Skip to content Skip to navigation Skip to collection information

OpenStax-CNX

You are here: Home » Content » Calculating Advanced Statistics » 10. Factor Analysis: Part II

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

In these lenses

  • Statistics

    This collection is included inLens: Mathieu Plourde's Lens
    By: Mathieu Plourde

    Click the "Statistics" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.
 

10. Factor Analysis: Part II

Module by: John R. Slate, Ana Rojas-LeBouef. E-mail the authors

ncpealogo.gif

Note:

This chapter is published by NCPEA Press and is presented as an NCPEA/Connexions publication "print on demand book." Each chapter has been peer-reviewed, accepted, and endorsed by the National Council of Professors of Educational Administration (NCPEA) as a significant contribution to the scholarship and practice of education administration.

About the Authors

  • John R. Slate is a Professor at Sam Houston State University where he teaches Basic and Advanced Statistics courses, as well as professional writing, to doctoral students in Educational Leadership and Counseling. His research interests lie in the use of educational databases, both state and national, to reform school practices. To date, he has chaired and/or served over 100 doctoral student dissertation committees. Recently, Dr. Slate created a website (Writing and Statistical Help) to assist students and faculty with both statistical assistance and in editing/writing their dissertations/theses and manuscripts.
  • Ana Rojas-LeBouef is a Literacy Specialist at the Reading Center at Sam Houston State University where she teaches developmental reading courses. Dr. LeBoeuf recently completed her doctoral degree in Reading, where she conducted a 16-year analysis of Texas statewide data regarding the achievement gap. Her research interests lie in examining the inequities in achievement among ethnic groups. Dr. Rojas-LeBouef also assists students and faculty in their writing and statistical needs on the Writing and Statistical Help website.

After clicking on Extraction, the following screen should now be present.

9.1.png

Under Display, click on Screen plot.

Unclick the Unrotated factor solution.

9.2.png

Click on Continue.

9.3.png

After clicking on Continue, the screen below should be present.

Now click on OK.

9.4.png

You should now have factor analysis results. If SPSS does not send you to your output screen, click on the Output icon at the bottom of your screen.

9.5.png

In your SPSS Output screen, the first table of importance is the Descriptive Statistics table. The sample size (n), M, and SD for each of the 10 subscales used in the factor analysis are present in this table.

9.6.png

Underneath the Descriptive Statistics table is the Scree plot. What the scree plot does is to plot the eigenvalue against the factor number (Cattell, 1966; Zwick & Velicer, 1986). The eigenvalue and factor number are present in the table labeled Total Variance Explained. You will note in the Scree Plot below that the line is essentially flat after the second factor. This plot below depicts the presence of two possible factors, 1 and 2.

9.7.png

In the Total Variance Explained table, statistical information that is depicted in the Scree Plot is presented. The column labeled Total reflects the eigenvalues for the two factors. To determine the number of factors you may have: look at the eigenvalue column. All factors with values less than 1 are considered to be statistically insignificant and are disregarded (Kaiser, 1958). Thus, an eigenvalue of at least 1.0 must be present for a factor to be possible. In the Total Variance Explained table below, two factors are present with eigenvalues greater than 1.00: Factor 1 has an eigenvalue of 3.545 and Factor 3 has an eigenvalue of 2.515.

9.8.png

After checking the eigenvalues to ensure that they are greater than one (Kaiser, 1958), the percent of variance must be examined. To constitute a viable factor, the factor should account for at least 5 percent of the variance to be used. In the example below, Factor 1 accounts for 35.45% of the variance and Factor 2 explains 25.15% of the variance. In both cases, the factors account for much more than the minimum 5%. Together these two factors account for 60.60% of the variance.

9.9.png

Next we will examine the Rotated Component Matrix. This table contains the factor loadings or pattern/structure coefficients for the 10 subscales analyzed in this Varimax procedure. To determine whether a subscale is a component of a specific factor, a cutoff value of .3 (Lambert & Durand, 1975) is recommended as an acceptable minimum value for pattern/structure coefficients. In this example, Verbal 1 (Information) has a pattern/structure coefficient of .782; Verbal 1 (Similarities) of .745; Verbal 3 (Arithmetic) of .661; Verbal 4 (Vocabulary) of .845; and Verbal 5 (Comprehension) of .797. Though above the cutoff of .3, Performance 2 (Coding), Performance 3 (Picture Arrangement), and Performance 4 (Block Design) are well below the coefficients for the Verbal subscales.

9.10.png

For Factor 2, the pattern/structure coefficients were .711 for Performance 1 (Picture Completion); .536 for Performance 3 (Picture Arrangement); .767 for Performance 4 (Block Design); and .865 for Performance 5 (Object Assembly). Two of the Verbal subscales were at or above the cutoff value of .3, however, their pattern/structure coefficients were markedly lower than the ones for the four Performance subscales mentioned above.

9.11.png

In this example, it appears that the Performance 2 (Coding) subscale is not part of Factor 2. It may be a component of Factor 1.

9.12.png

You have now conducted a Varimax factor rotation of the 10 subscales of the Wechsler Intelligence Scale for Children-Third Edition. To determine whether your factors are internally consistent, you would need to perform an internal consistency analysis for the subscales that constitute Factor 1 and a separate internal consistency analysis for the subscales that constitute Factor 2. See our chapter on steps and screenshots for conducting internal consistency analyses.

References

  • Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1, 245–276.
  • Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200.
  • Lambert, Z. V., & Durand, R. M. (1975). Some precautions in using canonical analysis. Journal of Market Research, 12, 468–475.
  • Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432–442.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks