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## Monday, November 11

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### ... teaches you about the importance of ... Ordinarily, one is well advised to take the largest sample ... You are asked to evaluate a new program to promote social ... – PowerPoint PPT presentation

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Title: Monday, November 11

1
Monday, November 11 Statistical Power
2
• Monday, November 12
• Statistical Power
• It teaches you about the importance of effect
size, ? (gamma).

3
• Monday, November 12
• Statistical Power
• It teaches you about the importance of effect
size, ? (gamma).
• It helps put the risk of Type I error, ? (alpha)
into perspective.

4
• Monday, November 12
• Statistical Power
• It teaches you about the importance of effect
size, ? (gamma).
• It helps put the risk of Type I error, ? (alpha)
into perspective.
• It helps you appreciate the value of the sample
size, N.

5
• Monday, November 12
• Statistical Power
• It teaches you about the importance of effect
size, ? (gamma).
• It helps put the risk of Type I error, ? (alpha)
into perspective.
• It helps you appreciate the value of the sample
size, N.
• It simply makes you a better person.

6
• Monday, November 12
• Statistical Power
• It teaches you about the importance of effect
size, ? (gamma).
• It helps put the risk of Type I error, ? (alpha)
into perspective.
• It helps you appreciate the value of the sample
size, N.
• It simply makes you a better person.
• ? ? x f (N)

7
? ? x f (N)
8
Lets sample from HSB universe of N300 where we
know the population values.
9
(No Transcript)
10
What causes you to decide on a value of ? under
H1?
11
What causes you to decide on a value of ? under
H1?
The alternative hypothesis should be the point at
which we say, aha, its important enough to pay
attention to!
12
What causes you to decide on a value of ? under
H1?
The alternative hypothesis should be the point at
which we say, aha, its important enough to pay
attention to! Would you pay attention to
Stanley Kaplan raising SATs by 10 points? 20
points? 30 points?
13
What causes you to decide on a value of ? under
H1?
The alternative hypothesis should be the point at
which we say, aha, its important enough to pay
attention to! Would you pay attention to
Stanley Kaplan raising SATs by 10 points? 20
points? 30 points? So you set the value of
alternative hypothesis at a point that you care
about -- a value of practical significance.
14
What causes you to decide on a value of ? under
H1?
The alternative hypothesis should be the point at
which we say, aha, its important enough to pay
attention to! Would you pay attention to
Stanley Kaplan raising SATs by 10 points? 20
points? 30 points? So you set the value of
alternative hypothesis at a point that you care
about -- a value of practical significance. Power
analysis says, if the effect is of that
magnitude, what is the risk that I will fail to
detect it, by failing to reject the null
hypothesis.
15
If I really care about a 5-point difference, then
16
Reality
H0 True
H0 False
Type I Error ?
Reject H0
Yeah!
Decision
Yeah!
Dont Reject H0
Yeah!
17
Reality
H0 True
H0 False
Yeah!
Type I Error ?
Reject H0
Yeah!
Decision
Yeah!
Type II Error ?
Dont Reject H0
Yeah!
18
Statistical Power
1 - ?
The ability to avoid Type II error (fail to
reject H0 that should be rejected).
19
Ordinarily, one is well advised to take the
largest sample that is practical and then
determine if this sample has adequate power for
detecting a difference large enough to be of
interest. Researchers often strive for power ?
80 with ? .05. More often, however, one finds
that power is low even for detecting
differences large enough to be of practical
importance.
20

Problem You develop a new measure of social
efficacy for adolescent girls, with 24 items on a
3-point scale. The scale seems to have ? 18,
and ? 16. You are asked to evaluate a new
program to promote social efficacy in adolescent
girls, and want to use your scale. You sample
16, but alas find that the sample mean of 22 does
not allow you to reject the null hypothesis at
?.05. Youre really really frustrated because
you think that a 4-point gain is meaningful.
What should your next steps be?
21
? ? x f (N)
? ? N 1/2
? 4/16 .25 N 16 ? 1.0
22
? ? x f (N)
? ? N 1/2
? 4/16 .25 N 16 ? 1.0
What would it take for power .80?
N (? / ? )2 N (2.8 / .25)2 125.44
23
What can you do to increase power?
• Increase n

24
What can you do to increase power?
• Increase n
• Decrease measurement error

25
What can you do to increase power?
• Increase n
• Decrease measurement error
• Increase ?, say, from .05 to .10 (or fiddle with
tails)

26
What can you do to increase power?
• Increase n
• Decrease measurement error
• Increase ?, say, from .05 to .10 (or fiddle with
tails)

27
What can you do to increase power?
• Increase n
• Decrease measurement error
• Increase ?, say, from .05 to .10 (or fiddle with
tails)
• Increase the magnitude of the effect