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By Sheila Wilson,
Bonnie Dompierre, and
What is Correlational Research?
The degree of relation
is expressed as a
P. 216 Textbook
These are not cause and effect relationships!
What is the process of
Low intelligence test score =
Low grade point average.
High intelligence test score. =
High grade point average
Example: Intelligence and academic achievement are related. Individuals with
high scores on intelligence tests tend to have high grade point averages, while
individuals with low scores on intelligence tests tend to have low grade point
What is the purpose of
*It might be used in a relationship study to determine
relations among variables, such as
IQ and GPA; IQ and Weight; IQ and Errors (Textbook); or
Living together and divorce rates; or
Internet usage and depression.
*It might be used in a prediction study to make
predictions, using the results of the examples above to
make predictions about GPA, Weight, Errors, Divorce
rates, and Internet usage.
Education Participants: A major complex variable,
achievement, is investigated in correlational research!
Variables that are not highly
related can be dropped.
Variables that are highly related
can be examined closer to
determine the nature of the
TABLE 8.1 • Hypothetical sets of data illustrating a strong
positive relation between two variables, no relation,
and a strong negative relation.
Strong Position Strong Negative
Relation No Relation Relation
IQ GPA IQ Weight IQ Errors
1. Iggie 85 1.0 85 156 85 16
2. Hermie 90 1.2 90 140 90 10
3. Fifi 100 2.4 100 120 100 8
4. Teenie 110 2.2 110 116 110 5
5. Tiny 120 2.8 120 160 120 9
6. Tillie 130 3.4 130 110 130 3
7. Millie 135 3.2 135 140 135 2
8. Jane 140 3.8 140 166 140 1
Correlation r = + .95 r = + .13 r = -.89
A way to interpret
Coefficient Relation Between
Between +0.35 and -0.35 Weak or none IQ:Weight = +0.13
Between +0.35 and
Between -0.35 and -0.65 Moderate
Between +0.65 and 1.00 Strong IQ:GPA = +0.95
Between -1.00 and -0.65 Strong IG:Errors= -0.89
Common new researcher mistakes, and the
shared variance is the variation of the variable.
Choose logical variables.
Use theoretical basis.
To determine common variance, square the correlation
coefficient: .80 = (0.80)2 or 0.64, or 64% common variance.
0.00, or [0.00]2 shows 0.0 or 00% common variance.
1.00 or [1.00]2 shows 1.00 or 100% common variance.
A .50 means only a 25% common variance, where 75% of the
variance is unexplained variance.
Statistical significance is the probability that the results
could have occurred due to chance.
It’s about the math:
Types of Correlational
Relationship Study – A researcher attempts to gain
insight into variables that are related to a complex
Academic achievement vs. Socioeconomic status
Prediction Studies – A researcher uses two highly
related variables to predict scores on other variables.
High GPA and IQ as a predictor of success in college.
In a Relationship
• Researchers gain insight to variables or factors that
are related to a complex variable.
• In Educational Research:
a) academic achievement
First: Identify the variables to be related.
Ex: Academic Achievement vs. Socioeconomic
Next, identify appropriate population to sample.
Pearson r is the most common technique.
Spearman rho is a rank correlation coefficient.
Others: phi coefficient (gender based, political
affiliation, smoking status, educational status),
Kendall’s tau, Biserial, Point biserial, Tetrachonic,
Intraclass, and Correlation ratio, or eta.
Correlational Techniques in
Prediction Studies and
Definition: An attempt to determine which number or variables are most highly related
to criterion variable.
Data collection requires participants to provide desired data and to be available to the
Shrinkage occurs when the second predictor group has less accurate data than the first
Cross-validation should occur if one-of-a-kind circumstances in one group result.
Data Analysis and Interpretation
of Prediction Studies
Each predictor variable must correlate with the
Two types of Prediction studies occur: single
prediction, and multiple prediction.
Single Variable prediction equation: Y= a + bX
Prediction and Relationship studies are similar, in
that they can be formulated for each number of
subgroups or total groups.
• Many sophisticated statistical analyses are based on
• Multiple Regression
• Discriminate Function Analysis
• Canonical Analysis
• Path Analysis
• Structural Equation Modeling, AKA LISREL
• Factor Analysis
Houston, we have a problem…
Problems in interpreting Correlational Coefficients:
Proper correlation method calculation may not have
Relations cannot be found if reliabilities are low.
Invalid variables produce meaningless results.
The range of scores could be too narrow or too broad.
Large samples may show correlations that are
statistically significant but unimportant.