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Describing Behavior
Chapter 4
Data Analysis

Two basic types

Descriptive


Summarizes and describes the nature and
properties of the data
Inferential

What is the likelihood the results in the sample
actually occur in the population

(e.g., differences between groups, relationships
between variables)
Describing Individual Differences

Measures of Central Tendency

Measures of Variability

Distribution of the data
Measures of Central Tendency

Mean


Median


average score of all observations in
distribution
midpoint of all scores in distribution
Mode

most frequently occurring score in
distribution
Measures of Variability

Range


Standard Deviation

–
subtract the lowest from the highest
score
measure of the “spread” of the
scores around the mean
Variance

square of the standard deviation
Calculating the standard deviation
√
Data
1
2
3
4
5
Sum 15
Mean 3
√
∑(xi – x)2
n-1
2+
(2)2 2+ (5 – 3)2
(1 – 3)2 +(-2)
(2 –2 +(-1)
3)42 ++21(3+(0)
–03)
+10
+21+(1)
+(442 –+ 3)
2.5
1.58
5 4-41
√ √ √√
Data Distributions
Descriptive Statistics

Distribution of the data

Shapes of distribution curves

Bell (normal distribution)



The bell curve has desirable statistical properties
A number of inferential statistics “assume” data is
normally distributed
Skewed Curves


Negative Skew - tail of the curve is to the left
Positive Skew - tail of the curve is to the right
Properties of a Normal Distribution

Measures of central tendency are the
same


mean = median = mode
We know percentage of scores that fall
within



 1 standard deviation (68%)
 2 standard deviations (95%)
 3 standard deviations (99%)
Correlation

The extent to which one variable
can be understood on the basis
of another

Properties of correlation coefficient


direction (positive or negative)
magnitude (strength of the
relationship)
Positive Correlation
Final Grade Points
350
r = .95
300
250
200
150
100
50
0
0
20
40
60
Exam Points
80
100
120
No Correlation
Final Grade Points
350
r = .00
300
250
200
150
100
50
0
0
20
40
60
Exam Points
80
100
120
Negative Correlation
High
Turnover Intentions
r = -.95
Low
Low
Job Satisfaction
High
Correlation: A Review
Distribution for Example
50
40
M = 3.00
SD = 1.10
40
30
20
20
20
10
10
10
0
1
2
3
4
5
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