## Using Principal Components Analysis

Although it’s one of the hardest components of an exam, Principal Components Analysis (PCA) is often the most misunderstood component. Let’s examine what PCA is, why it is the backbone of SAS Programming Help Online, and how it can improve your statistical skills.

The first thing you need to know about Principal Components Analysis is that it is a mixture of four primary components. The four primary components are Sample, Weighting, Dimensionality, and Dependency.

The last two components don’t come with SAS for Windows. They are available for purchase online and you can get them for free.

In short, the key to knowing the importance of Principal Components Analysis is learning about these four components. These components not only determine what portion of the analysis will be performed on the data, but they also account for the patterns in the distribution of the variables.

Sample is the first element of the analysis. It determines how many variables will be included in the analysis. It is important to note that the number of variables in the analysis is a threshold value, not a cut-off value; there is no upper limit to the number of variables.

This might seem contradictory to what you’ve learned about high school students, but it’s actually true. The threshold for variable selection is the largest number of observations, not the largest number of observations overall. In this case, we will focus on the sample size, which is the number of observations that will be used for the analysis.

Weighting determines the order in which the variables will be examined in the sample. It is not a critical factor in the process of selecting the variables that will be studied, but it can affect the decision making process.

Dimensionality determines how many categories are present in the data. We will examine this later in this lesson. If you wish to learn more about PCA and its contribution to your statistics homework, keep reading.

The next elements of the principal components are the linear and nonlinear dimensions. Linear dimensions include attributes of the variables, while nonlinear dimensions define the interrelationships between the variables.

There are three possible classes of samples. The conventional samples are the normal (also known as normality), the second sample is normal when the data is skewed and the third sample is normally distributed when the data is normal.

As we discussed in the last lesson, every group of data has a uniform distribution. To illustrate this, let’s go back to the example above.

All groups of data in the data set, both the sub-population and the general population, will have a mean and a standard deviation (SD). Now, all of the sub-populations will be distributed according to the normal distribution. And all of the data points will fall within the range of the normal distribution. The observed normal distribution will be considered the “mean” and the observed normal distribution will be considered the “standard deviation.”