# 11.2 - Factor Analysis

11.2 - Factor Analysis#### Case-Study: Second Article

Jin’s second article uses a survey to ask town residents about their perceptions of unemployment. The survey contains over 60 items and reports overall attitudes about unemployment long with subscales measuring perceived locus of control, the importance of sustainability, and optimism about the future. The article reports the overall score descriptive statistics along with descriptive statistics for the three subscales. Jin recognizes the descriptive statistics but wonders how the research arrived at the three subscales based on the 60 original times. Let’s help Jin better understand how the authors of the article moved from a 60 item survey to the three subscales.

**Foundational Concepts: **The key foundational concepts this article builds upon are: Covariance (correlations) among quantitative variables Descriptive statistics

When researchers, particularly those who use surveys, encounter many variables in their data, such as those produced by the 60 items survey in Jin’s article, they need to find ways to reduce the number of variables. Presenting the means, standard deviations, and graphing each of them is overwhelming, plus it often inflates the number of predictor variables in the model!

The idea of “reducing” the number of variables is grounded in the concept of creating reliability. While reliability is not something this course focuses on, it basically means that the items will measure similar ideas the same way. In Jin’s example, the survey might have three items measuring locus of control (how empowered people feel to take action to not be unemployed), yet each item asks the question a different way. For example, these are three questions from the survey in Jin’s article.

- There are enough jobs in this town I am qualified to apply for
- I have the skills that would qualify me for jobs in this town
- Industry in this town is related to my skillset

If you have ever taken a survey you may have perceived the survey asking very similar questions as the three questions related to empowerment do. This is done on purpose. The researcher can now analyze the questions to see how they relate to each other. This is done through a technique called factor analysis.

As a general overview factor analysis uses the correlations (actually the covariance) of items with one another. Items that co-vary can be grouped together into “factors”. This reduces the number of variables a researcher needs to include in any analysis. So instead of 60 items, the researchers in Jin’s article now only have to deal with three (the subscale scores) and the overall score! Jin is very happy now that he understands that in reading this article, he really only needs to focus on these three subscales, making it much easier to understand the perceptions of unemployment.