The factor analysis procedure for exploration: a short guide with examples

Surveys and tests contain multiple test items, sets of repeated tests or multiple survey questions. Commonly, these units are arranged within instruments subject to varying contexts of tests or questions. The analyst's goal is to discover communalities across these items such that items can be reduced down to common meaningful factors. We provide a literature review that supports our further choice between exploratory analytical models for analysing empirical data and for building a guide to interpreting results. The purpose of this research is to provide a methodological and systematic framework for researchers who consider exploratory analyses. Following a comparison between factor extraction methods, we suggest various approaches to look at the association between the original variables and the factor, as well as correlations between factors. Our empirical case study data is a survey instrument of 19 items from a questionnaire developed by the Branco Weiss Institute in Israel, for evaluating at-risk high school and intermediate school students. Properties of the data such as the sample size, the quality of data by means of distribution patterns and extreme values, and correlations between the original items are considered. We argue that a concurrent integration of two fundamental processes - the empirical model fit and the substantive meaning - are essential in the process of implementing exploratory analysis results. The main conclusion is that the process of exploring latent factors needs an allocation of analytical resources, similar to other statistical modelling practices. Data and context mutually function as the platform for arriving at the optimal number of factors and their item composition. The exploratory factor analysis is a powerful tool for researchers who are ready to operate this tool properly.