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

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

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What makes a test valid?

 

What makes a test valid? is a tricky question. 

The short, and rather obnoxious response is, “nothing.” 

Like reliability, validity is a property of test scores

 rather than tests but more accurately, an interpretation
of the scores.

But it is important to take the question seriously when test-takers and users are wondering how much confidence to place in a test score. As with many aspects of science, the answers can be simply stated but there is a complicated backstory.

Validity Traditions

For many, the traditional views of test score validity will be sufficient. Tests measure constructs. Scientific constructs are ideas that have features that can be measured like reading comprehension, dominance, short-term memory, and verbal intelligence.

Construct validity is not a single entity but rather the current state of knowledge about how a test instrument’s scores have functioned in many settings and in relation to criteria. Construct validity primarily includes findings from studies of content validity, convergent validity and discriminant validity.

Content validity is based on judgment analysis from experts who mostly agree that test items measure the construct (e.g., marital satisfaction).

The other types of validity are based on the concept of correlations with a criterion. Researchers ask participants to take a specific test X along with other tests Y and Z. Test X is the test of interest such as a new math achievement test. Test Y represents other similar tests such as other math tests. When test X and test Y yield similar scores we have evidence of convergent validity.

When test X and test Z yield dissimilar results such as a relationship between our test X math achievement and test Z vocabulary, we have evidence of discriminant validity—a math test ought not to measure vocabulary aside from the minimal vocabulary used in the instructions and word problems. The relationship between the tests is based on a statistic called the validity coefficient, which will vary anytime you have a group of people taking two tests—even the very same people will get different scores on two different testing dates.

Criterion validity compares test scores to some criterion. The relationship between depression test scores measuring depression today is called concurrent validity. The relationship between test scores today and some future measurable performance is predictive validity—for example, a pre-employment test may be correlated with supervisor ratings after six months on the job.

Aside from content validity, most traditional studies are looking at the strength of the relationship between one set of test scores and another.

Factor analysis is a complex correlational procedure that examines the underlying relationship among test items and how they relate to other test items. For example, a set of vocabulary items may be correlated with answers to questions about general knowledge and be considered a “verbal factor” when the two sets of items may be grouped as representing an underlying verbal factor. These abstract underlying factors are sometimes called latent variables or latent traits.

Read more about validity of surveys and tests in CREATING SURVEYS- Chapter 18.

Counselors, read more about validity of test scores in APPLIED STATISTICS: CONCEPTS FOR COUNSELORS- Chapter 20.

Related Post

RELIABILITY 

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