Research Methodology: CORRELATIONAL RESEARCH

WHAT IS CORRELATIONAL RESEARCH, WHEN Do

YOU USE IT, AND HOW DID IT DEVELOP?

Correlational designs provide an opportunity for you to predict scores and explain the

relationship among variables. 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 sets of scores. In this design, the researchers do not

attempt to control or manipulate the variables as in an experiment; instead, they relate,

using the correlation statistic, two or more scores for each person (e.g., a stunt motivation and a student achievement score for each individual).

A correlation is a statistical test to determine the tendency or pattern for two (or more)

variables or two sets of data to vary consistently. In the case of only two variables, this

means that two variables share common variance, or they co-vary together. To say that

two variables co-vary has a somewhat complicated mathematical basis. Co-vary means

that we can predict a score on one variable with knowledge about the individual’s score

on another variable. A simple example might illustrate this point. Assume that scores on

a math quiz for fourth-grade students range from 30 to 90. We are interested in whether

scores on an in-class exercise in math (one variable) can predict the student’s math quiz

scores (another variable). If the scores on the exercise do not explain the scores on the

ath quiz, then we cannot predict anyone’s score except to say that it might range from

30 to 90. If the exercise could explain the variance in all of the math quiz scores, then

we could predict the math scores perfectly. This situation is seldom achieved; instead,

we might fi nd that 40% of the variance in math quiz scores is explained by scores on the

exercise. This narrows our prediction on math quiz scores from 30 to 90 to something

less, such as 40 to 60. The idea is that as variance increases, we are better able to predict

scores from the independent to the dependent variable (Gall, Borg, & Gall, 1996).

The statistic that expresses a correlation statistic as a linear relationship is the product–moment correlation coefficient.

is also called the bivariate correlation, zero-order

corre lation, or simply r, and it is indicated by an “r” for its notation. The statistic is calculated for two variables ( r

xy ) by multiplying the z scores on X and Y for each case and then dividing by the number of case minus one (e.g., see the detailed steps in Vockell & Ashner, o

as the prediction that ability, quality of schooling, student motivation, and academic

coursework infl uence student achievement (Anderson & Keith, 1997). You also use this

design when you know and can apply statistical knowledge based on calculating the correlation statistical test.

How Did Correlational Research Develop?

The history of correlational research draws on the themes of the origin and development

of the correlation statistical test and the procedures for using and interpreting the test. Statisticians fi rst developed the procedures for calculating the correlation statistics in the late

19th century (Cowles, 1989). Although British biometricians articulated the basic ideas ofWHAT ARE THE KEY CHARACTERISTICS OF CORRELATIONAL DESIGNS?

As suggested by the explanatory and prediction designs, correlation research includes

specifi c characteristics:

◆ Displays of scores (scatterplots and matrices)

◆ Associations between scores (direction, form, and strength)

◆ Multiple variable analysis (partial correlations and multiple regression)

Displays of Scores

If you have two scores, in correlation research you can plot these scores on a graph (or

scatterplot) or present them in a table (or correlation matrix).

Scatterplots

Researchers plot scores for two variables on a graph to provide a visual picture of the

form of the scores. This allows researchers to identify the type of association among variables and locate extreme scores. Most importantly, this plot can provide useful information about the form of the association—whether the scores are linear (follow a straightline) or curvilinear (follow a U-shaped form). It also indicates the direction of the association (e.g., one score goes up and the other goes up as well) and the degree of the association (whether the relationship is perfect, with a correlation of 1.0, or less than perfect).

A plot helps to assess this association between two scores for participants. A scatterplot (or scatter diagram) is a pictorial image displayed on a graph of two sets of

scores for participants. These scores are typically identifi ed as X and Y, with X values

represented on the horizontal axis, and Y values represented on the vertical axis. A single

point indicates where the X and Y scores intersect for one individual.

