Transcript PPT on Chapter 11 & 12

MSE 600
Descriptive Statistics
Chapter 11 & 12 in 6th Edition
(may be another chapter in 7th edition)
• Hypothesis testing
• Scientific method tests the Null Hypothesis –
• That there is NO difference
• We reject or accept the null hypothesis
In experimental research we test the Null
Hypothesis.
Should we accept it or not?
In any study – 3 possible situations
1. In reality there IS a difference or a
relationship between variables (e.g.,
cause-effect)
2. Sampling error or alternative
explanations masks the truth
3. There is NO difference in reality
(see page 99)
Engine does
NOT have a
problem
Fix it
Don’t
Fix it
Waste
Money
Good
Engine
has a
problem
Good
Breaksdown
What kind of error will you accept?
Null H is True
No difference
Reject
the Null H
Accept
the Null H
Type I
Good
Null H is False;
There is a
difference
Good
Type II
(fail to reject)
What kind of error will you accept?
Science does not want to make a Type I error
Justice System
Reject Innocence
(Guilty Verdict)
Accept Innocence
(Not Guilty Verdict)
Defendant
Innocent
Defendant
Guilty
Type I
Good
Good
Type II
What kind of error will you accept?
Science does not want to make a Type I error
Null H is True
No difference
Reject
the Null H
Accept
the Null H
Type I
Good
Null H is False;
There is a
difference
Good
Type II
(fail to reject)
What kind of error will you accept?
Science does not want to make a Type I error
Significance Testing
Do we keep the Null H or not?
In inferential statistics
We use tests of significance
Basically a ratio of treatment difference to
sampling error.
Treatment error divided by sampling error
Difference due to treatment
sampling error
Difference due to treatment
sampling error
If the treatment error or difference is large
enough then we will reject the Null H
We will say there is a difference between the
groups or will accept a relationship exists.
Tests of Significance
.05 is conventional level
p<.05
(italicized lower-case p)
5 times out of 100 we are willing to make a Type I error
We are willing to make a mistake and say there is a difference
when in reality there is no difference
• Testing for a statistical significant difference
• Want to minimize the occurrence of a Type I error
• If the difference between the means of two
groups is “significant enough” – we reject the
NULL Hyp
• That is, we say there is a difference
• Conventional value of significance is when the
probability of a significance test will occur 5% of
the time or less.
• Statistical significance vs Practical Significance
Condition
Aspirin
Placebo
No Heart
Attack
10,933
10,845
significance: p< .0001
effect size: .03 (small)
Heart Attack
104
189
Fatal heart attacks
Condition
Aspirin
Placebo
Lived
99
171
Died
5
18
significance: p< .08
effect size = .08 (small)
Condition
Aspirin
Placebo
Lived
95.2%
90.5%
Died
4.8%
9.5%
5% increase in number of people who live by using aspirin.
Condition
Traditional texts
New texts
Avg Comp
Score
88.6
90.3
Statistically significant: p<.03
0.10
Effect size:
$250,000
Cost of program
number of
students
300
300
A Difference that Doesn’t Make a
Difference
(Figure 12.2)