Types of Relationships

• Social scientists are interested in discovering functional relationships between variables.

• In particular, researchers look for:– correlations (association,

covariation) among vaariables– differences between groups or

conditions

The nature of causation

• Cause-effect relationships--causation is always inferred, never directly observed

• “functional” relationships– one thing correlates with, or is associated with

another (correlation)– one thing predicts or explains the amount of

variance in another (analysis of variance)– one thing has a direct effect on another (path

analysis, multiple regression)

Graphic Representations of Relationships

X-axis

Y-axis

(independent variable)

(dependentvariable)

Note: “3/4 rule”the convention is to make the Y axis3/4 of the lengthof the x axis

Correlations

• displaying correlations using a scattergram• linear relationship

– can be positive or negative• curvilinear relationship

– also known as nonmonotonic relationships, quadratic trends, “u-shaped” or “inverted-u”

– requires a minimum of three levels of the variable being investigated

• no correlation• spurious effect

Do employees who drink a lot of coffee take more bathroom breaks?

employee cups of coffee consumed

bathroom trips

Fifi 1 2

Rex 2 1

Trudy 3 3

Pedro 3 4

Lulu 4 6

Thaddeus 5 5

Rudolfo 6 5

frequency table

scatterplot

Illustration of Scatterplots

• Scatterplots that are closer to a straight line have correlations closer to +1.0 or -1.0

• Must have interval or ratio data

• Correlation does not prove causation

Linear versus curvilinear relationships

Linear relationship Curvilinear relationship

Differences Between Groupsor Conditions• main effect (changes produced by one

independent variable alone)– one-way interaction

• interaction effect (changes produces by independent variables acting together, or in concert– two-way interaction– three-way interaction

interpersonal touch, social labeling, and the foot-in-the-door effect

touch no touch

positiveFITD

negativeFITD

.15 .40

.45 .25

communicator physical attractiveness and persuasion

attractive criminal

unattractive criminal

swindler

burglar

5.45 4.35

2.80 5.20

non-significant-interaction

A characteristic feature of non-significant interaction effects is that the lines are parallel, or nearly parallel

potentially significant interaction(ordinal)

potentially significant interaction(disordinal or “crossed”)

potentially significant interaction(ordinal)

Illustration of an interaction effect

2 3

3 6

evidence quality low high

Att

itude

cha

nge

0 1

2

3

4 5

6

7

Sou

rce

Cre

dibi

lity

lo

w

h

igh

low highSource Credibility

low qualityevidence

high qualityevidence

Illustration of an interaction effect

COLD ROOM

500

HOT ROOM

900

HARD TEST

60% 60%

EASY TEST

60% 80%

Te

st s

core

0 1

0 2

0 3

0 4

0 5

0 6

0 7

0 8

0 9

0 1

00

500 900

Hard test

Easy test

Overlapping normal distributions

• Which distribution has the higher mean? Which has the higher standard deviation?

Nonnormal distributions

• Positively skewed, negatively skewed , or a normal distribution?

What kind of correlation?

• Are people in richer nations happier??