In this article we will be discussing about how output of factor analysis can be interpreted. I discuss how to enter the data, select the various options, interpret the output e. Introduction the pleasure writers experience in writing considerably in. Factor analysis introduction factor analysis is used to draw inferences on unobservable quantities such as intelligence, musical ability, patriotism, consumer attitudes, that cannot be measured directly. We have already discussed about factor analysis in the previous article factor analysis using spss, and how it should be conducted using spss. Factor analysis is a statistical technique for identifying which underlying factors are measured by a much larger number of observed variables. Results including communalities, kmo and bartletts test, total variance explained, and the rotated component matrix. A correlation matrix is simply a rectangular array of numbers which gives the correlation coefficients between a single variable and every other variables in the investigation. Exploratory factor analysis reliability ronbachs alpha the data were analyzed using social sciences spss software version 23. Confirmatory factor analysis and structural equation modeling 57 analysis is specified using the knownclass option of the variable command in conjunction with the typemixture option of the analysis command. Factor analysis and item analysis applying statistics in. When the observed variables are categorical, cfa is also referred to as item response theory irt analysis fox, 2010. If it is an identity matrix then factor analysis becomes in appropriate.
For example, computer use by teachers is a broad construct that can have a number of factors use for testing. The scores that are produced have a mean of 0 and a variance equal to the squared multiple correlation between the estimated factor scores and the true factor values. Factor analysis is designed for interval data, although it can also be used for ordinal data e. Results including communalities, kmo and bartletts test, total. Development of psychometric measures exploratory factor analysis efa validation of psychometric measures confirmatory factor analysis cfa cannot be done in spss, you have to use. The default is to estimate the model under missing data theory using all available data. To run a factor analysis, use the same steps as running a pca analyze dimension reduction factor except under method choose principal axis factoring. Factor analysis is a data reduction technique that examines the relationship between observed and latent variables factors.
If missing values are scattered over variables, this may result in little data actually being used for the analysis. In particular, factor analysis can be used to explore the data for patterns, confirm our hypotheses, or reduce the many variables to a more manageable number. Pdf expert sessions delivered on factor analysis and structure equation modeling using spss and amos in national level two week. Throughout the spss survival manual you will see examples of research that is taken from a number of different data files. Factor analysis is a method for analyzing a whole matrix of all the correlations among a number of different variables to reveal the latent sources of variance that could account for the correlations among many seemingly diverse tests or other variables. Run this stepbystep example on a downloadable data file. A handbook of statistical analyses using spss sabine, landau, brian s. Ibm spss advanced statistics 21 university of sussex. Figure 5 the first decision you will want to make is whether to perform a principal components analysis or a principal factors analysis.
Andy field page 1 10122005 factor analysis using spss the theory of factor analysis was described in your lecture, or read field 2005 chapter 15. Kaisermeyerolkin kmo measure of sampling adequacy this test checks the adequacy of data for running the factor analysis. Such underlying factors are often variables that are difficult to measure such as iq, depression or extraversion. The goal of factor analysis is to describe correlations between pmeasured traits in terms of variation in few underlying and unobservable.
But what if i dont have a clue which or even how many factors are represented by my data. Be able to carry out a principal component analysis factor analysis using the psych package in r. Mar 17, 2016 this video demonstrates how interpret the spss output for a factor analysis. Overview this tutorial looks at the popular psychometric procedures of factor analysis, principal component analysis pca and reliability analysis. Factor analysis using spss pdf factor analysis spss. The scores that are produced have a mean of 0 and a variance.
The rest of the output shown below is part of the output generated by the spss syntax shown at the beginning of this page. Principal component analysis can be performed in sas using proc princomp, while it can be performed in spss using the analyzedata reductionfactor analysis menu selection. Factor analysis on spss factor analysis using spss. Factor analysis and pca are often confused, and indeed spss has pca as a method of factor analysis. Factor analysis can also be used to construct indices. Click on the descriptives button and its dialogue box will load on the screen. This process is called measurement model that links manifest variables to unobserved factors. Creates one new variable for each factor in the final solution. Factor analysis is a significant instrument which is utilized in development, refinement, and evaluation of tests, scales, and measures williams, brown et al. Spss, standing for statistical package for the social sciences, is a powerful, userfriendly software package for the manipulation and statistical analysis of data. Factor analysis in spss to conduct a factor analysis, start from the analyze menu.