Using scales on the horizontal (abscissa) axis and on the vertical (ordinate) axis,

the investigator plots points on a graph for each participant. Examine the scatterplot of

scores in Figure 11.1, which shows both a small data set for 10 students and a visual plot

of their scores. Assume that the correlation researcher seeks to study whether the use of

the Internet by high school students relates to their level of depression. (We can assume

that students who use the Internet excessively are also depressed individuals because

they are trying to escape and not cope with present situations.) From past research, we

would predict this situation to be the case. We measure scores on the use of the Internet

by asking the students how many hours per week they spend searching the Internet. We

measure individual depression scores on an instrument with proven valid and reliable

scores. Assume that there are 15 questions about depression on the instrument with a

rating scale from 1 ( strongly disagree) to 5 ( strongly agree). This means that the summed

scores will range from 15 to 45.

As shown in Figure 11.1, hypothetical scores for 10 students are collected and plotted on the graph. Several aspects about this graph will help you understand it:

◆ The “hours of Internet use” variable is plotted on the X axis, the horizontal axis.

◆ The “depression” variable is plotted on the Y axis, the vertical axis.

FIGURE 11.1

Example of a Scatterplot

Depression Scores

Y = D.V.

Hours of

Internet

Use per

Week

Depression

(Scores from

15 to 45)

Laura

Chad

Patricia

Bill

Rosa

Todd

Angela

Jose

Maxine

Jamal

Mean Score

45 Hours of Internet Use Per Week

X = I.V.

+ –

–

10 15 20Each student in the study has two scores: one for hours per week of Internet use

and one for depression.

◆ A mark (or point) on the graph indicates the score for each individual on depression and hours of Internet use each week. There are 10 scores (points) on the

graph, one for each participant in the study.

The mean scores ( M) on each variable are also plotted on the graph. The students

used the Internet for an average of 9.7 hours per week, and their average depression

score was 29.3. Drawing vertical and horizontal lines on the graph that relate to the

mean scores ( M), we can divide the plot into four quadrants and assign a minus (–) to

quadrants where scores are “negative” and a plus (+) to quadrants where the scores are

“positive.” In our example, to have a depression score below 29.3 ( M) is positive because

that suggests that the students with such a score have less depression. To score above

29.3 ( M) indicates more severe depression, and this is “negative.” Alternatively, to use the

Internet less than 9.7 ( M) hours per week is “positive” (i.e., because students can then

spend more time on homework), whereas to spend more time than 9.7 hours is “negative” (i.e., overuse of Internet searching is at the expense of something else). To be both

highly depressed (above 29.3 on depression) and to use the Internet frequently (above

9.7 on Internet use) is what we might have predicted based on past literature.

Note three important aspects about the scores on this plot. First, the direction of

scores shows that when X increases, Y increases as well, indicating a positive association.

Second, the points on the scatterplot tend to form a straight line. Third, the points would

be reasonably close to a straight line if we were to draw a line through all of them. These

three ideas relate to direction, form of the association, and the degree of relationship that

we can learn from studying this scatterplot. We will use this information later when we

discuss the association between scores in correlation research.

A Correlation Matrix

Correlation researchers typically display correlation coeffi cients in a matrix. A correlation

matrix presents a visual display of the correlation coeffi cients for all variables in a study.

In this display, we list all variables on both a horizontal row and a vertical column in the

table. Correlational researchers present correlation coeffi cients in a matrix in publishedWHAT ARE THE STEPS IN CONDUCTING

A CORRELATIONAL STUDY?

From our discussion about the key characteristics of correlational research, we can begin

to see steps emerge that you might use when planning or conducting a study. The following steps illustrate the process of conducting correlational research.

Step 1. Determine If a Correlational Study Best Addresses

the Research Problem

A correlational study is used when a need exists to study a problem requiring the identi-

fi cation of the direction and degree of association between two sets of scores. It is useful

for identifying the type of association, explaining complex relationships of multiple factors that explain an outcome, and predicting an outcome from one or more predictors.

Correlational research does not “prove” a relationship; rather, it indicates an association

between two or more variables.

