# What are the differences between principal components analysis and factor analysis?

Principal components analysis and factor analysis are similar because both analyses are used to simplify the structure of a set of variables. However, the analyses differ in several important ways:
• In Minitab, you can only enter raw data when using principal components analysis. However, you can enter raw data, a correlation or covariance matrix, or the loadings from a previous analysis when using factor analysis.
• In principal components analysis, the components are calculated as linear combinations of the original variables. In factor analysis, the original variables are defined as linear combinations of the factors.
• In principal components analysis, the goal is to explain as much of the total variance in the variables as possible. The goal in factor analysis is to explain the covariances or correlations between the variables.
• Use principal components analysis to reduce the data into a smaller number of components. Use factor analysis to understand what constructs underlie the data.

The two analyses are often conducted on the same data. For example, you can conduct a principal components analysis to determine the number of factors to extract in a factor analytic study.

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