Questionnaire evaluation with factor analysis and cronbachs alpha an example melanie hof 1. Exploratory factor analysis smart alexs solutions task 1 rerunthe analysis inthischapterusingprincipalcomponentanalysisandcomparethe resultstothoseinthechapter. In the descriptives window, you should select kmo and bartletts test of sphericity. Factor analysis factor analysis is used to uncover the latent structure dimensions of a set of variables. For an iterated principal axis solution spss first estimates communalities, with. The factor analysis can be found in analyzedimension reduction factor in the dialog box of the factor analysis we start by adding our variables the standardized tests math, reading, and writing, as well as the aptitude tests 15. This can be checked by looking at scatterplots of pairs of variables. To run a factor analysis on the standardized variables, from the menus choose.
Be able to select and interpret the appropriate spss output from a principal component analysis factor analysis. Factor analysis using spss 2005 discovering statistics. One or more factors are extracted according to a predefined criterion, the solution may be rotated, and factor values may be added to your data set. An introduction to exploratory factor analysis in ibm spss statistics. The alternative methods for calculating factor scores are regression, bartlett, and andersonrubin. This work is licensed under a creative commons attribution. Factor analysis is a multivariate technique for identifying whether the correlations between a set of observed variables stem from their relationship to one or more latent variables in the data, each of which takes the form. Spss also gives you a factor score covariance matrix. Kaisermeyerolkin measure of sampling adequacy this measure varies between 0 and 1, and values closer to 1 are better. How to conduct a factor analysis in spss click on analyze, data reduction, factor highlight the items you want to include in the analysis, and move them to the variables window using the right arrow moving from left to right, select each of the buttons and select the following. This will allow readers to develop a better understanding of when to employ factor analysis and how to interpret the tables and graphs in the output. This video demonstrates how interpret the spss output for a factor analysis.
The theory of factor analysis was described in your lecture, or read field 2005 chapter 15. The larger the value of kmo more adequate is the sample for running the factor analysis. Questionnaire evaluation with factor analysis and cronbachs. Exploratory factor analysis two major types of factor analysis exploratory factor analysis efa confirmatory factor analysis cfa major difference is that efa seeks to discover the number of factors and does not specify which items load on which factors. The kaisermeyerolkin test checks to see if your data is suitable for fa. On the main diagonal of this matrix are, for each factor, the r2 between the factor and the observed variables. Twolevel exploratory factor analysis with both individual and clusterlevel factor indicators 4. Development of psychometric measures exploratory factor analysis efa validation of psychometric measures confirmatory factor analysis cfa cannot be done in spss, you have to use e. Table 2 is a factor score matrix for our population of 301 participants on the six variables. Factor analysis in spss to conduct a factor analysis reduce. Exploratory factor analysis and principal components analysis exploratory factor analysis efa and principal components analysis pca both are methods that are used to help investigators represent a large number of relationships among normally distributed or scale variables in a simpler more parsimonious way. Bi factor exploratory factor analysis with continuous factor indicators example uses numerical integration in the estimation of the model. A simple explanation factor analysis is a statistical procedure used to identify a small number of factors that can be used to represent relationships among sets of interrelated variables. Expert sessions delivered on factor analysis and structure equation modeling using spss and amos in national level two week faculty development programme on advanced data analysis for business.
For factor analysis, items on the survey that did not exceed a 0. Spss does not include confirmatory factor analysis but those who are interested could take a look at amos. Factor analysis has no ivs and dvs, so everything you want to get factors for just goes into the list labeled variables. We will use iterated principal axis factor with three factors as our method of. Before using this information and the product it supports. This procedure is intended to reduce the complexity in a set of data, so we choose data reduction. Click on the check box of suppress absolute values less than to select it. Running a linear regression on factor component scores. Interpreting spss output for factor analysis youtube. Factor analysis using spss pdf factor analysis using spss pdf download direct download. In chapter 15 on factor analysis i refer to the zipped file for the montecarlo pca for windows, which is available here.
By default, spss uses only cases without missing values on the predictors and the outcome variable listwise deletion. The broad purpose of factor analysis is to summarize. Spss computes a principal components analysis as the default option. Nov 11, 2016 51 factor analysis after having obtained the correlation matrix, it is time to decide which type of analysis to use. For example, a confirmatory factor analysis could be performed if a researcher wanted to validate the factor structure of the big five personality traits using the big five inventory. The main difference between these types of analysis lies in the way the communalities are used.