Because you are not comparing groups in a correlational study, you use research

questions rather than hypotheses. Sample questions in a correlational study might be:

◆ 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)

◆Step 2. Identify Individuals to Study

Ideally, you should randomly select the individuals to generalize results to the population, and seek permissions to collect the data from responsible authorities and from

the institutional review board. The group needs to be of adequate size for use of the

correlational statistic, such as N = 30; larger sizes contribute to less error variance and better claims of representativeness. For instance, a researcher might study 100 high school

athletes to correlate the extent of their participation in different sports and their use of

tobacco. A narrow range of scores from a population may infl uence the strength of the

correlation relationships. For example, if you look at the relationship between height of

basketball players and number of baskets in a game, you might fi nd a strong relationship

among K–12th graders. But if you are selecting NBA players, this relationship may be

signifi cantly weaker.

Step 3. Identify Two or More Measures for

Each Individual in the Study

Because the basic idea of correlational research is to compare participants in this single

group on two or more characteristics, measures of variables in the research question

need to be identifi ed (e.g., literature search of past studies), and instruments that measure the variables need to be obtained. Ideally, these instruments should have proven

validity and reliability. You can obtain permissions from publishers or authors to use the

instruments. Typically one variable is measured on each instrument, but a single instrument might contain both variables being correlated in the study.

Step 4. Collect Data and Monitor Potential Threats

The next step is to administer the instruments and collect at least two sets of data from

each individual. The actual research design is quite simple as a visual presentation. Two

data scores are collected for each individual until you obtain scores from each person in

the study. This is illustrated with three individuals as follows:

Participants: Measures or Observations:

Individual 1 01 02

Individual 2 01 02

Individual 3 01 02

This situation holds for describing the association between two variables or for predicting

a single outcome from a single predictor variable. You collect multiple independent variables to understand complex relationships.

A small sample database for 10 college students is shown in Table 11.3. The investigator seeks to explain the variability in fi rst-year grade point averages (GPAs) for these

10 graduate students in education. Assume that our investigator has identifi ed these four

predictors in a review of the literature. In past studies, these predictors have positively

correlated with achievement in college. The researcher can obtain information for the

predictor variables from the college admissions offi ce. The criterion, GPA during the

fi rst year, is available from the registrar’s offi ce. In this regression study, the researcher

seeks to identify which one factor or combination of factors best explains the variance

in fi rst-year graduate-student GPAs. A review of this data shows that the scores varied on

each variable, with more variation among GRE scores than among recommendation andfi t-to-program scores. Also, it appears that higher college GPA and GRE scores are positively related to higher fi rst-semester GPAs.

In this example, because the data were available from admissions offices, the

researcher need not be overly concerned about procedures that threaten the validity of

the scores. However, a potential for restricted range of scores—little variation in scores—

certainly exists. Other factors that might affect the researcher’s ability to draw valid inferences from the results are the lack of standard administration procedures, the conditions

of the testing situation, and the expectations of participants.

Step 5. Analyze the Data and Represent the Results

The objective in correlational research is to describe the degree of association between

two or more variables. The investigator looks for a pattern of responses and uses statistical procedures to determine the strength of the relationship as well as its direction. A statistically signifi cant relationship, if found, does not imply causation (cause and effect) but

merely an association between the variables. More rigorous procedures, such as those

used in experiments, can provide better control than those used in a correlational study.

The analysis begins with coding the data and transferring it from the instruments into

a computer fi le. Then the researcher needs to determine the appropriate statistic to use.

