On-line resources
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•
•
•
http://wise.cgu.edu/powermod/index.asp
http://wise.cgu.edu/regression_applet.asp
http://wise.cgu.edu/hypomod/appinstruct.asp
http://psych.hanover.edu/JavaTest/NeuroAnim/stats/StatDec.
html
• http://psych.hanover.edu/JavaTest/NeuroAnim/stats/t.html
• http://psych.hanover.edu/JavaTest/NeuroAnim/stats/CLT.html
• Note demo page
Statistical power is how “sensitive” a study is
detecting various associations (magnification
metaphor)
If you think that the effect is small (.01), medium, (.06) or large (.15), and you want to
find a statistically significant difference defined as p<.05, this table shows you how
many participants you need for different levels of “sensitivity” or power.
Power ->
Effect size |
.01
.06
.15
.10
.20
.30
.40
.50
.60
21
5
3
53
10
5
83
14
6
113
19
8
144 179
24 30
10 12
.70
.80 .90
219 271 354
36 44 57
14 17 22
If you think that the effect is small (.01), medium, (.06) or large (.15), and you want to
find a statistically significant difference defined as p<.01, this table shows you how many
participants you need for different levels of “sensitivity” or power.
Power ->
.10
.20
.30
.40
.50
.60 .70
.80 .90
.01
70
116 156
194
232 274 323 385 478
.06
13
20
26
32
38
45
53
62
77
.15
6
8
11
13
15
18
20
24
29
Effect size |
What determines power?
1. Number of subjects
2. Effect size
3. Alpha level
Power = probability that your experiment will
reveal whether your research hypothesis is
true
Power = 1 - type 2 error
Power = 1 - beta
How increase power?
1.
2.
3.
4.
Increase region of rejection to p<.10
Increase sample size
Increase treatment effects
Decrease within group variability
Study feature
Practical way of raising
power
Disadvantages
Predicted difference
Increase intensity of
experimental procedures
Use a less diverse
population
Use standardized,
controlled circumstances
of testing or more precise
measurement
Use a larger sample size
May not be practical or
distort study’s meaning
May not be available,
decreases generalizability
Not always practical
Standard deviation
Standard deviation
Sample size
Significant level
One tailed vs. two tailed
test
Not practical, can be costly
Use a more lenient level of Raises alpha, the
significance
probability of type 1 error
Use a one-tailed test
May not be appropriate to
logic of study
What is adequate power?
.50 (most current research)
.80 (recommended)
How do you know how much power you have?
Guess work
Two ways to use power:
1. Post hoc to establish what you could find
2. Determine how many participants need
Outcome
statistically
significant
Sample Size
Conclusion
Yes
Small
Important results
Yes
Large
Might or might not
have practical
importance
No
Small
Inconclusive
No
Large
Research H.
probably false
5 steps to hypothesis testing
1. Restate the research question as an alternative
hypothesis and a null hypothesis about the
populations.
2. Determine the characteristics of the comparison
distribution.
3. Determine the cutoff sample score on the
comparison distribution at which the null
hypothesis should be rejected.
4. Determine your sample’s score on the
comparison distribution.
5. Decide whether to reject the null hypothesis.
Comparison table
Terms to know
• Random selection
• Convenience or haphazard selection
• Random assignment
• http://onlinestatbook.com/stat_sim/sampling_dist/index.html
Example 1
A doctor gives a patient a new type of antidepressant. Is there any improvement compared to
a larger population of depressed population?
Assume that depression scores follow a "normal
curve"
(Population) M = 69.5
SD = 14.1
X = 41
5 steps
1. Convert research questions to statistical hypotheses.
Null Hypothesis:
Alternative Hypothesis
2. What are the characteristics of our comparison distribution?
Why can we use the normal curve?
Not all distributions are normal.
3. Determine "cut-off" scores.
Conventional level of statistical significance
One tailed vs. two tailed
4. Determine your observation or sample score.
Convert observation to Z score.
5. Accept or reject the NULL hypothesis.
How would we write it down?
Z score distribution
http://davidmlane.com/hyperstat/z_table.html
Example 2
Is memory affected by stress? Ask 25 people to give a talk and
then remember a set of photographs.
Mean recall = 48, SD=7, General population mean=53
Shift to a sample of observations from a single observation.
3 key characteristics of a distribution of means.
–Mean of distribution of means is the same as the original
population of individual scores.
–Spread of distribution is narrower than spread of individual
scores (so we need to correct for that!)
–The shape is normal (but requires a sample size of 30 and
normal distribution of scores for the sample to make this
assumption)
Distribution of means graphs
How do we correct the problem?
Formula
Comparison of three types of
distributions
What if don’t know population?
• Move to t-tests