Correlation research examines the relationships between two or more non-manipulated variables without changing any variables. It can be used to predict scores on one variable based on scores of another predictor variable. Common techniques include explanatory design to look for associations between variables and prediction design to identify predictors of outcomes. Tools to analyze correlations include scatter plots, correlation coefficients, and regression analysis.

2. Correlation Research
 A procedure in which subjects’ scores on two variables are simply
measured, without manipulation of any variables, to determine whether
there is a relationship
 Correlation research examines the relationship between two or more non
manipulated variables.
 If a relationship of sufficient magnitude exists between two variables, it
becomes possible to predict a score on either variable if a score on the other
variable is known (Prediction Studies).
 The variable that is used to make the prediction is called the predictor
variable.

3. Definition
 A statistical analysis of covariant data to determine a pre-
existing relationship. Researcher makes no attempt to
manipulate an independent variable.
 Purpose: This research technique is used to relate two or
more variables and allow predictions of outcomes based
on causative relationships between the variables

4. Historical Perspective
 Karl Pearson introduced modern correlation techniques
in 1895 at a Royal Society meeting in London where he
illustrated his statistical model using Darwin’s evolution
and Galton’s heredity.
 Improvements were slow coming until the arrival of
microcomputers when complex regression analysis of
multiple variables was possible

5. Correlation Research Design Models
(Types)
 Explanatory Design: Research looks for simple
associations between variables and investigates the
extent to which the variables are related
 Prediction Design: Research designed to identify
variables that will positively predict outcomes

6.  Researchers have found that high school grades are
highly related to college grades. Hence , high school
grades can be used to predict college grades.
 The variable which is used to make the prediction is
called the predictor variable and the variable about which
the prediction is made is called the criterion variable.

7.  Correlations research is also some times referred to as a
form of descriptive research because it describes an
existing relationship between variables
 It describes the degree to which two or more quantative
variables are related and it does so by using correlation
coefficient

8. Explanatory Design Model
characteristic
 Correlation of two or more variables
 Data collected at one time
 Single group
 At least two scores recorded
 Correlation Statistical Test- Strength and Direction of
correlation determined
 Researcher draws conclusions from statistics alone

9. Prediction Design Characteristics
 Author states that prediction capability is the goal of the
research
 Use of predictor variable followed with a criterion variable
 Author forecasts future performance

11. Regression analysis
 a scattered plot like this has been constructed, a straight line , known as
regression line can be calculated mathematically. The regression line
comes the closest to all the score depicted on the scattered plot of any
straight line that could be drawn. The researcher can thus use the line as a
basis for prediction.
 A teacher with a score of 10 on expectation of failure would be predicted
to have a class with a score of 9 on the amount of disruptive behavior.

12. Primary Tools for Correlation Designs
Mathematical Tools
 Product-Moment
correlation coefficient
 Coefficient of
determination
 Spearman rho
 Phi-coefficient
 Point-biserial correlation
 Regression lines
Graphical Tools:
 Scatter Plots
 Correlational matrix
 Simple graphical
regression
 Venn diagram

13. Techniques
Multiple Regressions; technique that enables researchers to determine a
correlation between a criterion variable and the best combination of two or
more predictor variables. Example
Suppose we come up that a high positive correlation (r= 0.68) exist between
first semester college GPA and verbal scores in college SAT exam and
moderately high positive correlation (r= 0.51) between mathematics scores in
SAT and first semester college GPA. It is possible, using a multiple regression
prediction formula, to use all three variables to predict what a students GPA
will be during his or her first semester in college.

14. The Coefficient of Multiple
Correlation
 Symbolized by R; indicates the strength of the
correlation between the combination of the predictor
variables and the criterion variables. It can be though of
as a simple Pearson correlation between the actual
scores on criterion variable and the predicted score on
that variable.
 predicted GPA 3.15 and original 2.95 .

15.  The Coefficient of Determination : The square of the correlation between
predictor and a criterion variable
 Indicates the percentage of the variability among the criterion scores that
can be attributed to differences in the scores on the predictor variable
 Discriminate Function Analysis• Technique used when the technique of
multiple regression cannot be used when the criterion variable is categorical

16.  Factor Analysis: (FANOVA) Technique that allows a researcher to
determine if many variables can be described by a few factors.
 Approach: group a larger number of variables into a smaller number of
clusters; derive factors by finding groups of variables that are highly among
each other, but lowly with other variables; use factors as variables.
 Path Analysis: Used to test the likelihood of a causal connection among
three or more variables.
 Structural Modeling: Sophisticated method for exploring and possibly
confirming causation among several variables.

17. How to conduct a correlation
 Variables are identified
 Questions and/or hypotheses are stated
 A sample is selected
 Data are collected
 Correlations are calculated
 Results are reported

18. Sampling
 Random Sampling,
 Convenient / Purposeful sampling,
 A minimum of 30 samples is required

19. Data collection
 Naturalistic Observation : Naturalistic observation
involves observing and recording the variables of
interest in the natural environment without interference
or manipulation by the experimenter.
 The Survey Method: In this method, a random sample
of participants completes a survey, test, or questionnaire
that relates to the variables of interest.
 Archival Research: Archival research is performed by
analyzing studies conducted by other researchers or by
looking at historical patient records.

20. Data Analysis
 The scores for one variable are correlated with the scores for another
variable and expressed in the form of a correlation coefficient.
 The method for computing a correlation coefficient depends upon the type
of data represented by each variable types of data:
 nominal (dichotomous)
 ordinal (rank)
 interval (continuous)
 ratio (continuous)

21. with continuous data
use the product moment
correlation, Pearson r (ρ, rho)
with curvilinear data
with dichotomous data
with rank data use the rank difference
correlation, Spearman r (ρ, rho)
use the phi correlation (ψ)
use the eta correlation (η)

22. Calculating correlations
 To calculate a numerical value of a correlation we can use
Pearson’s product moment correlation co-efficient or
correlation coefficient with the symbol of the lowercase
letter „r‟.
 A correlation co-efficient ranges from - 1.0 to +1.0, with -
1.0 indicating a perfect linear negative correlation and
+1.0 a perfect linear positive correlation.

23. Interpretation of the Strength of
Correlations
 00 - .20 – Very Weak
 .21 - .40 – Weak
 .41 - .60 – Moderate
 .61 - .80 – Strong
 .81 – 1.00 - Very Strong
 Different statisticians may have similar but slightly
different scales.

24. Reporting results
 Positive Correlations: Both variables increase or
decrease at the same time. A correlation coefficient close
to +1.00 indicates a strong positive correlation.
 Negative Correlations: Indicates that as the amount of
one variable increases, the other decreases (and vice
versa). A correlation coefficient close to -1.00 indicates a
strong negative correlation.
 No Correlation: Indicates no relationship between the
two variables. A correlation coefficient of 0 indicates no
correlation.

25. A positive correlation…
y
x

26. A negative correlation…
y
x

27. No correlation…
y
x

28. How to calculate correlations
 Excel has a statistical function. It calculates Pearson
Product Moment correlations.
 SPSS (a statistical software program for personal
computers used by graduate students) calculates
correlations.

29. Understanding and interpreting the
Pearson Correlation
 Correlation simply describes a relationship between two
variables. It does not explain why two variables are
related. Specifically, a correlation should not and cannot
be interpreted as a proof of a cause and effect
relationship between the two variables. Example of
number of mosques in big cities and crime rates.

30. Understanding and interpreting the
Pearson Correlation
 The value of the correlation can be affected greatly by the
range of scores represented in the data.
 One or two extreme data points, often called outriders,
can have a dramatic effect on the value of a correlation.