CORRELATIONAL DESIGNS
Based on Creswell's book (2012)
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 math 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.
When Use Correlational Research
You use this design when you seek to relate two or more variables to see if they influence each other, such as the relationship between teachers who endorse developmentally appropriate practices and their use of the whole-language approach to reading instruction (Ketner, Smith, & Parnell, 1997). This design allows you to predict an outcome, such 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.
TYPES OF CORRELATIONAL DESIGNS
1. The 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), or “explanatory” research (Fraenkel & Wallen, 2000, p. 360). Because one basic objective of this form of correlational research is to explain the association between or among variables, we will use the term explanatory research in this discussion. An explanatory research design is a correlational design in which the researcher is interested in the extent to which two variables (or more) co-vary, that is, where changes in one variable are refl ected in changes in the other. Explanatory designs consist of a simple association between two variables (e.g., sense of humor and performance in drama) or more than two (e.g., pressure from friends or feelings of isolation that contribute to binge drinking).
The Characteristics of Explanatory Design:
The investigators correlate two or more variables. They report the correlation statistical test and mention the use of multiple variables. Readers fi nd these variables specifi cally mentioned in the purpose statement, the research questions, or the tables reporting the statistical procedures.
The researchers collect data at one point in time. Evidence for this procedure will be found in the administration of instruments “in one sitting” to students. In explanatory correlational research, the investigators are not interested in either past or future performance of participants.
The investigator analyzes all participants as a single group. Compared to an experiment that involves multiple groups or treatment conditions, the researcher collects scores from only one group and does not divide the group into categories (or factors). Unlike experimental research, all levels of information from the group are used. Rather than divide scores on self-esteem into “high” and “low” categories of scores, as would be done in experimental research, a correlational researcher uses all scores on a continuum, such as from 10 to 90.
The researcher obtains at least two scores for each individual in the group—one for each variable. In the method discussion, the correlational investigator will mention how many scores were collected from each participant. For example, for each individual in a study of optimism and appropriate health behaviors, the researcher would collect two scores: an optimism score and a health behavior score.
The researcher reports the use of the correlation statistical test (or an extension of it) in the data analysis. This is the basic feature of this type of research. In addition, the researcher includes reports about the strength and the direction of the correlational test to provide additional information.
Finally, the researcher makes interpretations or draws conclusions from the statistical test results. It is important to note that the conclusions do not establish a probable cause-and-effect (or causal inference) relationship because the researcher can use only statistical control (e.g., control over variables using statistical procedures) rather than the more rigorous control of physically altering the conditions (i.e., such as in experiments
2. The Prediction Design
Instead of simply relating variables—two variables at a time or a complex set such as in our last example—in a prediction design, researchers seek to anticipate outcomes by using certain variables as predictors. For example, superintendents and principals need to identify teachers who will be successful in their schools. To select teachers who have a good chance of success, the administrators can identify predictors of success using correlational research.
The purpose of a prediction research design is to identify variables that will predict an outcome or criterion. In this form of research, the investigator identifi es one or more predictor variable and a criterion (or outcome) variable.
The following characteristics of Prediction design:
The authors typically include the word prediction in the title. It might also be in the purpose statement or research questions.
The researchers typically measure the predictor variable(s) at one point in time and the criterion variable at a later point in time. a study to determine if the researchers build a “time” dimension into the design.
The authors forecast future performance. They usually state this intent in the purpose statement or in the research questions. In the justifi cation of the research problem, writers also mention their intent to “predict” some outcome.
THE KEY CHARACTERISTICS OF CORRELATIONAL DESIGNS
There are three keys characteristics, they are:
1. Displays of Scores
2. Associations between Scores
3. Multiple Variable Analysis
1. 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).
There are 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.
• 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.
2. Associations between Scores
After correlation researchers graph scores and produce a correlation matrix, they can then interpret the meaning of the association between scores. This calls for understanding the direction of the association, the form of the distribution, the degree of association, and its strength.
• Direction
a) A positive correlation (the points move in the same direction)
when X increases, so does Y or, alternatively, if X decreases, so does Y.
b) A negative correlation (the points move in the opposite direction)
when X increases, Y decreases, and when X decreases, Y increases
• Form
a) A positive linear relationship
b) A negative linear relationship
c) Uncorrelated and Nonlinear Relationships
d) A curvilinear distribution
• Degree and Strength of Association
With numbers indicating strength and valence signs indicating direction (+1.00 to –1.00) the statistic provides a measure of the magnitude of the relationship between two variables.
3. Multiple Variable Analysis
In many correlation studies, researchers predict outcomes based on more than one predictor variable. Thus, they need to account for the impact of each variable. Two multiple variable analysis approaches are partial correlations and multiple regression.
• Partial Correlations
In many research situations, we study three, four, or fi ve variables as predictors of outcomes. The type of variable called a mediating or intervening variable “stands between” the independent and dependent variables and infl uences both of them. This variable is different from a control variable that infl uences the outcome in an experiment. We use partial correlations to determine the amount of variance that an intervening variable explains in both the independent and dependent variables.
• Multiple Regression
Correlation researchers use the correlation statistic to predict future scores. To see what impact multiple variables have on an outcome, researchers use regression analysis. We will start with understanding a regression line and then move on to analysis using regression. A regression line is a line of “best fit” for all of the points of scores on the graph. This line comes the closest to all of the points on the plot and it is calculated by drawing a line that minimizes the squared distance of the points from the line.
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 complete statement of fi ndings 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 about relationships rather than causation, a willingness to share data, and publishing in scholarly outlets.
THE STEPS IN CONDUCTING A CORRELATIONAL STUDY
1. Determine If a Correlational Study Best Addresses the Research Problem
2. Identify Individuals to Study
3. Identify Two or More Measures for Each Individual in the Study
4. Collect Data and Monitor Potential Threats
5. Analyze the Data and Represent the Results
6. Interpret 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.
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 coefficient of determination,
p values, effect size, or the size of the coefficient.
• The choice of an appropriate statistic for analysis.
• The identification 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 identification of the statistical procedures.
Taken from:
Creswell, John W. 2012. Educational Research Planning, Conducting, and Evaluating Quantitative and Qualitative Research fourth edition. Boston: Pearson Education, Inc.
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