**Testing for the Factorability of the Data**

Before applying PCA to the data, we need to test whether they are suitable for reduction. SPSS provides two tests to assist users:

198 Principal Component Analysis

2. Highlight all of the quantitative variables and Click on the **Variables** button. The character variable Country is an identifier variable and should not be included in the

3. Click on the **Descriptives** button to select **Univariate Descriptives, Initial Solution,** 

4. Click on the **Extraction** button, and select **Method=Principal Components, Display Unrotated factor solution, Scree Plot**. Select **Extract Eigenvalue over 1** (by default).

6. Click on **Scores** and select **Save as variables**, **Method=Regression**. Select the case

To discover the pattern of intercorrelations among variables, we examine the correlation

exp Mortality Urban Iliteracy Water Telephone Vehicles Fertility Hosp\_

Life\_exp 1.000 -0.956 0.732 -0.756 0.780 0.718 0.621 -0.870 0.514 0.702 Mortality 1.000 -0.736 0.809 -0.792 -0.706 -0.596 0.895 -0.559 -0.733 Urban 1.000 -0.648 0.692 0.697 0.599 -0.642 0.449 0.651 Iliteracy 1.000 -0.667 -0.628 -0.536 0.818 -0.603 -0.695 Water 1.000 0.702 0.633 -0.746 0.472 0.679 Telephone 1.000 0.886 -0.699 0.622 0.672 Vehicles 1.000 -0.602 0.567 0.614 Fertility 1.000 -0.636 -0.763 Hosp\_beds 1.000 0.701 Physicians 1.000

The variables can be grouped into two groups of correlated variables. We will see this later.

Before applying PCA to the data, we need to test whether they are suitable for reduction.

beds

Physicians

To perform a principal components analysis with SPSS, follow these steps:

5. Click on the **Rotation** button, and select **Display Loading Plot(s).**

In what follows, we review and comment on the main outputs.

Note : Figures reported in this table are correlation coefficients.

**Testing for the Factorability of the Data** 

SPSS provides two tests to assist users:

7. Click on **Options**, and select **Exclude Cases Listwise** (option by default).

1. Select **Analyze/Data Reduction/ Factor** 

**KMO and Bartlett's test of Sphericity**.

Variables list.

below.

**Correlation Matrix** 

matrix. That is given in Table 7:

Life\_

Table 7. **Correlation Matrix**

**Kaiser-Meyer-Olkin Measure of Sampling Adequacy (**Kaiser, 1974): This measure varies between 0 and 1, and values closer to 1 are better. A value of 0.6 is a suggested minimum for good PCA.

**Bartlett's Test of Sphericity** (Bartlett, 1950): This tests the null hypothesis that the correlation matrix is an identity matrix in which all of the diagonal elements are 1 and all off diagonal elements are 0. We reject the null hypothesis when the level of significance exceeds 0.05.

The results reported in Table 8 suggest that the data may be grouped into smaller set of underlying factors.


Table 8. **Results of KMO and Bartlett's Test** 