An initial question is whether the data are linearly or curvilinearly related. A scatterplot of

the scores (if a bivariate study) can help determine this question. Also, consider whether:

◆ Only one independent variable is being studied (Pearson’s correlation coeffi cient)

◆ A mediating variable explains both the independent and dependent variables and

needs to be controlled (partial correlation coeffi cient)◆ More than one independent variable needs to be studied to explain the variability

in a dependent variable (multiple regression coeffi cient)

Based on the most appropriate statistical test, the researcher next calculates whether

the statistic is signifi cant based on the scores. For example, a p value is obtained in a

bivariate study by:

◆ Setting the alpha level

◆ Using the critical values of an r table, available in many statistics books

◆ Using degrees of freedom of N = 2 with this table

◆ Calculating the observed r coeffi cient and comparing it with the r-critical value

◆ Rejecting or failing to reject the null hypothesis at a specifi c signifi cance level, such

as p 6 0.05

In addition, it is useful to also report effect size ( r 2). In correlational analysis, the

effect size is the Pearson’s correlation coeffi cient squared. In representing the results, the

correlational researcher will present a correlation matrix of all variables as well as a statistical table (for a regression study) reporting the R and R 2

values and the beta weights

for each variable.

Step 6. Interpret the Results

The fi nal step in conducting a correlational study is interpreting the meaning of the

results. This requires discussing the magnitude and the direction of the results in a correlational study, considering the impact of intervening variables in a partial correlation

study, interpreting the regression weights of variables in a regression analysis, and developing a predictive equation for use in a prediction study.

In all of these steps, an overall concern is whether your data support the theory, the

hypotheses, or questions. Further, the researcher considers whether the results confi rm

or disconfi rm fi ndings from other studies. Also, a refl ection is made about whether some

of the threats discussed above may have contributed to erroneous coeffi cients and the

steps that might be taken by future researchers to address these concern◆ More than one independent variable needs to be studied to explain the variability

in a dependent variable (multiple regression coeffi cient)

Based on the most appropriate statistical test, the researcher next calculates whether

the statistic is signifi cant based on the scores. For example, a p value is obtained in a

bivariate study by:

◆ Setting the alpha level

◆ Using the critical values of an r table, available in many statistics books

◆ Using degrees of freedom of N = 2 with this table

◆ Calculating the observed r coeffi cient and comparing it with the r-critical value

◆ Rejecting or failing to reject the null hypothesis at a specifi c signifi cance level, such

as p 6 0.05

In addition, it is useful to also report effect size ( r 2). In correlational analysis, the

effect size is the Pearson’s correlation coeffi cient squared. In representing the results, the

correlational researcher will present a correlation matrix of all variables as well as a statistical table (for a regression study) reporting the R and R 2

values and the beta weights

for each variable.

Step 6. Interpret the Results

The fi nal step in conducting a correlational study is interpreting the meaning of the

results. This requires discussing the magnitude and the direction of the results in a correlational study, considering the impact of intervening variables in a partial correlation

study, interpreting the regression weights of variables in a regression analysis, and developing a predictive equation for use in a prediction study.

In all of these steps, an overall concern is whether your data support the theory, the

hypotheses, or questions. Further, the researcher considers whether the results confi rm

or disconfi rm fi ndings from other studies. Also, a refl ection is made about whether some

of the threats discussed above may have contributed to erroneous coeffi cients and the

steps that might be taken by future researchers to address these concerns.s.HOW DO YOU EVALUATE A CORRELATIONAL STUDY?

To evaluate and assess the quality of a good correlational study, authors consider:

◆ An adequate sample size for hypothesis testing.

◆ The display of correlational results in a matrix or graph.

◆ An interpretation about the direction and magnitude of the association between

two (or more) variables.

◆ An assessment of the magnitude of the relationship based on the coeffi cient of

determination, p values, effect size, or the size of the coeffi cient.

◆ The choice of an appropriate statistic for analysis.

◆ The identifi cation of predictor and the criterion variables.

◆ If a visual model of the relationships is advanced, the researcher indicates the

expected direction of the relationships among variables, or the predicted direction

based on observed data.

◆ The clear identifi cation of the statistical procedures.The Defi nition, Use, and Development of Correlational Research

In some educational situations, neither the treatment nor the ability to manipulate the

conditions are conducive to an experiment. In this case, educators turn to a correlational design. In correlational research, investigators use a correlation statistical technique

to describe and measure the degree of association (or relationship) between two or

more variables or sets of scores. You use a correlational design to study the relationship

between two or more variables or to predict an outcome.

