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Psychometric methods involve several distinct areas of study. First, psychometricians have developed the theory of mental tests. This work can be roughly divided into classical test theory (CTT) and the more recent item response theory (IRT). Second, psychometricians have developed methods for working with large matrices of correlations and covariances. Techniques in this general tradition include factor analysis (finding important underlying dimensions in the data), multidimensional scaling (finding a simple representation for high-dimensional data) and data clustering (finding objects which are like each other). In these multivariate descriptive methods, users try to simplify large amounts of data. More recently, structural equation modeling and path analysis represent more rigorous, statistically sophisticated approaches to solving this problem of large covariance matrices. These methods allow statistically sophisticated models to be fitted to data and tested to determine if they are adequate fits. The key concepts of classical test theory are reliability and validity. A reliable measure is measuring something consistently, while a valid measure is measuring what it is supposed to measure. A reliable measure may be consistent without necessarily being valid, .e.g., a measurement instrument like a broken ruler may always under-measure a quantity by the same amount each time (consistently), but the resulting quantity is still wrong, that is, invalid. For another example, a reliable rifle will have a tight cluster of bullets in the target, while a valid one will center that cluster around the center of the target.
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