# Measurement Development and Validation in Research: Statistical Techniques and Illustrations

Lihua Xu (University of Central Florida, USA)
DOI: 10.4018/978-1-4666-7409-7.ch022
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## Abstract

This chapter describes the importance of measurement in social research and education research. In order to validly compare across groups, whether it is age, gender, ethnicities, or cultures, measurement invariance needs to be established. This is accomplished through single-group and multi-group confirmatory factor analysis. The procedural approach is presented with a detailed illustration from real research in servant leadership in K-12 principals in the United States. Second-order confirmatory factor analysis is described due to its popularity. Procedural steps are cited, and an example is given for illustration. As a major statistical technique in instrument development, exploratory factor analysis is discussed and illustrated at the beginning of this chapter.
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## Structural Equation Modeling And Confirmatory Factor Analysis

Structural equation modeling (SEM) refers to a general approach of multivariate data analysis that models the relations between observed and latent variables. SEM is the multivariate data analysis method that has undergone the most refinement and extension over the years and has continued to be developed (Hershberger, 2003). In comparison to the traditional regression analysis, ANOVA or MANOVA, SEM has the advantage of taking the measurement error into consideration while comparing group differences.

## Key Terms in this Chapter

Measurement: It is used interchangeably with instrument. It refers to the questionnaire or inventory etc. that researchers use to collect data to test their research hypothesis.

Multi-Group Confirmatory Factor Analysis: It is a statistical technique used to test measurement invariance. It is confirmatory by nature and theory based.

Latent Variables: It is used interchangeable with factors, constructs, unobserved variables. It is the underlying variables that cause the intercorrelations among observed variables.

Measurement Invariance: it refers that the measurement can be used in the groups other than the one it was originally developed for without bias. Testing of measurement invariance between groups involves a few hierarchical steps with constraints added as the hierarchy is becoming more stringent.

Confirmatory Factor Analysis: It is one category of statistical techniques in factor analysis. Different from exploratory factor analysis, confirmatory factor analysis tests the theoretical model against data to see how closely the hypothesized model fit the data. The model fit is evaluated based on goodness-of-fit indices, factor loadings, residuals, modification indices etc.

Second-Order Multi-Group Confirmatory Factor Analysis: Second-order factors cause the intercorrelations among first-order factors. The procedures of conducting second-order multi-group confirmatory factor analysis is similar yet not identical to those in conducting multi-group confirmatory factor analysis. They are of higher levels in measurement invariance testing.

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