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

Mean average score of all observations in

distribution Median

midpoint of all scores in distribution Mode

most frequently occurring score in distribution

Measures of Central Tendency

Range subtract the lowest from the highest

score Standard Deviation

measure of the “spread” of the scores around the mean

– Variance square of the standard deviation

Measures of Variability

∑(xi – x)2

n-1√

(1 – 3)2 + (2 – 3)2 + (3 – 3)2 + (4 – 3)2 + (5 – 3)2

5 - 1√

(-2)2 +(-1)2 +(0)2 + (1)2 + (2)2

5 - 1√ 4 + 1 + 0 + 1 + 4

4√12345

153

SumMean

Data

10

4√ 2.5√1.58

Calculating the standard deviation

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

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%)

Properties of a Normal Distribution

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)

Correlation

0

50

100

150

200

250

300

350

0 20 40 60 80 100 120

Exam Points

Fin

al G

rade

Poi

nts r = .95

Positive Correlation

0

50

100

150

200

250

300

350

0 20 40 60 80 100 120

Exam Points

Fin

al G

rade

Poi

nts r = .00

No Correlation

Job Satisfaction

Tur

nove

r In

tent

ions

r = -.95

Low HighLow

High

Negative Correlation

Correlation: A Review

Distribution for Example

10

20

40

20

10

0

10

20

30

40

50

1 2 3 4 5

M = 3.00SD = 1.10