Transcript Inferential Statistics - People Server at UNCW

Analyzing the Results of an
Experiment…
• -not straightforward..
– Why not?
Variability and Random/chance
outcomes
Inferential Statistics
• Statistical analysis appropriate for inferring
causal relationships and effects.
• Many different formulas…which one do
you use?
Inferential Stat selection
• -Determine that you are analyzing the
results of an experimental manipulation,
not a correlation
• Identify the IV and DV.
• The IV Will always be nominal on some level, even when it may
seem to be continuous..low, medium and high doses of a drug
Inf. Stat Selection
• What is the scale of the DV?
– Scale of DV
-Statistic to use
Nominal
Chi-squared
Ordinal
Mann-Whitney U-test
Continuous
T-test or ANOVA
t-test or ANOVA?
How many levels of the IV are there?
2 levels
more than 2 levels
T-test or ANOVA
ANOVA
There are different forms of T-tests and ANOVA’s:
Did the Study Use a Within Group or Between
group Experimental Design?
Only 2 levels of the IV
More than 2 levels of the
IV
Between Group
Within Group
Unpaired t-tests (or “t for
independent samples”).
“Paired t-tests ( or “t for
dependent samples”)
Or…ANOVA ( the basic
ANOVA is fitted for
between group designs)
Or…Within group ANOVA
(often referred to as a
“repeated measures
ANOVA”)
ANOVA
Repeated Measures
ANOVA
In some ways all inferential
Stats are similar.
• They calculate the probability that a result
was due to the IV as opposed to random
variability…
• Let’s focus on the Basic ANOVA since it is
likely to be the statistic you may use most
commonly.
ANOVA
• ANOVA produces an F-value.
• F values are the ratio of overall between
group Variability to the Mean within
group variability
/
Between Var. (+ chance) Mean within grp.
Variability (+ chance)
What does this mean?
Lets suppose:
• Experiment- IV marijuana
– Control
– Placebo control
– Low dose
– High dose
Dependent Variable is:
• Performance on a short term memory task
measured number correct out of 10 test
items.
• 9 subjects in each group
Possible out come 1
Possible Outcome 1
Control
•
•
•
•
•
•
•
•
•
4
5
6
5
5
6
4
3
7
Placebo
2
3
4
6
5
5
4
4
3
Low dose
2
3
4
4
5
4
5
6
3
High dose
2
3
5
3
4
4
4
6
5
Distribution of scores for control
sample
3.5
3
Count
2.5
2
1.5
1
.5
0
0
2
4
6
control
8
10
12
Placebo scores
3.5
3
Count
2.5
2
1.5
1
.5
0
0
2
4
6
placebo
8
10
12
Low dose scores
3.5
3
Count
2.5
2
1.5
1
.5
0
0
2
4
6
low
8
10
12
High dose scores
3.5
3
Count
2.5
2
1.5
1
.5
0
0
2
4
6
high
8
10
12
The population distribution of
scores
12
10
Count
8
6
4
2
0
0
1
2
3
4
5
6
7
population
8
9
10
11
F value relatively low
High
low placebo
control
w/in grp.
var
Between grp.
Var
Now consider this: Possible Outcome 2
Control
•
•
•
•
•
•
•
•
•
4
5
6
5
5
6
4
3
7
Placebo
2
3
4
6
5
5
4
4
3
Low dose
2
3
4
4
5
4
5
6
3
High dose
2
3
5
3
4
4
4
6
5
Distribution of scores for control
sample
3.5
3
Count
2.5
2
1.5
1
.5
0
0
2
4
6
control
8
10
12
Placebo scores
3.5
3
Count
2.5
2
1.5
1
.5
0
-2
0
2
4
6
placebo
8
10
12
Low dose scores
3.5
3
Count
2.5
2
1.5
1
.5
0
0
2
4
6
low
8
10
12
High dose scores
3.5
3
Count
2.5
2
1.5
1
.5
0
0
2
4
6
high
8
10
12
F value relatively High
High
low
placebo
control
w/in grp. var
Between grp. Var
The high F value reflects
• Logic!
• Distribution of score are much more
obviously separated, and in this case are
completely non-overlapping
• Low F values indicate highly overlapping
score distributions
So how do we decide if an F value is large
enough to consider the result as causal?
• We consult a table of established probabilities of different F values,
within the context of Degree of freedom terms:
ANOVA Significance table
Where is/are the difference (s)?
70
60
50
Neutral
40
Positive
Negative
Sex
Drug
30
Taboo
20
10
0
Neutral
Positive
Negative
Sex
Drug
Taboo
Inferential Statistics
The story of “Scratch”
Why not jus use repeated t-tests?
Probability pyramiding
• 15 t-tests required for this
data set
70
60
50
• Post-hocs include
compensations for
repeated testing of a large
data set
Neutral
40
Positive
Negative
Sex
Drug
30
Taboo
20
10
0
Neutral
Positive
Negative
Sex
Drug
Taboo
After all this where so we stand?
We can still be wrong.
Factors that affect “power.”
Sample size
One vs two-tailed testing
• Effect size