Correlational research design

Objectives:
 Define the purpose and use of
correlational research.
 Distinguish between the explanatory
and prediction correlational designs
 Draw a scatter plot of scores and
create a correlation matrix of scores
Technical Writing: Educational Research

Objectives:
 Analyze correlation coefficients for
two sets of scores in terms of
direction, form, degree, and the
strength of the association
 Explain the reasons for using partial
correlations and multiple regression
in correlational research

Objectives:
 Identify steps in conducting a
correlation study
 List the criteria for evaluating a
correlational study

Situation

“Your brain can do really some cool
things. For instance, you learn that
a particular jingle means the ice
cream trucks are nearby. The
louder the jingle, the closer it is.

And if you were lucky enough to have
several types of ice cream trucks, you
will recognize which jingle goes with
which ice cream truck. The world is full
of things where if thing A happens, then
there is a good chance that thing B, the
ice cream truck, is close by.

We can also make things more
complicated by thing A being the
loudness of the jingle and thing B being
the distance to the ice cream truck. As
the loudness increases, the distance
shrinks. As the distance increases, the
loudness goes down.”

What is
Correlational
Research?

In correlational research designs,
investigators use the correlation
statistical test to describe and
measure the degree of association
(or relationship) between two or
more variables or set of scores.

When do you use
Correlational Research?

o To examine the relationship
between two or more variables
o To predict an outcome
o Statistic that expresses linear
relationships is the Product-
Moment Correlation Coefficient

How did
Correlational
Research develop?

• 1895 – Pearson develops correlation
formula
• 1897 – Yule develops solutions for
correlating two, three and four variables
• 1935 – Fisher pioneers significance
testing and analysis of variance

• 1963 – Campbell and Stanley write about
experimental and quasi-experimental
designs
• 1970s and 1980s – computers give the
ability to statistically control variables
and do multiple regression

What are the types
of Correlational
Designs?

1. The Explanatory Design
2. The Prediction Design

Explanatory Design
• Various authors refer to explanatory
correlational research as:
– Relational research (Cohen & Manion, 1994, p.123)
– Accounting-for –variance studies (Punch, 1998, p.78)
– Explanatory research (Fraenkel & Wallen, 2000,
p.360)

Explanatory Design
• It’s basic objective is to explain the
association between or among
variables.
• It does not deal with the formulation
of predictions since it is explanatory.

Characteristics of Explanatory Designs
• Correlates two or more variable
• Collect data at one point in time
• Analyze all participants as a single
group

Characteristics of Explanatory Designs
• Obtain at least two scores for each
individual in the group – one for each
variable
• Report the correlation statistic
• Interpretation based on statistical test
results

Prediction design: Variables
• Predictor Variable: a variable that is used
to forecast about an outcome in the
correlational study
• Criterion Variable: outcome being
predicted

Characteristics of Prediction design
• Prediction: usually is a word in the title
• Predictor Variables: usually measured at
one point in time and the criterion variable
at a later point in time
• Purpose is to forecast future performance

What are the key
characteristics of
Correlational Designs?

• Displays of scores
–Scatterplots and matrices
• Association between scores
–Direction, Form and Strength
• Multiple variable analysis
–Partial correlation and Multiple regression

Display of scores in a Scatterplot
• Researchers plot scores for two variables
on a graph to provide a visual picture of
the form of scores.
• A scatterplot or scatter diagram is a
pictorial image displayed on a graph of
two sets of scores for participants.

Display of scores in a Scatterplot
• These scores are typically identified a X
and Y values with X represented on the
horizontal and Y on the vertical axis.

Display of scores in Correlation Matrix
• A correlation matrix presents a visual
display of the correlation coefficient for
all variables in a study.

Displays of scores in a
correlation matrix
1.School satisfaction
2. Extra-curricular activities
3. Friendship
4. Self-esteem
5. Pride in school
6. Self-awareness
1 2 3 4 5 6
-
-
-
-
-
-
-.33**
.24 -.03
-.15 .65** .24*
-.09 -.02 .49** .16
.29** -.02 .39** .03 .22

Association between two scores
• Direction
–Positive or negative
• Form
–Linear or non-linear
• Degree and strength
–Size of coefficient

What is the direction of the
association?
• Direct or Positive correlation (indicated
by a “1” correlation coefficient): the
points move in the same direction; that
is, when X increases, so does Y and vice
versa.

association?
• Inverse or Negative Correlation (indicated
by a “-” correlation coefficient): the
points move in the opposite direction;
that is, when X increases, Y decreases
and vice versa.

association?
• If score of one variable do not relate in
any pattern on the other variable, then
no linear relationship exist or
sometimes called as zero relationship.

