Content Validity

What sort of hypotheses does content validity include?

Relationships among constructs, structure of constructs

What are the steps in McQuitty’s elementary linkage analysis (cluster analysis)?

Begin with set of variables measured on a group of people to operationalize a construct that has an underlying multidimensional structure

Compute intercorrelation matrix of the scores, including both upper and lower triangles

Identify the highest correlation for each variable (column)

Find the highest correlation in the matrix, beginning the first cluster

Identify any other variables that have their highest correlation with variables in the cluster, adding them to the cluster

Repeat the previous two steps to form additional clusters until run out of variables

What is a cluster?

Subset of variables that each has its highest correlation with another variable in the cluster

What is this?

Visual diagram of cluster linkages

What is factor analysis?

Method for analyzing intercorrelations among a set of variables in order to determine the number of factors (dimensions) underlying those intercorrelations; creates constructs (factors) that account for the shared variance of variables as evidenced in the observed correlation matrix

How are cluster and factor analysis different?

Cluster analysis classifies entire variance (i.e. variance is kept intact) while factor analysis partitions the variance of each variable and allocates portions of it to potentially different factors

What is a factor?

Hypothesized construct assumed to account for portions of the common variance among a subset of variables

What are some uses of factor analysis?

Content validation (does content of instrument adequately reflect hypothesized structure of the construct it is intended to measure?)

Instrument construction (do the questions/items in instrument measure a single construct or is it multidimensional?)

Assessment of dimensionality (does test measure more than one dimension or just a single general dimension?)

What are the two types of dimensionality analysis?

Component analysis and factor analysis

How are component and factor analysis different?

Component analysis uses a correlation matrix with 1.0s on the diagonal (total variance) while factor analysis uses a matrix with some estimate of the common variance on the diagonal

What are the three types of variance that factor analysis divides a variable into?

Common, unique, and error variance

What is common variance?

Variance that a variable has in common with other variables, quantified in “factor loading” of a variable on a given factor

What is unique variance?

Variance that is “reliable” but not correlated with other variables in the matrix

What is error variance?

Variance that is random and does not correlate with other variables in the matrix

What is factor loading?

Correlation of the variable with the factor

What is h² in factor analysis?

Proportion of the variable variance accounted for by the factors (communality)

What is eigenvalue in factor analysis?

Sum of the squared factor loadings, aka the number of units of variance accounted for by the factor

What values does factor rotation change? What values does it not change?

Changes the factor loadings and can change eigenvalues; does not change variable communalities

What is a squared multiple correlation?

Estimates of the common variance for each variable, proportion of variance of each variable in common with others, utilized by factor analysis

How do you assess validity of factor analysis?

Create factor analysis correlation matrix from the data

Create factor analysis correlation matrix from randomly generated data

Create a screeplot of eigenvalues of the two matrices, compare; those that are substantially different from random data account for common variance, while those that are the same as random data do not