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 been conducted in the area. Various databases are available for the psychology literature. One of the most useful is PsycINFO. Review articles, books, chapters in books, edited volumes, and chapters in edited volumes are also found in the research databases. Peer-reviewed journals are the best sources of original research. Searching the literature for relevant research will be more successful if appropriate search terms are used.
Original research journal articles generally include an abstract, an introduction, a method section, a results section, and a discussion section. The purpose of the abstract is to summarize the article. There should be enough information in the abstract for the reader to decide if he or she should read the entire research article. In the introduction, there will be a description of the relevant research and a description of the specific research hypotheses of the authors. The IV and DVs are often described in the introduction as well.
The method section is typically divided into subsections such as Participants or Subjects, Materials, and Apparatus. The method section always contains a subsection called Procedure. Enough details of the procedure must be included so that researchers elsewhere could replicate the research.
In the results section, the statistical data are presented. Both descriptive and inferential statistics will be reported. Descriptive measures of central tendency, variability, and the strength of the relationship between variables will be reported. Typically, the inferential statistics follow the descriptive statistics. A lot of psychology research involves testing hypotheses. Any tests of significance that were used to assess the research hypotheses will be reported in the results section. Basic tests of significance include t tests, F tests, chi-square tests, correlation and regression tests, and so on. The authors will indicate whether or not the hypotheses they put forth in the introduction were supported by the statistical analyses.
More complex analyses that are common in the research literature include multiple regression, partial correlation, semipartial correlation, logistic regression, factor analysis, cluster analysis, structural equation modeling, and discriminant function analysis.
Although hypothesis testing is more common in psychology research, confidence interval estimation is also used. A confidence interval is a range of values with a known probability of containing a parameter.
The discussion section of a research article contains the authors’ interpretation of the statistical findings and suggestions about future research directions.
Chapter Resources
Answers to Conceptual Exercises
Conceptual Exercise 2A
1a. IV is amount of practice; DV is reaction time.
1b. IV is amount of exercise; DV is ratings of depression.
Conceptual Exercise 2B