Skip to main content

Factor Analysis Principal Components Analysis

 


Factor analysis (FA) is a statistical method of reducing a large set of data to a smaller set by identifying patterns in the data that have common characteristics. Factor analysis is sometimes called data reduction or dimension reduction.

The original numerical values in the data set are observed variables (also called manifest variables) such as the items in a large survey or test. Factor analysis may find patterns characterized by a shared statistical relationship representing a factor, which is also called a dimension. A researcher examines the content of the items linked to this factor and chooses a factor label such as verbal skills for related items on an intelligence test.

The factors may be treated as variables in additional research. These are secondary variables. Because they are created from the observed variables, they are considered latent variables. For example, if 5 items on a personality test are associated with one factor labeled "agreeableness" then agreeableness is a latent variable.

The set of identified factors is referred to as the structure of the data set. If the data are from a test then researchers refer to the structure of the test.

Factors are identified based on the variance they account for in the data. The amount of variance explained by a factor is represented by an eigenvalue. Researchers look for eigenvalues of 1.0 or more to consider a factor to be a valuable contribution to explaining the underlying structure of a data set.

Not all factors are equal. That is, when more than one factor have been identified, they will contribute differently to explaining the variance in the data set.


Different kinds of Factor Analysis

Exploratory Factor Analysis (EFA). When researchers do not know the structure of a data set, they use EFA to discover the set of factors.

Confirmatory Factor Analysis (CFA).  When researchers wish to test a hypothesis about a data set, they perform CFA. For example, if they believe their forgiveness questionnaire contains one factor called forgiveness, they can examine the structure to see if one factor best accounts for the data set. If one factor is the best solution then they have found support for their hypothesis.

Principal Components Analysis (PCA) is a common form of confirmatory factor analysis. 

Factor Analysis is important to understanding tests in Counseling and Psychotherapy. See

Buy Applied Statistics for Counselors

 

GOOGLE BOOKS

 

AMAZON

 

 


Factor Analysis is often used to reduce the data collected from survey research. 

Buy Creating Surveys on

GOOGLE BOOKS

 

AMAZON








Please check out my website   www.suttong.com

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

   TWITTER  @Geoff.W.Sutton    

You can read many published articles at no charge:

  Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton 







Comments

Popular posts from this blog

Personal Self-Concept Questionnaire (PSQ)

  The Personal Self-Concept Questionnaire  ( PSQ )   Overview The Personal Self-Concept Questionnaire (PSQ) measures self-concept based on ratings of 18 items, which are grouped into four categories: Self-fulfilment, autonomy, honesty, and emotional self-concept. It is a likert-type rating scale with high internal consistency values and has been used with youth and adults. Subscales : The PSQ has four subscales 1. Self-fulfilment (6 items) 2. Autonomy (4 items) 3. Honesty (3 items) 4. Emotional self-concept (5 items)  ðŸ‘‰ [ Read more about Self-Concept and Self-Identity] The PSQ is a Likert-type scale with five response options ranging from totally disagree to totally agree. Reliability and Validity In the first study, coefficient alpha = .85 and in study two, alpha = .83. Data analysis supported a four-dimensional model (see the four categories above). Positive correlations with other self-concept measures were statistically significant. Other notes The authors e...

Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ)

  Scale name: Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ) Scale overview: The Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ) is a 29-item self-report measure of both mathematics self-efficacy and mathematics anxiety. Author: Diana Kathleen May Response Type: Items are rated on a 5-point Likert-type scale following a “no response” option: 1 = Never 2 = Seldom 3 = Sometimes 4 = Often 5 = usually Sample items 1. I feel confident enough to ask questions  in my mathematics class. 6. I worry that I will not be able to get a  good grade in my mathematics course.   Subscales and basic statistics for the MSEAQ       Self-Efficacy M = 44.11, SD = 10.78, alpha = .93       Anxiety M = 46.47, SD = 12.61, alpha = .93       Total Scale M = 90.58, SD = 22.78, alpha = .96 Reliability: See the Cronbach’s alpha levels reported above. Validity: There were significant ...

Academic Self-Efficacy Scale ASE

  Overview The  Academic Self-Efficacy Scale is an application of Self-Efficacy Theory   to examine the relationship between self-efficacy and academic performance using 8-items rated on a 7-point scale. The work of Chemers et al. (2001) has been widely cited. Format The 8-items are rated on a 7-point Likert-type scale ranging from 1 = Very Untrue to 7 = Very True. Sample Items 2. I know how to take notes. 6. I usually do very well in school and at academic tasks.   Reliability, Validity, and Other Research notes In the article describing the development and use of the ASE, the authors observed: “As predicted, academic self-efficacy was significantly and directly related to academic expectations and academic performance.” (Chemers et al., 2001, p. 61)   Sutton et al. (2011) reported Cronbach's alpha of .83 in their study of academic self-esteem and personal strengths. ASE was highly positively correlated with ACT scores (.24) and GPA (.39)....