The history of correlational research draws on the themes of the origin and development of the correlation statistical test and the procedures for using and interpreting the

statistical test. Statisticians fi rst identifi ed the procedures for calculating the correlation

statistics in the late 19th century. In the late 1800s, Karl Pearson developed the familiar

correlation formula we use today. With the use of multiple statistical procedures such as

factor analysis, reliability estimates, and regression, researchers can test elaborate models

of variables using correlational statistical procedures.

Types of Correlational Designs

Although a correlation is a statistic, its use in research has contributed to a specifi c

research design called correlational research. This research has taken two primary forms

of research design: explanation and prediction. An explanatory correlational design

explains or clarifi es the degree of association among two or more variables at one point

in time. Researchers are interested in whether two variables co-vary, in which a change

in one variable is refl ected in changes in the other. An example is whether motivation

is associated with academic performance. In the second form of design, a prediction

design, the investigator identifi es variables that will positively predict an outcome or criterion. In this form of research, the researcher uses one or more predictor variables and

a criterion (or outcome) variable. A prediction permits us to forecast future performance,

such as whether a student’s GPA in college can be predicted from his or her high school

performance.

Key Characteristics of Correlational Designs

Underlying both of these designs are key characteristics of correlational research.

Researchers create displays of scores correlated for participants. These displays are scatterplots, a graphic representation of the data, and correlation matrices, a table that shows

the correlation among all the variables. To interpret correlations, researchers examine

the positive or negative direction of the correlation of scores, a plot of the distribution of

scores to see if they are normally or nonnormally distributed, the degree of association

between scores, and the strength of the association of the scores. When more than two

variables are correlated, the researcher is interested in controlling for the effects of the

third variable, and in examining a prediction equation of multiple variables that explains

the outcome.

Ethical Issues in Conducting Correlational Research

Ethical issues arise in many phases of the correlational research process. In data collection, ethics relate to adequate sample size, lack of control, and the inclusion of as many

predictors as possible. In data analysis, researchers need a comjto include effect size and the use of appropriate statistics. Analysis cannot include making up data. In recording and presenting studies, the write-up should include statements

about relationships rather than causation, a willingness to share data, and publishing in

scholarly outlets.

Steps in Conducting a Correlational Study

Steps in conducting a correlational study are to use the design for associating variables or

making predictions, to identify individuals to study, to specify two or more measures for

each individual, to collect data and monitor potential threats to the validity of the scores,

to analyze the data using the correlation statistic for either continuous or categorical data,

and to interpret the strength and the direction of the results.

Criteria for Evaluating a Correlational Study

Evaluate a correlational study in terms of the strength of its data collection, analysis, and

interpretations. These factors include adequate sample size, good presentations in graphs

and matrices, clear procedures, and an interpretation about the relationship among variables.

USEFUL INFORMATION FOR PRODUCERS OF RESEARCH

◆ Identify whether you plan to examine the association between or among variables

or use correlational research to make predictions about an outcome.

◆ Plot on a graph the association between your variables so that you can determine

the direction, form, and strength of the association.

◆ Use appropriate correlational statistics in your design based on whether the

data are continuous or categorical and whether the form of the data is linear or

nonlinear.

◆ Present a correlation matrix of the Pearson coeffi cients in your study.

USEFUL INFORMATION FOR CONSUMERS OF RESEARCH

◆ Recognize that a correlation study is not as rigorous as an experiment because

the researcher can only control statistically for variables rather than physically

manipulate variables. Correlational studies do not “prove” relationships; rather,

they indicate an association between or among variables or sets of scores.

◆ Correlational studies are research in which the investigator seeks to explain the

association or relationship among variables or to predict outcomes.

◆ Realize that all correlational studies, no matter how advanced the statistics, use a

correlation coeffi cient as their base for analysis. Understanding the intent of this

coeffi cient helps you determine the results in a correlational study.to include effect size and the use of appropriate statistics. Analysis cannot include making up data. In recording and presenting studies, the write-up should include statements