# Factor Analysis

Topics: Factor analysis, Principal component analysis, Pearson product-moment correlation coefficient Pages: 56 (6014 words) Published: February 13, 2013
C8057 (Research Methods II): Factor Analysis on SPSS

Factor Analysis Using SPSS
The theory of factor analysis was described in your lecture, or read Field (2005) Chapter 15.

Example
Factor analysis is frequently used to develop questionnaires: after all if you want to measure an ability or trait, you need to ensure that the questions asked relate to the construct that you intend to measure. I have noticed that a lot of students become very stressed about SPSS. Therefore I wanted to design a questionnaire to measure a trait that I termed ‘SPSS anxiety’. I decided to devise a questionnaire to measure various aspects of students’ anxiety towards learning SPSS. I generated questions based on interviews with anxious and non-anxious students and came up with 23 possible questions to include. Each question was a statement followed by a five-point Likert scale ranging from ‘strongly disagree’ through ‘neither agree or disagree’ to ‘strongly agree’. The questionnaire is printed in Field (2005, p. 639). The questionnaire was designed to predict how anxious a given individual would be about learning how to use SPSS. What’s more, I wanted to know whether anxiety about SPSS could be broken down into specific forms of anxiety. So, in other words, are there other traits that might contribute to anxiety about SPSS? With a little help from a few lecturer friends I collected 2571 completed questionnaires (at this point it should become apparent that this example is fictitious!). The data are stored in the file SAQ.sav. Questionnaires are made up of multiple items each of which elicits a response from the same person. As such, it is a repeated measures design. Given we know that repeated measures go in different columns, different questions on a questionnaire should each have their own column in SPSS.

Initial Considerations
Sample Size
Correlation coefficients fluctuate from sample to sample, much more so in small samples than in large. Therefore, the reliability of factor analysis is also dependent on sample size. Field (2005) reviews many suggestions about the sample size necessary for factor analysis and concludes that it depends on many things. In general over 300 cases is probably adequate but communalities after extraction should probably be above 0.5 (see Field, 2005). Data Screening

SPSS will nearly always find a factor solution to a set of variables. However, the solution is unlikely to have any real meaning if the variables analysed are not sensible. The first thing to do when conducting a factor analysis is to look at the inter-correlation between variables. If our test questions measure the same underlying dimension (or dimensions) then we would expect them to correlate with each other (because they are measuring the same thing). If we find any variables that do not correlate with any other variables (or very few) then you should consider excluding these variables before the factor analysis is run. The correlations between variables can be checked using the correlate procedure (see Chapter 4) to create a correlation matrix of all variables. This matrix can also be created as part of the main factor analysis. The opposite problem is when variables correlate too highly. Although mild multicollinearity is not a problem for factor analysis it is important to avoid extreme multicollinearity (i.e. variables that are very highly correlated) and singularity (variables that are perfectly correlated). As with regression, singularity causes problems in factor analysis because it becomes impossible to determine the unique contribution to a factor of the variables that are

Dr. Andy Field

Page 1

10/12/2005

C8057 (Research Methods II): Factor Analysis on SPSS
highly correlated (as was the case for multiple regression). Therefore, at this early stage we look to eliminate any variables that don’t correlate with any other variables or that correlate very highly with other variables (R < .9). Multicollinearity can be...