To illustrate how a G theory-based analysis might im-prove testing accuracy, let’s further develop our example of the hypothetical medical test. Suppose that the medical test in the example problem involves a laboratory analy-sis of a specimen provided by a patient. Suppose further that a team of expert medical researchers identify three variables or potential sources of error over which the collection of test results tend to vary and which might be relevant to the outcome of the medical test in question. The first identified potential source of error concerns the occasion on which the patient is tested. Specifically, the researchers suspect that short-term fluctuations in patient values may lead to inconsistent test results. Hence, the test outcome may depend on when the patient was tested. For purposes of this illustration, we will designate this type of error as “Error Type 1”. The second hypothesized source of error (Error Type 2) relates to an unobservable and temporally stable patient attribute that causes certain patients to be consistently more or less likely to generate false positive or false negative test results. The third identified error source (Error Type 3) is related to labo-ratory processing. In particular, the researchers hypothe-sized that variation in laboratory procedure may contrib-ute to the generation of false negative or false positive test results.
In order to understand how these sources of error in-fluence the test’s outcome, the researchers design an ex-periment that samples test results from across the vari-ables that tend to vary in the real world administration of the test within the population and that are hypothesized to contribute to error. The experiment draws a large ran-dom sample of patients from the clinical population of interest. Each patient in the sample is scheduled for mul-tiple random appointment times at a clinic where speci-mens are collected. After each clinic visit, the collected specimen is divided into sub samples and sent for proc-essing at multiple randomly selected laboratories. In G study terminology, the experiment’s object of measure-ment is patient (p), and the two study variables over which sampling occurred, usually referred to as facets, are occasion (o) and laboratory (l). For purposes of analysis, the test’s outcomes are analyzed using analysis of variance (ANOVA) with each cell containing the re-sult of a single test outcome (i.e. either positive or nega-tive, 0/1, or a continuous variable with or without a threshold value). Equation (5) displays the G study model for the decomposition of the total observed score vari-ance σ2(Xpol) into seven variance components that are estimated using ANOVA-based mean squares to derive estimates of the quantitative effects that compose a single test outcome (Xpol).