For cases with missing values, pairwise deletion tries to use all non missing values for the analysis. Factor analysis seeks linear combinations of variables, called factors, that. Confirmatory factor analysis cfa is used to study the relationships between a set of observed variables and a set of continuous latent variables. Factor transformation matrix this is the matrix by which you multiply the unrotated factor matrix to get the rotated factor matrix. Spss multiple regression analysis in 6 simple steps. Spss will extract factors from your factor analysis. Factor analysis, exploratory factor analysis, factor retention decisions, scale development, extraction and rotation methods. Spss factor analysis absolute beginners tutorial spss tutorials. Chapter 4 exploratory factor analysis and principal.
The most common way to construct an index is to simply sum up all the items in an index. Rotation dialogue box from the factor analysis dialogue box click on the options button and its dialogue box will be loaded on the screen. Exploratory factor analysis rijksuniversiteit groningen. Questionnaire evaluation with factor analysis and cronbach. Exploratory factor analysis smart alexs solutions task 1 reruntheanalysisinthischapterusingprincipalcomponentanalysisandcomparethe resultstothoseinthechapter. Words, if your data contains many variables, you can use factor analysis to reduce the economics terms definitions pdf number. Are all of these elements separate, or can we identifygroup them into an underlying structure.
Factor analysis researchers use factor analysis for two main purposes. It reduces attribute space from a larger number of variables to a smaller number of factors and as such is a nondependent procedure that is, it. Factor analysis statistical associates blue book series. Spss will not only compute the scoring coefficients for you, it will also output the factor scores of your subjects into your spss data set so that you can input them into other procedures. Factor analysis is an extremely complex mathematical procedure and is performed with software. This paper is only about exploratory factor analysis, and will henceforth simply be named factor analysis. Analysis of variance is robust to departures from normality, although the data should be. This is treated as an indictor of the internal consistency of the solution. Note that we continue to set maximum iterations for convergence at 100 and we will see why later.
The sample is adequate if the value of kmo is greater than 0. Focusing on exploratory factor analysis quantitative methods for. Conduct and interpret a factor analysis statistics solutions. In this process, the following facets will be addressed, among others. Factor analysis in spss to conduct a factor analysis. Results including communalities, kmo and bartletts test, total variance explained, and.
Exploratory factor analysis 4 in spss a convenient option is offered to check whether the sample is big enough. Efa cannot actually be performed in spss despite the name of menu item used to perform pca. Factor scores, structure and communality coefficients. Validity and reliability of the instrument using exploratory. You can do this by clicking on the extraction button in the main window for factor analysis see figure 3. Jun 30, 2011 i demonstrate how to perform and interpret a factor analysis in spss. Within this dialogue box select the following check boxes univariate descriptives, coefficients, determinant, kmo and bartletts test of sphericity, and reproduced.
In this paper an example will be given of the use of factor analysis. A value of 0 indicates that the sum of partial correlations is large relative to the sum of correlations, indicating diffusion in the pattern of correlations hence, factor analysis is likely to be inappropriate. For the example below, we are going to do a rather plain vanilla factor analysis. Factor analysis in spss means exploratory factor analysis. Factor analysis using spss 4 the correlation matrix the next output from the analysis is the correlation coefficient.
Furthermore, spss can calculate an antiimage matrix. Twolevel exploratory factor analysis with continuous factor indicators 4. Newsom, spring 2017, psy 495 psychological measurement. Factor analysis using spss 2005 university of sussex. Factor analysis is a multivariate technique for identifying whether the correlations between a set of observed variables stem from their relationship to one or more latent variables in the data, each of. Be able explain the process required to carry out a principal component analysis factor analysis.
Spss computes a principal components analysis as the. In the factor analysis window, click scores and select save as variables, regression, display factor score coefficient matrix. As for the factor means and variances, the assumption is that thefactors are standardized. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. If the determinant is 0, then there will be computational problems with the factor analysis, and spss may issue a warning message or be unable to complete the factor analysis. Running a common factor analysis with 2 factors in spss. As part of a factor analysis, spss calculates factor scores and automatically saves them in the data file, where they are easily accessible for further analyses see table 2.
The variables used in factor analysis should be linearly related to each other. With respect to correlation matrix if any pair of variables has a value less than 0. Used properly, factor analysis can yield much useful information. It is an assumption made for mathematical convenience. This tutorial looks at the popular psychometric procedures of factor analysis, principal component analysis pca and reliability analysis.