Correlational Designs
A correlational research design is a specific type of non-experimental design used to describe the relationship between or among variables. It provides empirical evidence suggesting two or more variables are – or are not – related. While this evidence does not establish causal relationships, it does contribute to a deeper understanding of the variables being studied and their relationship.
Without such knowledge, there is little sense in studying the relationship in an experimental design context. For example, if high levels of student engagement have been shown to statistically relate to high levels of achievement, further research would logically pursue questions related to the causal nature of this relationship as well as ways to influence higher levels of engagement.
Types of Correlational Designs
The design has two forms. The first is called a relational design because the basic intent is to explain the relationship – or association – between two or more variables. An examination of the relationship between students’ attitudes toward math and their math achievement is an example of a relational design. In fact, this is a specific design known as a simple bivariate correlational design. This design can be extended to include more variables to more precisely describe the relationships among variables. Suppose, for example, a researcher obtained students’ prior math achievement scores and wondered if they – in conjunction with math attitudes – would result in a higher correlation. This application is called multiple regression, and it provides much more insight into the relationship between and among the variables being studied..
There are five general characteristics associated with relational designs. These are as follows.
1.
2.
3.
4.
Two or more variables are collected from each individual in the sample.
Data is collected at a single point in time.
The data is analyzed as a single group.
A correlational coefficient (e.g., Pearson Product Moment, multiple R) is reported and
5. discussed in terms of strength, direction, and statistical significance.
Interpretations from the statistical results are drawn about the relationship.
A second type of correlational design is called a prediction design. The purpose of this design is to identify variables that can effectively predict some outcome or criterion. The variable being predicted is called the criterion variable, and the variable or variables being used to predict the criterion are called predictors. When a study involves only two variables, the predictive relationship is estimated with a statistical procedure called simple linear regression. When more than one predictor variable is used to predict a criterion, the analysis is called multiple regression.
This is an extremely powerful statistical procedure that can estimate the collective as well as the individual contributions of all predictor variables. This analysis makes it is possible to develop not only an effective prediction, but also an efficient one.
While the general characteristics of prediction designs are similar to those for relational designs, they differ several important ways. These are as follows.
1.
2.
Two or more variables are collected from each individual in the sample.
Data for the predictor variables is typically collected prior to that of the criterion variable.
3. The data is analyzed as a single group.
4.1. A correlation coefficient – typically a multiple R – is reported and discussed in terms of its
4.2 strength, direction, and statistical significance.
The contribution of each predictor variable is examined in terms of its unique contribution to the prediction of the criterion variable. A regression coefficient – b i
– is reported for each predictor variable and is discussed in terms of its significance to the prediction of the criterion variable. In some cases, a specific analysis is used to evaluate the efficiency and effectiveness of the predictor variables. This is called stepwise regression and
- 1 -

5. results in the prediction of the criterion variable in which the effectiveness of each predictor variable is examined for redundancy with other predictors. Those predictors that do not uniquely contribute to the prediction are eliminated.
A regression equation is produced which can be used to predict the criterion variable from data collected only on the predictor variables.
Interpretations from the statistical results are drawn about the predictive process. 6.
Issues for Correlational Designs
1. One of the most important issues surrounding any correlational design is the lack of
2. manipulation of an independent variable that does NOT allow the researcher to conclude causality. Without such manipulation, the only justifiable conclusions are about relationships between or among variables. In a correlational design, attitudes might be found to be related to achievement. Based on the design a researcher would be incorrect in concluding attitudes cause achievement. This is one reason why many researchers conducting correlational research use the terminology of predictor and criterion variables rather than independent and dependent variables.
Most of the correlation coefficients discussed in introductory statistics classes approach the data assuming it is linear in nature. That is, there is a consistent relationship between variables that holds across all values of the variables. This relationship can be graphed as a straight line, hence the term “linear.” Many of the statistical procedures focus on issues related to the variation of data points from the prediction line.
3.
4.
However, some data can be better described by curvilinear relationships. For example, researchers often talk about how the learning curve increases exponentially once students get to a certain point. A graph of this relationship would look more like curve in which the prediction line begins close to horizontal and at some point moves to vertical.
The actual depictions of these curves are called functions.
The typical concern when one uses a correlational design comes when the data collected is curvilinear, yet it is assumed to be linear. Before assuming a problem exists, an examination of a scatterplot of the data is in order. If a curvilinear relationship does exist, alternative analyses can be used to understand the nature of the relationships.
A correlation coefficient has two characteristics: strength and direction. The former is the focus of statistical analysis. The latter simply indicates whether the variables move in the same or opposite directions. A positive correlation indicates variables move in consistent manners. A good example is the relationship between levels of engagement and achievement. As levels of engagement increase, so does achievement. A negative relationship indicates variables move in opposite directions. For example, as levels of engagement increase, levels of inappropriate behavior decrease. Please note that the terms “positive” or “negative” do not indicate the value or worth of the relationship. That is, a high positive correlation is not better than a high negative correlation.
There are no set rules for interpreting correlation coefficients. The most common way to do so is to discuss them in terms of statistical significance. That is, does a particular correlation differ significantly from 0.00 (i.e., Is it different from no correlation). A problem with this relates to the sensitivity of the inferential tests to sample size. Large sample sizes can identify very small correlations as statistically significant while there is little if any practical significance. A way to deal with this matter is quite simple. If one squares a correlation coefficient (e.g., r 2 or R 2 ) the result is interpreted as the proportion of the criterion variable that can be explained – or predicted – from the knowledge of the predictor variable or variables. For example, while a correlation of .40 is often interpreted as moderate, only 16% of the variation in the criterion variable that can be accounted for by the predictor. Depending on the context in which a study is being conducted, this might be interpreted as meaningful or not.
- 2 -