious and claims that the coin is not fair.
There are two possibilities:
1. Tom is telling truth – the chance of tails is 50% and the observation
of 7 tails out of 10 tosses was only due to sampling variability.
2. Tom is lying – the chance of tails is greater than 50%.
Statistics 528  Lecture 22
Prof. Kate Calder
4
Suppose they call you to decide between the two possibilities.
To be fair to both of them, you toss the quarter 25 times. Suppose you get
21 tails.
What would you conclude? Why?
=> The coin is probably not fair. Even with sampling variability it is
unlikely that a fair coin would result give such a high percentage of
tails. (The actual probability of getting 21 or more tails in 25 tosses is
0.000455
if the coin is fair
.)
Statistics 528  Lecture 22
Prof. Kate Calder
5
Moral of the story:
an outcome that would rarely happen
if a claim were
true
is good evidence that the claim is in fact not true.
This is the idea behind
Hypothesis Testing
.
Statistics 528  Lecture 22
Prof. Kate Calder
6
•
A
hypothesis
is a statement about the parameters in a population; we
will be making statements about
&
in Section 6.2.
•
A
hypothesis test (
or
significance test)
is a formal procedure for
comparing observed data with a hypothesis whose truth we want to
assess.
•
The results of a test are expressed in terms of a probability that
measures how well the data and hypothesis agree.
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View Full DocumentStatistics 528  Lecture 22
2
Statistics 528  Lecture 22
Prof. Kate Calder
7
Performing a Hypothesis Test
1. State Hypotheses
State your research question as two hypotheses  the
null
and the
alternative
hypotheses. These hypotheses are written in terms of the
population parameters.
The
null hypothesis (
H
0
)
is the statement being tested. This is
assumed “true” and compared to the data to see if there is evidence
against
it. A null hypothesis that we will see often is that the mean
μ
is equal to some standard value. Usually, null hypotheses give a
statement of “no difference” or “no effect.”
Statistics 528  Lecture 22
Prof. Kate Calder
8
Suppose we want to test the null hypothesis that
μ
is some specified value,
say
μ
0
. Then
H
0
:
&
=
μ
0
Note
: We will always express H
0
using an equality sign.
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 Winter '09
 Calder

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