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Nov 24, 2014




Factor Analysis in Educational ResearchDr. Soon Seng ThahInstructional Objectives: After studying this module, you will be able to: 1. Run factor analysis using SPSS; 2. Understand conceptual underpinnings of the factor analytic approach in educational research; and 3. Interpret SPSS factor analysis output and make inferences from the output generated.


Factor Analysis in Educational ResearchSoon Seng Thah, Ph.D 1. Introduction Due to the complexity of human interactions in education, there is a general tendency for educational researchers to use numerous variables in their study. When this happens, reporting research findings becomes cluttered with too much information which may not necessarily yield the desired results. Due to this, there is a need for some sort of summarisation on the number of variables and portray what is necessary without substantial loss of meaning. This is possible through the use of factor analysis. Basically, factor analysis can be used to examine the underlying patterns or relationships for a large number of variables and to determine whether the information can be condensed or summarised in a smaller set of factors or components with a minimal loss of information. By providing an empirical estimate of the structure of variables, factor analysis becomes an objective basis for creating summated scales. A good understanding of factor analysis is imperative for educational researchers who intend to venture into the more complex realm of variable relationships. 2. What is factor analysis? Factor analysis is an inter-dependence technique, meaning the variables cannot be classified as either dependent or independent but instead all the variables are analysed simultaneously in an effort to find an underlying structure to the entire set of variables or subjects. Factor analysis involves defining sets of variables that are highly interrelated known as factors. Basically, there are two types of factor analysis exploratory as used in the SPSS Base module and confirmatory as in SPSS Amos. Confirmatory factor analysis is also called structural equation modeling (SEM). Assuming that you have designed a questionnaire with 100 items outlining separate characteristics of effective management in schools. With so many items, it would be difficult to evaluate the effect of these variables separately as they are too specific. You may want some general evaluative dimensions rather than just those specific items. However, to ascertain these general evaluative dimensions, you must still obtain information about the 100 specific items. These items which correlate highly are assumed to be a member of the a broader dimension. These dimensions become composites of the specific variables which in turn allow the dimensions to be interpreted and described. Thus, a factor analysis might identify certain dimensions such as motivation, climate, structure, interactions, etc. as the broader evaluative dimensions prevalent among the respondents. Each of these dimensions contains specific items that together constitute a broader evaluative dimension. The school administrators could then use these dimensions or factors to define what constitute leadership effectiveness and work towards a plan of action which will lead to the attainment of the desired objectives.


3. How do you go about running factor analysis using SPSS? Due to the advanced statistical concepts used in factor analysis, it is very tedious to calculate factor analysis computations manually. However, there are a number of statistical software which can do this chore systematically one of which is SPSS. The following shows you a step-by-step approach in running factor analysis using SPSS. Step 1: From the menus, select Analyze Data reduction Factor (see Figure 1).

Figure 1: Factor analysis menu Step 2: The factor analysis dialog box appears as follows (see Figure 2):

Figure 2: Factor analysis dialog box


Select the variables for factor analysis by transferring the variables to the Variables box (click (right arrow) to transfer the variables). Step 3: Select Descriptives from the tab at the bottom of the factor analysis dialog box and the Descriptives dialog box appears (see Figure 3).

Figure 3: Descriptives dialog box Tick the following: Under Statistics - Univariate descriptives, Initial solution, under Correlation Matrix Coefficient, Significance levels, Anti-image and KMO and Bartletts test of sphericity. Click Continue. Step 4: Select Extraction from the tab at the bottom of the factor analysis dialog box and the Factor Analysis: Extraction dialog box appears (see Figure 4).

Figure 4: Extraction dialog box Tick the following: Under Method Principal components, under Analyze Correlation matrix, under Display Unrotated factor solution and Scree plot, under


Extract Eigenvalues over: 1, and accept the default value of 25 for Maximum Iterations for Convergence. Click Continue. Step 5: Select Rotation from the tab at the bottom of the factor analysis dialog box and the Factor Analysis: Rotation dialog box appears (see Figure 5).

Figure 5: Rotation dialog box Tick the following: Under Method Varimax, under Display Rotated solution and Loading plot(s). Accept the default value of 25 for Maximum Iterations for Convergence. Click Continue. Step 6: Select Options from the tab at the bottom of the factor analysis dialog box and the Factor Analysis: Options dialog box appears (see Figure 6).

Figure 6: Options dialog box Select the following: Under Missing Cases Exclude cases listwise, under Coefficient Display Format Sorted by size.


Click Continue. Step 7: Select OK to run the factor analysis and display output. Step 8: Interpret the factor analysis output. When interpreting the factor analysis output generated by SPSS, you need to know and understand a number of fundamental principles associated with this type of analysis. Lets discuss these principles systematically while doing away with the technical jargon. Running a factor analysis using SPSS and interpreting its output entails understanding 7 principal stages in the factor analysis procedure. These stages are as follows: 8.1 Stage 1: Objectives of factor analysis a. Knowing the type of factor analysis You must consider which type of factor analysis you need. Basically, as far as exploratory factor analysis is concerned, there are two - i. R factor analysis; and ii. Q factor analysis. The R factor analysis is the most common and analyses a set of variables to identify the dimensions that are latent (not easily observed). On the other hand, Q factor analysis combines or condenses large number of people (cases) into distinctly different groups within a larger population. Due to computational difficulties, the Q factor analysis is not frequently used, but instead cluster analysis is used to group individual respondents. With the two types of exploratory factor analyses in mind, you then select either variables as in R factor analysis or cases (respondents) as in Q factor analysis. Our concern in this write-up is on the R factor analysis. b. Data summarisation versus data reduction Using factor analysis will result in two outcomes data summarisation and data reduction. When summarising data, factor analysis describes data in smaller number of concepts than the original individual variables. The fundamental concept involved in data summarisation is the definition of structure. Using this structure, you can view the set of variables at various levels of generalisations from the most detailed variables to the more generalised level where individual variables are grouped and viewed not for what they represent individually but for what they represent collectively in expressing a concept. On the other hand, data reduction extends this process by deriving an empirical value called factor score for each dimension or factor and then substituting this value for the original values. c. Variable selection When selecting variables for factor analysis, variable selection must be done with care. You must specify variables with the potential dimensions that can be identified through the character and nature of the variables submitted to factor analysis. For example, if you would like to extract a factor on leadership styles in educational


administration, make sure that items pertaining to this aspect are included, otherwise factor analysis would not be able to identify this dimension. The phenomenon garbage in, garbage out is very real in factor analysis! If you indiscriminately include a large number of variables and hope that factor analysis will figure it out, then the possibility of poor results is high. It must be pointed out that the quality and meaning of the derived factors reflect the conceptual underpinnings of the variables included in the analysis. You yourself as the researcher must know what the elements and their relationships are to be able to optimise the use of factor analysis in educational research. 8.2 Stage 2: Designing a factor analysis When designing a factor analysis, the researcher has to bear in mind three basic elements: a. correlations among variables or respondents; b. variable selection and measurement; and c. sample size. a. Correlations among variables or respondents Factor analysis uses a correlation matrix which shows relationships among the variables as the basic data input. An example of this correlation is reflected in Table 1: Correlations among variables. Variables b1 b5 shown as columns correlate with variables b1 b5 shown as rows in a correlation matrix. This table shows the existence of strong correlations among the variables with values greater than .7 this reflects one of the ideal situations for running factor analysis. Table 1: Corr