Chapter 7 Summary

Chapter 7 Summary
Correlational and Differential
Methods of Research

In correlational and differential research, the focus is on the measurement of relationships between variables (correlational) and differences between groups defined by preexisting variables (differential).

Correlational Research Methods

In correlational research, the strength of the relationship between two or more variables is quantified. In many ways, correlational research is an extension of naturalistic research in that variables are not manipulated in correlational research and there is usually a single group of participants that is a sample of a larger population.

A correlation does not imply causality, but the observed correlation between variables serves two useful functions in science. The first is that any consistent relationship can be used to predict future events. The second is to provide data that are either consistent or inconsistent with some currently held theory. Like naturalistic research, a correlation cannot prove a theory, but it can negate a theory.

Differential Research Methods

In differential research, we observe two or more groups that have been differentiated on the basis of some preexisting variable, such as gender, religious affiliation, age of participant, and so on. The independent variable in differential research is a nonmanipulated independent variable. Since differential research involves only measuring variables and not manipulating them, we are actually studying relationships among variables; thus, differential research is conceptually similar to correlational research. This similarity means that the same general principles are used in interpreting results from each of these research methods; we must be cautious in drawing causal inferences from each.

Cross-Sectional vs. Longitudinal Research

A special case of differential design is cross-sectional research, which is often used in studying child development. Interpreting differences between groups in differential designs can be difficult because of cohort effects. Cross-sectional designs are contrasted with longitudinal and time-series designs.

Artifacts and Confounding Variables

In differential research, we compare observations of one group of participants with observations of another group. In order to compare the two groups, the observations must be made the same way in each. If they are not, then we would not know if any differences detected are due to real differences between the groups or to the differences in the observational methods--that is, the two variables would be confounded. An artifact is any apparent effect of major conceptual variables that is actually the result of confounding.

Understanding Correlational and Differential Methods

To understand correlational and differential research methods, it is necessary to understand how they are conceptually similar, what makes one higher constraint than the other, and when to use each.

Comparing these Methods

In both correlational and differential research, relationships between variables are measured. However, researchers conducting differential research are often interested in causal questions. Without control over confounding, drawing a causal inference is impossible.

In differential research, the researcher tries to maximize the control over confounding variables by carefully selecting appropriate controls. Although not as effective as random assignment of participants to groups in controlling extraneous variance, this manipulation does provide more control than is found in a typical correlational study.

When to Use These Methods

Correlational and differential research is used most often in situations in which the manipulation of an independent variable is impractical, impossible, or inappropriate.

Conducting Correlational Research

Correlational research seeks to quantify the direction and strength of the relationship between two or more variables. Correlational designs with more than two variables are multivariate designs.

Problem Statements

Problem statements for correlational research typically involve two statements of interest to the researcher: "What is the strength and direction of the relationship between variable X and variable Y?" and "How well can variable Y be predicted from variable X?" (i.e., what is the best equation for predicting Y from X?). The latter is called the regression equation.

Secondary Analyses

A common use of correlational methods is to carry out secondary analyses in order to determine the relationship of dependent variables to demographic, gender, or cultural factors. Such relationships can help to explain the results of a study.

Measuring the Variables

Measurement, the assignment of numbers to variables, depends on the adequacy of operational definitions. In making observations, experimenter expectancy and experimenter reactivity must be avoided.

Using objective measures helps reduce the effect of experimenter expectancy. One way to avoid experimenter reactivity is to use two independent observers, with each observer responsible for measuring only one of the variables. Measurement reactivity (the participant's own influences on their responses) is another problem in correlational research. The use of filler items and unobtrusive observations can reduce that problem.

Sampling

Obtaining a representative sample is critical. Another sampling issue in correlational research is whether the relationship between the variables is the same in all segments of the population under study. Moderator variables are variables that modify the relationship among other variables.

Analyzing the Data

In correlational research, data analysis involves computing an index of the degree of relationship between variables under study. The type of correlation coefficient computed depends on the level of measurement used for both of the variables. Other correlational procedures include multiple correlation (one variable is correlated with an entire set of variables), canonical correlation (sets of variables are correlated), and partial correlation (one variable is correlated with another after statistically removing the effects of a third variable). Path analysis is another recent correlational procedure.

Interpreting the Correlation

In interpreting a correlation, the size and direction of the correlation should first be noted. Next, statistical significance tests are carried out to see if the observed correlation is large enough for us to believe that there is a nonzero correlation between variables in the population from which the sample was drawn. It is also useful to calculate the coefficient of determination by squaring the obtained correlation. This indicates the proportion of variance in one variable that can be accounted for or predicted by knowing the scores on the other variable.

Conducting Differential Research

Differential research is used to compare existing groups when experimental techniques are impossible or unethical.

Problem Statements

In differential research, the typical problem statement is straightforward. "Does Group A differ from Group B on the dependent measures?" The complications in differential research are not in testing for differences between groups, but in interpreting differences that are found. Remember, there is no active manipulation of the independent variables in differential research; therefore, the groups used in differential research must be different on only one dimension to avoid confounding.

Measuring the Variables

In differential research, the dependent variable is usually a continuous variable, although it can be a discrete (categorical) measure. The nonmanipulated independent variable is usually a discrete or categorical variable.

Selecting Appropriate Control Groups

A control group is any group selected as a basis for comparison with the experimental group. (Note that the usage of the term "experimental group" is traditional with differential studies, even though this is not experimental research.) The ideal control group is identical to the experimental group on all variables except the independent variable that defines the groups.

We must be alert to confounding variables. To reduce the threat of confounding variables in differential research, a control group is selected that is as similar as possible to the experimental group. It is rare to find an ideal control group. Instead, researchers try to obtain a control group that controls some of the most important potential confounding variables. An alternative is to select multiple control groups, with each control group controlling for one important confounding variable.

Sampling

Obtaining a representative sample in order to generalize research results is as important in differential research as it is at other levels of research. Using nonrepresentative samples can threaten the generalizability of the study. In differential research, another serious threat to generalizability is the number of participants who drop out of the study or who cannot be used in the study. This could restrict the sample to participants with only certain characteristics, making generalization difficult.

Analyzing the data

The type of statistical analysis will depend on the number of groups and the scale of measurement of the dependent variable. We have included a flowchart system on this website to help students to select an appropriate statistical procedure.

Interpreting the Data

Regardless of what statistical test may be used, the meaning of the results are interpreted in the same way. The probability value obtained by the statistic is compared to the alpha level selected to determine whether the null hypothesis should be rejected. In addition to testing the null hypothesis, we must take into account all of the possible confounding variables in order to interpret the data properly.

Limitations of Correlational and Differential Research

As useful as they are, correlational and differential procedures have serious limitations, two of which are (1) problems in determining causation and (2) problems with confounding variables.

Problems in Determining Causation

The major limitation in the use of these methods is the kind of conclusions we can draw from the results. A correlation does not imply causality.

Confounding Variables

A second limitation in correlational and differential research is that it is difficult to avoid confounding variables. In differential research in particular, confounding is more the rule than the exception. Some potential confounding variables may be controlled with a carefully selected control group, but rarely will we be able to eliminate confounding. Such problems will always make interpretation difficult, although some researchers choose to think of this as making the task more challenging.

Ethical Principles

If one has a choice between experimental research and correlational or differential research, one would always want to experiment. However, some experiments are impossible to conduct and many more are unethical. Most correlational and differential studies are done because experimental studies cannot be ethically conducted.