Chapter 8: Bivariate Correlational Research

Correlational Research

focuses on the degree to which measured variables are related and allows us to predict outcomes

(Association Claims)

Correlation doesn’t =

Causation

Bivariate Correlation

the degree to which two measured variable are related

Scatterplots

a graph where the x-axis is one variable and the y-axis is another and each dot represents an individual participant’s relation to them

Pearson’s correlation coefficient symbol

r

Pearson’s correlation coefficient

a statistic that describes the relationship between two variables

(r=slope)

• only works for linear relationships

• most common

range of r?

-1 (<=) r(<=) 1

direction is indicated by

r’s sign

(+) means positive direction

(-) means negative direction

Strength is indicated by

|r|

1 and -1 are the strongest

0 is weakest

effect size

magnitude or strength of r

Is there a perfect benchmark for describing the size of correlations?

no

Average correlation size in psych

r=± 0.20

Confidence Intervals tell us

1. statistical significance

2. precision of estimate

When is a correlation NOT significant?

when the confidence interval includes zero

Factors that distort correlations

1. Restricted Range'

2. Curvilinear Relationships

3. Outliers

4. Unreliable Measures

Restricted Range

by limiting the scope of attention, it leads to the unintentional exclusion of data points that may be necessary to visualize the trend.

UNDERESTIMATES strength

Curvilinear Relationships

non-linear/curved line relationship

Pearson’s r only works for linear relationships

UNDERESTIMATES strength

Outliers

Extreme scores that stand out from the pack

Underestimate or Overestimate

why are outliers problematic

they exert a disproportionate influence on correlation

When are outliers most influential?

smaller samples

Unreliable Measures

introduce erroneous variability/ noisy data obscuring the relationship

UNDERESTIMATES strength

Moderator

a variable that, depending on the level, affect the relationship between two variables

ex: stress at work’s (x) and job performance’s (Y) association changes based on social support (z)

(level 1: low support; level 2: High support)

Moderators tell us

when, for whom, and under what conditions are 2 variables related

Why can’t bivariate correlations establish cause?

1. covariance (establishes)

2. temporal precedence (fails to establish)

3. internal validity (fails to establish)

Bivariate’ correlations temporal precedence issue is an issue of _______

directionality. Can’t establish which came first.

Bivariate’ correlations internal validity issue is an issue of _______

the third variable problem

The third variable problem

a potential third variable (e.g confound) that is the actual reason for the perceived association despite it being spurious

spurious association

a relationship between two variables that is attributable to a 3rd variable that the study didn’t measure