Transcript statistics

Statistical Analysis of Data
______________ statistics – summarize data
Proportion of Responses
0.4
Histogram –
(Frequency
distribution)
Used for continuous
measures
0.3
0.2
0.1
0.0
<.51
.51-.55 .56-.60 .61-.65 .66-.70 .71-.75
>.75
Inter-response time
Lect 10b
1
Bar Graph:
Used for ______________ measures
Mean Number Correct
80
60
40
20
0
A
B
C
Condition
Lect 10b
2
Descriptive statistics

Central tendency- _____ score
 ______,
______, _____
2, 2, 3, 5, 5, 7, 8
Mean = _____
Median = ____
Mode = _____
2, 3, 3, 4, 6, 7
Mean = _____
Median = _____
Mode = ____
Lect 10b
3
Descriptive statistics

Central tendency- typical score

mean, median, mode
2, 2, 3, 5, 5, 7, 8
Mean = 4.57
Median = 5
Mode = 2, 5
2, 3, 3, 4, 6, 7
Mean = 4.33
Median = 3.5
Mode = 3
Lect 10b
4

Measure of variability – how spread
out are the scores
1. Range – difference between ________
and _______ score
1, 2, 9, 6, 9
Range?
2.
______________________ - square root
of the variance (average squared
deviation from the mean).
Lect 10b
5
1 Standard deviation = 68% scores
2 Standard deviations = 95% scores
3 Standard deviations = 99.7% scores
e.g., if the SD of scores on a test was 6.9 we can
conclude that ____% of the class fell within plus or
minus 6.9 points of the mean.
12
Little variability –
_____ convinced of
effect
Group 1
Group 2
Test Outcome
10
8
6
4
2
0
0
1
2
3
2
3
Group
16
Group 1
Group 2
14
Test Outcome
12
Large amount
of variability –
_____ convinced of
effect
10
8
6
4
2
0
0
1
Group
Lect 10b
Measures of central tendency presented
without measures of variability
can be _______________!
7
Inferential Statistics
 Most common method for analyzing data
in studies using ______________

(Single-subject designs use _______ only)
 ________ used to evaluate whether or
not there is a functional relationship.


p<_____ = suggests a functional relation
Statistical significance never _____ a
hypothesis, only shows that it isn’t _____
Lect 10b
8
Inferential Statistics
 Imagine you are doing a study with two groups. One gets
treatment and one doesn’t.
 There are differences across groups due to the IV (hopefully
not a confound) – _______________________
 Even if the IV had no effect, we would expect variability
across groups due to sampling error and chance factors and
variability within a group due to chance factors (_______
___________)
Lect 10b
9
Rats in maze are given food for going the right way
either immediately or after a delay.
Rat #
Immediate
Food
Rat #
Delayed
Food
1
12
6
19
2
13
7
20
3
16
8
16
4
11
9
18
5
14
10
15
M1 = 13.2
SD = 1.9
M2= 17.6
SD=2.1
How do tell whether this difference is a difference
due to the IV or error? – Inferential statistics
Inferential Statistics


Inferential statistics give you the probability of obtaining
the difference in means you observed if there really was
___________________
The difference is judged significant if the probability is
below α (_______), usually set to 0.05
10b
Image from Introductory Statistics: Concepts, Models,Lect
and Applications
David W. Stockburger
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Null hypothesis
 _______________in population means
 Can either be _______ or ________
 Rejecting the null means you support the
________________ hypothesis
 P value = calculated probability of obtaining
these data given the null is true. (The _______
the p value the better)
 Obtain a p value of .05 means that there is a
___% chance that you would have obtained
the results given that there really was ___
____________ between the two groups
Lect 10b
12
Inferential Statistics
 Statistics for calculating significance
usually compare:
Test statistic = Between-group variance (M1-M2)
Error variance (standard error)
Rat maze example:
t = -6.4/1.55 = -4.13 (significant at the α =.01 level).
Reject Null: Supports the hypothesis that reinforcer
delay affects choice.
Lect 10b
13
Errors in Hypothesis Testing
 ________ error - “False alarm”


There is ____ difference (Null is true) but
We conclude that there _____ a difference
(We reject null)
 _________ error – “Miss”


There ____ a difference (Null is false) but
We conclude that there is ____ difference
(We accept null)
Lect 10b
14