Form of the Association
• Positive linear relationship occur when
high scores in one variable relate to
high scores for the second variable or
vice versa.
• Negative linear relationship occur
when high scores of one variable relate
to low scores in the second variable.
(Creswell, 2008)

• Uncorrelated relationship occurs
when two variables are not related
to one another and are instead
independent of each other.

Association Between Two Scores Linear and
non-linear patterns
A. Positive Linear (r=+.75) B. Negative Linear (r=-.68)
C. No Correlation
(r=.00)

• A curvilinear or nonlinear
relationships are characterized by a
U-shaped relationship between
variables. The direction of the
relationship between the variables
differs according to different levels
of the variable (Lodico et al., 2006).

Linear and non-linear patterns
E. Curvilinear F. Curvilinear
D. Curvilinear

Non-linear associations statistics
• Spearman rho (rs) – or Spearman’s rank
correlation coefficient for nonlinear ordinal data.
• Point-biserial - used to correlate continuous
interval data with a dichotomous variable.
• Phi-coefficient - used to determine the degree of
association when both variable measures are
dichotomous.

What is the Degree and
Strength of Association?

Degree of Association
• It means that the association between
two variables or sets of scores is a
correlation coefficient of -1.00 to a +1.00,
with 0.00 indicating no linear association
at all (Gravetter & Wallnau, 2000).

Degree of Association
• Coefficient of determination: which
assesses the proportion of variability in
one variable that can be determined or
explained by a second variable.

Example
• This means that almost half
(49%) of the variability in Y can
be determined or explained by
X.

Consider the following interpretations
given the following size of coefficients:
• .20–.35: When correlations range from .20
to .35, there is only a slight relationship
• .35–.65: When correlations are above .35,
they are useful for limited prediction.

• .66–.85: When correlations fall into this
range, good prediction can result from one
variable to the other. Coefficients in this
range would be considered very good.

• .86 and above: Correlations in this
range are typically achieved for
studies of construct validity or test-
retest reliability.

Multiple Variable
Analysis

Partial Correlation
• Used to determine the amount of
variance that an intervening variable
explains in both the independent and
dependent variables

Multiple Variable Analysis: Partial
correlations
Independent
Variable
Dependent
Variable
Time on Task Achievement
r=.50
r squared=(.50)2
Partial Correlations:
use to determine extent
to which a mediating variable
influences both independent
and dependent variable
Motivation
Time-on-Task Achievement
Motivation
r squared = (.35)2

Regression Line: a line of “best fit”
for all the points of scores on the
graph.

Simple Regression Line
Slope
Depression
Scores
Regression Line
Hours of Internet Use Per Week
14 15 20105
50
41
40
30
20
10
Intercept

Steps In Conducting A
Correlational Study

STEP 1:
DETERMINE IF A CORRELATIONAL
STUDY BEST ADDRESSES THE
RESEARCH PROBLEM

Is creativity related to IQ test
scores for elementary
children? (associating two
variables)

What factors explain a student
teacher’s ethical behavior
during the student-teaching
experience? (exploring a
complex relationship)

Does high school class rank
predict a college student’s
GPA in the first semester of
college? (prediction)

STEP 2:
IDENTIFY INDIVIDUALS TO
STUDY

Step 3:
Identify two or more measures
for each individual in the study

Step 4:
Collect data and Monitor Potential
Threats

Step 5:
Analyze the Data and represent
the Results

Step 6:
Interpret the Results

Evaluating a
Correlational Study

• Is the size of the sample adequate for
hypothesis testing?
• Does the researcher adequately display
the results in matrixes or graphs?
• Is there an interpretation about the
direction and magnitude of the
association between the two variables?

• Is there an assessment of the magnitude of
the relationship based on the coefficient of
determination, p-values, effect size, or the
size of the coefficient?
• Is the researcher concerned about the form
of the relationship so that an appropriate
statistic is chosen for analysis?

APPLYING WHAT YOU HAVE LEARNED:
A CORRELATIONAL STUDY

Correlational research design

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