Factor Analysis

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Writing Up A Factor Analysis

James Neill

Centre for Applied Psychology

University of Canberra

30 March, 2008

Creative Commons Attribution 2.5 Australia


Table of Contents

Theoretical underpinning2
Assumption testing2
Type of FA2
Number of Factors & Items Removed2
Factor Loadings2
Label Factors3
Reliability Analyses3
(Summary of the) Introduction (as related to the factor analysis)4 (Summary of the) Method5
Data Screening6
Factor Analysis6
Discussion (key points)10



This section provides a checklist of content to consider covering for factor analysis in your lab report. This is not an exhaustive-to-be-followed-to-the-letter list. Rather, you should take your own approach, whilst complying with APA style, in order to clearly demonstrate your understanding of factor analysis and the way in which you have applied the technique in your study.

Theoretical underpinning

A good report will also explain the theoretical underpinning of the structure of the constructs being measured in the introduction and discussion. The introduction might review and critique previous conceptualisations and measurements and could summarise previous factor analyses. The discussion might summarise and critique the present study’s findings about the structure of the constructs of interest.


Assumption testing

In the results, describe how you went about testing the assumptions for FA. Details regarding Measures of Sampling Adequacy should be reported. Strive to be thorough, but clear and succinct.

Type of FA

In the results, explain what FA extraction method (usually PC or PAF) was used and why.

Number of Factors & Items Removed

In the results, explain the criteria and process used for deciding how many factors and which items were selected. Clearly explain which items were removed and why, plus the number of factors extracted and the rationale for key decisions.


In the results, explain what rotation methods were attempted, the reasons why, and the results.

Factor Loadings

Final (pattern matrix or rotated component matrix) factor loadings should be reported in the results, in a table. This table should also report the communality for each variable (in the final column). Factor loadings should be reported to two decimal places and use descriptive labels in addition to item numbers. Correlations between the factors should also be included, either at the bottom of this table, in a separate table, or in an appendix. The correlation matrix should be included so that others people can re-conduct a factor analysis.

Label Factors

Meaningful names for the extracted factors should be provided. You may like to use previously selected factor names, but on examining the actual items and factors you may think a different name is more appropriate. One factor naming technique is to use the top one or two loading items for each factor. A well labeled factor provides an accurate, useful description of the underlying construct, and thus enhanced the clarity of the report.

Reliability Analyses

Following presentation of the factor analysis results, reliability analyses should be provided. Reporting of reliability analyses can be combined with a descriptives table which includes names of the factors, the number of items in each factor, descriptive statistics for the composite scores (e.g. mean, SD, Skewness and Kurtosis), and the Cronbach’s alpha (().


Discussion of the factor analysis(es)...
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