Correlational research

Correlational Research
Research Writing
Aiden Yeh, PhD
Wenzao Ursuline College of Languages

 In general, correlational research examines the
covariation of two or more variables. For
example, the early research on cigarette smoking
examine the covariation of cigarette smoking
and a variety of lung diseases. These two
variable, smoking and lung disease were found
to covary together.

http://www2.webster.edu/~woolflm/statmethods.html

 Correlational research can be accomplished by a variety
of techniques which include the collection of empirical
data.
 Often times, correlational research is considered type of
observational research as nothing is manipulated by the
experimenter or individual conducting the research. For
example, the early studies on cigarette smoking did not
manipulate how many cigarettes were smoked.
 The researcher only collected the data on the two
variables.
 Nothing was controlled by the researchers.

 It is important to not that correlational research
is not causal research. In other words, we can
not make statements concerning cause and
effect on the basis of this type of research.


 Correlational research is often conducted as
exploratory or beginning research. Once
variables have been identified and defined,
experiments are conductable.


Conducting Correlational Research
 Research Design
 In general, a correlational study is a quantitative
method of research in which you have 2 or more
quantitative variables from the same group of
subjects, & you are trying to determine if there is a
relationship (or covariation) between the 2 variables
(a similarity between them, not a difference between
their means).

http://www.capilanou.ca/psychology/student-resources/research-guidelines/Correlational-
Research-Guidelines/

Research Design
 Theoretically, any 2 quantitative variables can be
correlated (for example, midterm scores &
number of body piercings!) as long as you have
scores on these variables from the same
participants; however, it is probably a waste of
time to collect & analyze data when there is little
reason to think these two variables would be
related to each other.


When two things are correlated
 Positive correlation means that high scores on one are
associated with high scores on the other, and that low
scores on one are associated with low scores on the
other.
 Negative correlation, on the other hand, means that
high scores on the first thing are associated with low
scores on the second. Negative correlation also means
that low scores on the first are associated with high
scores on the second.

http://statisticalconcepts.blogspot.tw/2010/04/interpretation-of-correlation.html

Another Example of data
 An example is the correlation between body
weight and the time spent on a weight-loss
program. If the program is effective, the higher
the amount of time spent on the program, the
lower the body weight. Also, the lower the
amount of time spent on the program, the
higher the body weight.


 Try to have 30 or more participants; this is
important to increase the validity of the research.


 Your hypothesis might be that there is a positive
correlation (for example, the number of hours of study
& your midterm exam scores), or a negative correlation
(for example, your levels of stress & your exam scores).
 A perfect correlation would be an r = +1.0 & -1.0, while
no correlation would be r = 0.
 Perfect correlations would almost never occur; expect to
see correlations much less than + or - 1.0.
 Although correlation can't prove a causal relationship, it
can be used for prediction, to support a theory, to
measure test-retest reliability, etc.

Data Collection
 You may collect your data through testing (e.g.
scores on a knowledge test (an exam or math
test, etc.), or psychological tests, numerical
responses on surveys & questionnaires, etc.
Even archival data can be used (e.g.
Kindergarten grades) as long as it is in a
numerical form.


Data Analysis of Correlational
Research
 With the use of the Excel program, calculating correlations is
probably the easiest data to analyze. In Excel, set up three
columns: Subject #, Variable 1 (e.g. hours of study), & Variable 2
(e.g. exam scores).
 Then enter your data in these columns. Select a cell for the
correlation to appear in & label it. Click "fx" on the toolbar at the
top, then "statistical", then "Pearson".
 When asked, highlight in turn each of the two columns of data,
click "Finish", & your correlation will appear. Charts in any
statistics textbook can tell you if the correlation is significant,
considering the number of participants.
 You can also do graphs & scatter plots with Excel, if you would
like to depict your data that way (See Chart wizard).

Pearson r
 Pearson r is a statistic that is commonly used to
calculate bivariate correlations.
 For an Example Pearson r = -0.80, p < .01.
What does this mean?


Interpreting Correlation
 1.   The numerical value of the correlation
coefficient.
 2.   The sign of the correlation coefficient.
 3.   The statistical significance of the
correlation.
 4.   The effect size of the correlation.


 1. The numerical value of the correlation
coefficient.

 Correlation coefficients can vary numerically
between 0.0 and 1.0. The closer the correlation
is to 1.0, the stronger the relationship between
the two variables. A correlation of 0.0 indicates
the absence of a relationship. If the correlation
coefficient is –0.80, which indicates the
presence of a strong relationship.


 2. The sign of the correlation coefficient.

 A positive correlation coefficient means that as variable
1 increases, variable 2 increases, and conversely, as
variable 1 decreases, variable 2 decreases. In other
words, the variables move in the same direction when
there is a positive correlation.
 A negative correlation means that as variable 1
increases, variable 2 decreases and vice versa. In other
words, the variables move in opposite directions when
there is a negative correlation. The negative sign
indicates that as class size increases, mean reading
scores decrease.


 3. The statistical significance of the correlation.

 A statistically significant correlation is indicated by a
probability value of less than 0.05. This means that the
probability of obtaining such a correlation coefficient by
chance is less than five times out of 100, so the result
indicates the presence of a relationship.
 For -0.80 there is a statistically significant negative
relationship between class size and reading score (p < .
001), such that the probability of this correlation
occurring by chance is less than one time out of 1000.


 4. The effect size of the correlation.

 For correlations, the effect size is called the coefficient of
determination and is defined as r2. The coefficient of
determination can vary from 0 to 1.00 and indicates that
the proportion of variation in the scores can be predicted
from the relationship between the two variables. For r =
-0.80 the coefficient of determination is 0.65, which
means that 65% of the variation in mean reading scores
among the different classes can be predicted from the
relationship between class size and reading scores.
(Conversely, 35% of the variation in mean reading scores
cannot be explained.)

Presentation of Results
 In the Method section, present a general
description of the group of participants (their
number, mean age, gender, etc.) in
the Participants section, any materials you may
have used (e.g. tests, surveys, etc.) in
the Materials section, & in
the Procedure section, note that your general
research strategy was a correlational study, &
describe your methods of data collection (e.g.
survey, test, etc.).

 In the Results section of the report, present
your correlation statistic in both a table & in
words, & note whether or not it is significant. If
you have more than 2 variables to correlate,
present a correlational matrix, showing the
correlation between each of the variables.


 In the following example, 4 variables were
correlated in one study. The correlation between
Exam scores & hours of study, for example, is r
= +.67, p <.01. This indicates a significant
positive relationship between the number of
hours of study & subsequent exam scores.

 A correlation can only indicate the presence or
absence of a relationship, not the nature of the
relationship. Correlation is not
causation. There is always the possibility that a
third variable influenced the results. For
example, perhaps the students in the small
classes were higher in verbal ability than the
students in the large classes or were from higher
income families or had higher quality teachers.

 In the Discussion section, relate your results to
past or current research & theory you had cited
& described in the Introduction. Do note the
statistical significance of your findings, & limits
to their generalizability. Remember that even if
you did not obtain the significant differences
you had hoped to, your results are still
interesting, & must be explained, with reference
to other research & theory.

http://www.surveysystem.com/correlation.htm

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