Assumption of Factor Analysis
Factor analysis is a data reduction and statistical analysis technique that tries to explain observed relationships among multiple outcome measures as a function of some underlying variables, or factors. Factor analysis is especially popular in survey research and has other applications in multiple disciplines. However, factor analysis is not appropriate for all research questions, and it is important to ensure that your data meet certain assumptions before attempting the technique.
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Correlated Variables
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The fundamental assumption underlying factor analysis is that one or more underlying factors can account for the patterns of covariation among a number of observed variables. Covariation exists when two variables, such as price and sales of a particular good, vary together. Therefore, before conducting a factor analysis, it is important to analyze your data for patterns of correlation. If no correlation exists, then a factor analysis is needless. If, however, you find at least moderate levels of correlation among variables in your data, factor analysis can help uncover underlying patterns that explain these relationships.
Multiple Dependent Variables
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As a data-reduction technique concerned with exploring patterns, factor analysis assumes that a researcher has multiple dependent variables. This can be as few as three or as many as several hundred. According to Cornell University psychologist Richard Darlington, the number of dependent variables examined in factor analysis commonly range from 10 to 100.
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Function
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Many statistical procedures, such as regression analysis, examine the relationships between a dependent variable and one or more independent variables. Factor analysis differs in that it focuses on multiple dependent variables and tries to uncover patterns of relationships. For example, a researcher might hypothesize that 10 different outcome measures (dependent variables) can be explained by a one or more underlying factors. This is one reason factor analysis is so popular in analyzing survey data.
Interval Data
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Factor analysis is generally intended for analyzing interval scale data. The interval scale means that the distance between any two adjacent points is the same. The temperature scale is an example of an interval measurement. The distance between 71 degrees Fahrenheit and 72 degrees Fahrenheit is exactly the same as the distance between 32 and 33.
Considerations
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Although factor analysis is intended for interval scale data, many researchers also use the technique to analyze ordinal data, especially survey responses. The ordinal level is a ranking scale in which the differences between ranks are not necessarily equal. The Likert scale used in many surveys (strongly agree, agree, disagree, strongly disagree) in which the responses are assigned a numerical value is an example of ordinal measurement.
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