The Professional Counselor | Volume 11, Issue 3 269 Psychometric Term Technical Definition Layperson’s Definition Factorial Validity See internal structure. See internal structure. Higher-Order Confirmatory Factor Analysis Extension of confirmatory factor analysis for examining nested models and determining if a second-order (or beyond) latent variable explains the co-variation between the single-order factors. A type of confirmatory factor analysis for identifying if the relationship between factors is explained by a larger and more general latent variable. Internal Structure A method for measuring construct validity that involves the degree to which the relationships among test items and test components conform to the construct that the proposed test score interpretations are based upon. One way to examine the construct validity of test scores by evaluating how, if at all, and in what ways the test questions group together to form factors. Latent Variable Theoretical or abstract traits that are inferred based on the compilation of scores on a series of observed variables. A variable that cannot be measured directly by one test question; for example, a group of observed variables about temperament might collectively measure the latent variable of personality. Multiple-Group Confirmatory Factor Analysis Extension of confirmatory factor analysis for examining the invariance (psychometric equivalence) of instrumentation across subgroups of a larger sample or population. A type of confirmatory factor analysis for evaluating if the scales/subscales of a test have the same meaning with smaller groups of a larger sample. Observed Variable Data that is directly measured, usually by one test item. Information that can be gathered directly from a single test question; for example, asking a test taker to specify their age. Psychometrics The field of study centered on the theory and practice of psychological measurement. Approaches and strategies for measuring the mental and emotional states of human beings. Validity The degree to which the inferences made from test scores accurately reflect the test taker’s experiences. The extent to which a test actually measures what the test developers claim it measures. Note. Italicized terms are defined in this figure. Exploratory Factor Analysis EFA is “exploratory” in that the analysis reveals how, if at all, test items band together to form factors or subscales (Mvududu & Sink, 2013; Watson, 2017). EFA has utility for testing the factor structure (i.e., how the test items group together to form one or more scales) for newly developed or untested instruments. When evaluating the rigor of EFA in an existing psychometric study or conducting an EFA firsthand, counselors should consider sample size, assumption checking, preliminary testing, factor extraction, factor retention, factor rotation, and naming rotated factors (see Figure 2). EFA: Sample Size, Assumption Checking, and Preliminary Testing Researchers should carefully select the minimum sample size for EFA before initiating data collection (Mvududu & Sink, 2013). My 2021 study (Kalkbrenner, 2021b) recommended that the minimal a priori sample size for EFA include either a subjects-to-variables ratio (STV) of 10:1 (at least 10 participants for each test item) or 200 participants, whichever produces a larger sample. EFA tends to be robust to moderate violations of normality; however, results are enriched if data are normally distributed (Mvududu & Sink, 2013). A review of skewness and kurtosis values is one way to test for univariate normality; according to Dimitrov (2012), extreme deviations from normality include skewness values > ±2 and kurtosis > ±7; however, ideally these values are ≤ ±1 (Mvududu & Sink, 2013). The ShapiroWilk and Kolmogorov-Smirnov tests can also be computed to test for normality, with non-significant p-values indicating that the parametric properties of the data are not statistically different from a normal
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