Transcript Basic Concepts of Statistics

INTRODUCTION TO DATA
ANALYSIS
Lawrence R. Gordon
Psychology Research Methods I
Why ALL “Psychologists”?
Clinician
Scientists
(MD, Clin Psy)
(Incl “psychologists”)
“Problem”
“TRUTH”
“Reality”
“Symptoms”
DATA
“Observations”
{Feelings, Readings}
{Behavior, Experience}
“Diagnosis”
HYPOTHESIS
“Theory”
“Treatment”
ACTION
“Knowledge”
{Findings, Laws}
BACK FOR MORE DATA
Basic Concepts of Statistics
 What is/are “statistics”?
 An application of probability
 A guide to decision making
 A way to communicate knowledge
TYPICAL JOURNAL ARTICLE
INTRODUCTION
Problem
Literature  Hypothesis
METHOD
Variables (op defs)
Design
Subjects
Procedures
Data summary: descriptive
Hypothesis tests: inferential
RESULTS
DISCUSSION
Interpretation
Limitations
Ideas for further work
Basic Concepts of Statistics
 What are the major “types” of statistics used
by researchers?
 DESCRIPTIVE STATISTICS
 INFERENTIAL STATISTICS
Basic Concepts of Statistics
 VIDEO to reinforce these ideas, and show
many uses in “real life” issues
 “Viewer Notes”
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handout
somewhat “dated”, but content is sound
no product “endorsements” are intended -examples only
Basic Concepts of Statistics
 QUESTIONS ON THE VIDEO
 What are the IV and DV in the Amabile study at the
beginning?
 What ideas from the previous two classes were mentioned
or reinforced in the video?
 Which of the other studies had aspects of “applied”
psychology?
Displaying Data
Displaying Data
 What’s a picture worth?
 What can they do for us?
 Tell us more about our data -- distributions
 Tell us more about our results -- figures
 Help us communicate these to others!
Displaying Data: Distributions
 Verbal descriptions and characteristics of
distributions of data:
 Symmetry (including “normal” or “bell curve”)
 Modality (how many “peaks”)
 Skewness
• Positive (“right”) skew
• Negative (“left”) skew
EMPIRICAL DISTRIBUTIONS
16
20
14
12
10
8
10
6
50
5.
00
5.
50
4.
00
4.
50
3.
00
3.
50
2.
00
2.
50
1.
00
1.
0
.5
00
0.
0
-.5 0
.0
-1
0
.5
-1
0
.0
-2
83
2.
43
2.
03
2.
63
1.
23
1.
89
5.
57
5.
25
5.
94
4.
62
4.
30
4.
99
3.
67
3.
35
3.
04
3.
72
2.
40
2.
09
2.
77
1.
45
1.
39
4.
07
4.
75
3.
44
3.
12
3.
80
2.
49
2.
17
2.
85
1.
54
1.
22
1.
0
.9
9
.5
7
.2
5
-.0
Score
Score
3
.8
3
.4
3
.0
7
-.3
7
-.7
7
.1
-1
7
.5
-1
8
.9
-1
8
.3
-2
8
.7
-2
30
40
N = 200.00
0
N = 200.00
0
Score
Score
N = 200.00
0
Mean = 1.54
2
Mean = -.01
0
N = 200.00
Std. Dev = 1.79
Std. Dev = 1.02
4
30
20
20
10
10
Std. Dev = .91
Std. Dev = .73
Mean = 4.85
Mean = .96
Displaying Data
 What else can distributions tell us?
 Baseball salary example
 1994 strike
 Question: “…the newspapers continually talk about the
average salary ($1,183,416), but they never said what the
median is. What is it?”
 A little data to the rescue….
Frequency
BASEBALL SALARIES 1994
BASEBALL SALARIES 1994
300
200
100
Std. Dev = 1390922
Mean = 1183416.7
0
0.
0
0.
00
00 .0
60 000
00 .0
55 000
00 .0
50 000
00 .0
45 000
00 .0
40 000
00 .0
35 000
00 .0
30 00
0
00 .0
25 000
00 .0
20 000
00 .0
15 000
00
10 0.0
0
00
50
N = 747.00
0
SALARY94
Displaying Data
 A quick example:
 Scatterplot: “Solar Radiation and Cancer”
 POINT: “communication” of results
Scatterplot of Solar Radiation
and Cancer
Cancer Rate and Solar Radiation
for 24 U.S. Cities
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32
30
28
26
24
22
20
200
300
400
Solar radiation
500
600
(To be continued…)
Central Tendency and Variability