# Principal Component Analysis (PCA)

There are two basic approaches to factor analysis: principal component analysis (PCA) and common factor analysis. Overall, factor analysis involves techniques to help produce a smaller number of linear combinations on variables so that the reduced variables account for and explain most the variance in correlation matrix pattern. Principal component analysis is an approach to factor analysis that considers the total variance in the data, which is unlike common factor analysis, and transforms the original variables into a smaller set of linear combinations. The diagonal of the correlation matrix consists of unities and the full variance is brought into the factor matrix. The term factor matrix is the matrix that contains the factor loadings of all the variables on all the factors extracted. The term ‘factor loadings’ are the simple correlations between the factors and the variables. Principal component analysis is recommended when the researcher’s primary concern is to determine the minimum number of factors that will account for the maximum variance in the data in use in the particular multivariate analysis, like in Delphi studies. While conducting principal component analysis, the researcher can get well versed with terms such as standard deviations and eigenvalues. The eigenvalues refer to the total variance explained by each factor. The standard deviation measures the variability of the data. The task of principal component analysis is to identify the patterns in the data and to direct the data by highlighting their similarities and differences.

**Questions Answered:**

What survey questions should be grouped together that best measure X, Y, and Z domains?

Should sections X and Y account for any variance in Z domain?

**Assumptions:**

**Sample size**: ideally, there should be 150+ cases and there should be ratio of at least five cases for each variable (Pallant, 2010)

**Correlations: **there should be some correlation among the factors to be considered for PCA

**Linearity: **it is assumed that the relationship between the variables are linearly related

**Outliers: **PCA is sensitive to outliers; they should be removed.

To conduct this using SPSS, first click **Analyze** then select **Dimension Reduction** and then **Factor**.

Select all required variables and move them into the **Variables **box.

You can do **Descriptives** if desired.

Click on the **Extraction** button and make sure **Principal components** is checked under the **Method **section

**For assistance with factor analysis or other quantitative analyses **click here**.*

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