Factor analysis is a statistical technique used to identify constructs, or factors, that statistically explain the patterns of variations among multiple values. In brief, factor analysis involves generating one or more unobserved independent variables that correlate with the observed measures. Commonly used in survey research and other applications, factor analysis can be considered a data reduction technique because it reduces a large number of variables that often overlap to a smaller number of factors. This technique requires use of a computer with specialised statistical software.

- Skill level:
- Easy

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### Things you need

- Statistical software program
- Statistics book or manual

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## Instructions

- 1
Determine the purpose of your factor analysis before running the procedure and interpreting the output. A common use of factor analysis is to define a set of dimensions (factors) underlying a set of existing measures. For example, suppose you want to define the underlying factors for a set of responses to a questionnaire that is designed to assess a person's political attitudes. Your hypothesis may be that a certain number of underlying factors help shape attitudes about politics and government.

- 2
Examine your factor extraction output. Factor extraction is the first of two stages in factor analysis; the second being factor rotation. Extraction helps identify the number of underlying factors. You determine this by examining two parts of your output: the initial eigenvalues and the scree plot. Eigenvalues measure the amount of variation in a group of measures that is explained by a particular factor. A useful guideline is to include all factors with an eigenvalue greater than one.

- 3
Turn your attention to the scree plot, a graphic display of the relative magnitude of the eigenvalues. Retain all factors with eigenvalues in the sharply descending part of the plot. Suppose for this example, you have three such eigenvalues in the plot, and they are each greater than one. This means you have three factors.

- 4
Conduct a three-factor rotation of the three factors extracted. Rotation statistically manipulates the factors to make them more meaningful. Your statistical software or statistics guide will provide steps on how to conduct a factor rotation. Running the factor rotation will produce additional output.

- 1
Examine the correlation patterns in the factor rotation matrix part of your output. This matrix will display the correlation score, or factor loading, between each variable and the underlying factor. Items with high factor loadings--between between .300 and 1.00, for example (plus or minus) are related to the corresponding factor.

- 2
Identify for each of your three factors the measures that are positively correlated. You may find that some items can be excluded because of low factor loadings across all factors.

- 3
Based on the content of the items with high factor loadings, name or label each of the three factors.

#### Tips and warnings

- Most popular spreadsheet programs, such as Microsoft Excel, cannot run a factor analysis without an extra program that conducts such analysis. One such program, XLStat, enables Excel to run factor analysis and other advanced statistical procedures.