Two basic types Descriptive

Describes the nature and properties of the data Helps to organize and summarize information

Inferential Used in testing hypothesis

(e.g., differences between groups, relationships between variables)

Statistics

Describing Individual Differences Measures of Central Tendency

Measures of Variability

Distribution of the data

Measures of Central Tendency Mean

average score of all observations in distribution

Median midpoint of all scores in distribution

Mode most frequently occurring score in distribution

Descriptive Statistics

Measures of Variability Range

subtract the lowest from the highest score and add 1

Standard Deviation measure of the “spread” of the scores around the

mean

Descriptive Statistics

∑(xi – x)2

n-1√

Calculating the standard deviation

(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

Frequency Plots

Scores Tallies Frequency

6 I 1

5 III 3

4 IIII 4

3 IIIII 5

2 III 3

1 II 2

0 II 2

Frequency Distribution

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%)

Normal Distributions

The extent to which one variable can be understood on the basis of another

Two 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

Negative Correlation

Job Satisfaction

Tur

nove

r In

tent

ions

r = -.95

Low HighLow

High

Data Set 3 Example Scatter Plot

1.5

1.8

2.1

2.4

2.7

3

3.3

500 600 700 800 900 1000 1100 1200 1300 1400 1500

SAT Score

GP

A