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Principal Components Analysis (PCA) using SPSS Statistics

Introduction

Principal components analysis (PCA, for short) is a variable-reduction technique that shares many similarities to exploratory factor analysis. Its aim is to reduce a larger set of variables into a smaller set of 'articifial' variables, called 'principal components', which account for most of the variance in the original variables.

There are a number of common uses for PCA: (a) you have measured many variables (e.g., 7-8 variables, represented as 7-8 questions/statements in a questionnaire) and you believe that some of the variables are measuring the same underlying construct (e.g., depression). If these variables are highly correlated, you might want to include only those variables in your measurement scale (e.g., your questionnaire) that you feel most closely represent the construct, removing the others; (b) you want to create a new measurement scale (e.g., a questionnaire), but are unsure whether all the variables you have included measure the construct you are interested in (e.g., depression). Therefore, you test whether the construct you are measuring 'loads' onto all (or just some) of your variables. This helps you understand whether some of the variables you have chosen are not sufficiently representative of the construct you are interested in, and should be removed from your new measurement scale; (c) you want to test whether an existing measurement scale (e.g., a questionnaire) can be shortened to include fewer items (e.g., questions/statements), perhaps because such items may be superfluous (i.e., more than one item may be measuring the same construct) and/or there may be the desire to create a measurement scale that is more likely to be completed (i.e., response rates tend to be higher in shorter questionnaires). These are just some of the common uses of PCA. It is also worth noting that whilst PCA is conceptually different to factor analysis, in practice it is often used interchangably with factor analysis, and is included within the 'Factor procedure' in SPSS Statistics.

In this "quick start" guide, we show you how to carry out PCA using SPSS Statistics, as well as the steps you'll need to go through to interpret the results from this test. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for PCA to give you a valid result. We discuss these assumptions next.

SPSS Statistics

Assumptions

When you choose to analyse your data using PCA, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using PCA. You need to do this because it is only appropriate to use PCA if your data "passes" four assumptions that are required for PCA to give you a valid result. In practice, checking for these assumptions requires you to use SPSS Statistics to carry out a few more tests, as well as think a little bit more about your data, but it is not a difficult task.

Before we introduce you to these four assumptions, do not be surprised if, when analysing your own data using SPSS Statistics, one or more of these assumptions is violated (i.e., not met). This is not uncommon when working with real-world data rather than textbook examples. However, even when your data fails certain assumptions, there is often a solution to try and overcome this. First, let’s take a look at these four assumptions:

You can check assumptions #2, #3, #4 and #5 using SPSS Statistics. Just remember that if you do not run the statistical tests on these assumptions correctly, the results you get when running PCA might not be valid. This is why we dedicate number of articles in our enhanced guides to help you get this right. You can find out about our enhanced content as a whole here, or more specifically, learn how we help with testing assumptions here.

In the section, Procedure, we illustrate the SPSS Statistics procedure that you can use to carry out PCA on your data. First, we introduce the example that is used in this guide.

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SPSS Statistics

Example

A company director wanted to hire another employee for his company and was looking for someone who would display high levels of motivation, dependibility, enthusiasm and commitment (i.e., these are the four constructs we are interested in). In order to select candidates for interview, he prepared a questionnaire consisting of 25 questions that he believed might answer whether he had the correct candidates. He adminstered this questionnaire to 315 potential candidates. The questions were phrased such that these qualities should be represented in the questions. Questions Qu3, Qu4, Qu5, Qu6, Qu7, Qu8, Qu12, Qu13 were associated with motivation; Qu2, Qu14, Qu15, Qu16, Qu17, Qu18, Qu19 were associated with dependability; Qu20, Qu21, Qu22, Qu23, Qu24, Qu25 for enthusiasm; and Qu1, Qu9, Qu10, Qu11 for commitment. The director wanted to determine a score for each candidate so that these scores could be used to grade the potential recruits.

SPSS Statistics

Setup in SPSS Statistics

In our enhanced PCA guide, we show you how to correctly enter data in SPSS Statistics to run a PCA. You can learn about our enhanced data setup content here. Alternately, we have a generic, "quick start" guide to show you how to enter data into SPSS Statistics, available here.

SPSS Statistics

Test Procedure in SPSS Statistics

The 18 steps below show you how to analyse your data using PCA in SPSS Statistics when none of the five assumptions in the previous section, Assumptions, have been violated. At the end of these 18 steps, we show you how to interpret the results from your PCA. If you are looking for help to make sure your data meets assumptions #2, #3, #4 and #5, which are required when using PCA, and can be tested using SPSS Statistics, we help you do this in our enhanced content (see here).

The SPSS Statistics procedure for PCA is not linear (i.e., only if you are lucky will you be able to run through the following 18 steps and accept the output as your final results). You will often have to re-run these 18 steps based on (a) the results from your assumptions tests that are run during this procedure and (b) the values of the initial components that are extracted when you carry out these 18 steps. In re-running your analysis, you may have to select different options from the SPSS Statistics procedure below, or follow additional SPSS Statistics procedures to arrive at the best possible solution. We explain more about these next steps towards the end of this guide (see here). First, follow the 18 steps below to attain your initial SPSS Statistics output:

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SPSS Statistics

Analysing the Output from Principal Components Analysis

The output generated by SPSS Statistics is quite extensive and can provide a lot of information about your analysis. However, you will often find that the analysis is not yet complete and you will have to re-run the SPSS Statistics analysis above (possibly more than once) before you get to your final solution. Below we briefly explain the seven steps that you will need to follow to interpret your PCA results, and where required, perform additional analysis in SPSS Statistics. We take you through all these sections step-by-step with SPSS Statistics output in our enhanced PCA guide. You can learn more about our enhanced content here. First, take a look through these seven steps:

If you are unsure how to interpret your PCA results, or how to check for linearity, carry out transformations using SPSS Statistics, or conduct additional PCA procedures in SPSS Statistics such as Forced Factor Extraction (see Step #4), we show you how to do this in our enhanced PCA guide. We also show you how to write up the results from your assumptions tests and PCA output if you need to report this in a dissertation/thesis, assignment or research report. We do this using the Harvard and APA styles. You can learn more about our enhanced content here.

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