can tell us if a large number of variables can be explained by a much smaller number of uncorrelated constructs or factors.
In psychology, one of the best examples of factor analysis is in the area of personality theory. What psychology student hasn’t heard of OCEAN? These five personality factors of openness, conscientiousness, extraversion, agreeableness, and neuroticism were described by McCrae and Costa (1987) as the only factors needed to describe someone’s personality. Though we may use hundreds of traits and characteristics to describe someone’s personality, these all factor down to just five unique dimensions. This factoring down was accomplished by factor analysis.
In factor analysis, the researcher is looking for underlying and independent factors that have not been directly measured to explain a lot of variables that have been measured. The procedure involves identifying the variables that are interrelated. Once the factors have been identified, it is up to the researcher to decide what construct this group of variables is measuring. These underlying factors are hypothetical—that is, inferred by the researcher. The researcher attempts to find the smallest number of factors that can adequately explain the observed variables and to determine the fundamental nature of those factors.
When you read a research report where factor analysis has been used, you will probably see a complicated-looking matrix called a correlation matrix. Don’t be discouraged. Keep in mind that although the mathematics are complex and beyond the scope of this book, the concept is reasonably simple. Can an underlying variable such as general intelligence explain a whole lot of variation in measures of mental abilities?
Cluster Analysis.
Cluster analysis includes a range of algorithms and methods used to group similar objects into categories, or clusters. The members of each cluster are thus more similar to each other than they are to members of other clusters. Unlike factor analysis, where the goal is to group similar variables together, in cluster analysis, the idea is to group similar members. Organizing data into meaningful structures or taxonomies is a task many researchers face. Cluster analysis is a method that can discover structure in data, but it does not in and of itself have any explanatory function. In other words, the analysis can find structure but does not explain it.
Imagine a hospital where patients are assigned to wards based on similar symptoms or perhaps similar treatments. Each ward could be considered a cluster. A cluster analysis might discover the similarities among the patients in each ward, and the researcher then has the job of determining why the cluster or ward is similar (i.e., symptoms, treatment, age, etc.).
Cluster analysis is often used when researchers have no a priori hypotheses and are in the beginning phase of their research. As such, statistical significance testing often has no role in such analyses.
Structural Equation Modeling.
Structural equation modeling is a complex endeavor that can involve various techniques, including factor analysis, regression models, path analysis, and so on. We know that human behavior can be influenced by many variables. The purpose of structural equation modeling is to test whether data can confirm a model of how a number of variables are associated. These models are a way of testing how well theory can account for available evidence by testing whether the variables are associated in a way that would be predicted by the theory. We will just be able to give you an idea of the purpose of structural equation modeling here.
We hope you will remember what happens when we transform a set of numbers by adding a constant to each or multiplying each by a constant. Let’s say we multiply all the numbers in a list by a constant, c. The mean of that set of transformed numbers will be equal to the old mean times c, the standard deviation of the new set of numbers will equal the old standard deviation times the absolute value (i.e., ignore the sign) of c, and the variance will equal the old variance times c squared. Simple, right?
What is our point, you might be wondering? Well, bear with us. If we suspected that two sets of numbers were related, we could compare the variances of the two sets of numbers, for example, to confirm our suspicions. If one set was related to the other set by the equation Y = 2X, the variance of Y must be four times the variance of X. So we could confirm our hypothesis about the relationship between the two sets of numbers by comparing their variances rather than the numbers themselves. We hope you are not too confused by this somewhat odd way of doing things, but we think it might help you understand structural equation modeling. Two sets of numbers could be related in much more mathematically complex ways than by Y = 2X, but we hope you are getting the idea. You can determine if variables are related by looking at their variances and covariances.
Structural modeling is a way of determining whether a set of variances and covariances fits a specific structural model. In essence, the researcher hypothesizes that the variables are related in a particular way, often with something called a path diagram that shows the interrelationships among the variables. Then the researcher figures out what this model predicts about the values of the variances and covariances of the variables. This is the really complex part of the process, and we just can’t go there in this book! Then the researcher examines the variances and covariances of the variables to see if they fit the predictions of the model. If the model is supported by the statistical evidence, it is one possible way in which these variables are related. It’s important to know that this does not prove that the model is the only way these variables are related, and indeed there may be better models that someone will propose at a later time; however, it does provide researchers with useful information for further study.
As we said earlier, this is a complex procedure well beyond the scope of our book, but we hope our brief discussion gives you some idea of the purpose of structural equation modeling.
Discriminant Function Analysis.
As we mentioned earlier, at our school, we offer an applied psychology degree program. One of our objectives is to prepare students for graduate work in applied areas. Imagine that we classified our graduates over the past 10 years into two groups: (1) students who were accepted into graduate school and (2) students who were not. We could use discriminant function analysis to predict acceptance into graduate school using grade point average and workshop attendance, for example. Our analysis might help us determine how grade point average and workshop attendance individually predict acceptance into graduate school and how a combination of both predicts acceptance.
This is the idea behind discriminant function analysis. Of course, we might have many more variables, and the analysis allows us to determine the predictive ability of each variable alone and in combination with other variables. If discriminant function analysis sounds like logistic regression, it is because they are related. They have similar applications, but discriminant function analysis is calculated as ANOVA with more than one DV (MANOVA). The various DVs are used to predict group membership.
This analysis, like the others discussed in this section, is much more complex than this, but, again, we hope our brief discussion gives you an inkling of the use of these techniques, so that when you read the literature, you will have some understanding about the research outcomes.
We hope that this chapter has prepared you, on a conceptual level, to understand the literature you will be reading as you continue with your social science studies. We now turn to a topic that is so important in social science research that we have devoted an entire chapter to it: research ethics.
Chapter Summary
Once a general research topic has been selected, a literature search is necessary to determine what research has already
