A model is proposed for the description of ordinal test scores based on the definition of true score as expected rank. Derivations from the model are compared with results from clasiscal test theory as developed by Lord and Novick, in particular with respect to parallel tests and composites. An unbiased estimator of population true score from sample data is derived and its variance is shown to decrease with increasing sample size. Population reliability is shown to be analytically related to expected sample reliability, and methods of reliability estimation are discussed.

A dilemma was created for factor analysts by Ferguson (Psychometrika, 1941, 6, 323–329) when he demonstrated that test items or sub-tests of varying difficulty will yield a correlation matrix of rank greater than 1, even though the material from which the items or sub-tests are drawn is homogeneous, although homogeneity of such material had been defined operationally by factor analysts as having a correlation matrix of rank 1. This dilemma has been resolved as a case of ambiguity, which lay in (1) failure to specify whether homogeneity was to apply to content, difficulty, or both, and (2) failure to state explicitly the kind of correlation to be used in obtaining the matrix. It is demonstrated that (1) if the material is homogeneous in both respects, the type of coefficient is immaterial, but (2) if content is homogeneous but difficulty is not, the homogeneity of the content can be demonstrated only by using the tetra chorie correlation coefficient in deriving the matrix; and that the use of the phi-coefficient (Pearsonian r) will disclose only the nonhomogeneity of the difficulty and lead to a series of constant error factors as contrasted with content factors. Since varying difficulty of items (and possibly of sub-tests) is desirable as well as practically unavoidable, it is recommended that all factor analysis problems be carried out with tetrachoric correlations. While no one would want to obtain the constant error factors by factor analysis (difficulty being more easily obtained by counting passes), their importance for test construction is pointed out.

Inference is considered for the marginal distribution of X, when (X, Y) has a truncated bivariate normal distribution. The Y variable is truncated, but only the X values are observed. The relationship of this distribution to Azzalini's “skew-normal” distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for large n. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.

It is shown that approaches other than the internal consistency method of estimating test reliability are either less satisfactory or lead to the same general results. The commonly attendant assumption of a single factor throughout the test items is challenged, however. The consideration of a test made up of K sub-tests each composed of a different orthogonal factor disclosed that the assumption of a single factor produced an erroneous estimate of reliability with a ratio of (n−K)/(n−1) to the correct estimate. Special difficulties arising from this error in application of current techniques to short tests or to test batteries are discussed. Application of this same multi-factor concept to item-analysis discloses similar difficulties in that field. The item-test coefficient approaches √1/K as an upper limit rather than 1.00 and approaches √1/n as a lower limit rather than .00. This latter finding accounts for an over-estimation error in the Kuder-Richardson formula (8). A new method of isolating sub-tests based upon the item-test coefficient is proposed and tentatively outlined. Either this new method or a complete factor analysis is regarded as the only proper approach to the problem of test reliability, and the item-sub-est coefficient is similarly recommended as the proper approach for item analysis.

A formal theory of appropriateness for statistical operations is presented which incorporates features of Stevens’ theory of appropriate statistics and Suppes’ theory of empirical meaningfulness. It is proposed that a statistic be regarded as appropriate relative to statements made about it in case the truths of these statements are invariant under permissible transformations of the measurement scale. It is argued that the use of inappropriate statistics leads to the formulation of statements which are either semantically meaningless or empirically nonsignificant.

A new method of test selection, which attempts to combine the merits of the Toops L-Method with those of the Wherry-Doolittle Method, is presented. It results in integral (unit if desired) positive and/or negative (optional) weights. This flexibility makes the method applicable to all kinds of material and for both selecting items for tests and tests for batteries. An explicit solution of one test construction problem is presented. Necessary changes in method for the solution of five other types of test construction problem are presented. A few cautions are provided for potential users.

The Deterministic, Gated Item Response Theory Model (DGM, Shu, Unpublished Dissertation. The University of North Carolina at Greensboro, 2010) is proposed to identify cheaters who obtain significant score gain on tests due to item exposure/compromise by conditioning on the item status (exposed or unexposed items). A “gated” function is introduced to decompose the observed examinees’ performance into two distributions (the true ability distribution determined by examinees’ true ability and the cheating distribution determined by examinees’ cheating ability). Test cheaters who have score gain due to item exposure are identified through the comparison of the two distributions. Hierarchical Markov Chain Monte Carlo is used as the model’s estimation framework. Finally, the model is applied in a real data set to illustrate how the model can be used to identify examinees having pre-knowledge on the exposed items.

We employ direct numerical simulations to investigate the heat transfer and flow structures in turbulent Rayleigh–Bénard convection in both cylindrical cells and laterally periodic domains, spanning an unprecedentedly wide range of aspect ratios $0.075 \leqslant \varGamma \leqslant 32$. We focus on Prandtl number ${Pr}=1$ and Rayleigh numbers ${{Ra}}=2\times 10^7$ and ${{Ra}}=10^8$. In both cases, with increasing aspect ratio, the heat transfer first increases, then reaches a maximum (which is more pronounced for the cylindrical case due to confinement effects), and then slightly goes down again before it finally saturates at the large aspect ratio limit, which is achieved already at $\varGamma \approx 4$. Already for $\varGamma \gtrsim 0.75$, the heat transfers in both cylindrical and laterally periodic domains become identical. The large-$\varGamma$ limit for the volume-integrated Reynolds number and the boundary layer thicknesses are also reached at $\varGamma \approx 4$. However, while the integral flow properties converge at $\varGamma \approx 4$, the confinement of a cylindrical domain impacts the temperature and velocity variance distributions up to $\varGamma \approx 16$, as thermal superstructures cannot form close to the sidewall.

To assess the psychosocial functioning concerning obsessive-compulsive symptoms (OCS) and/or obsessive-compulsive disorder (OCD) comorbidity in people with schizophrenia, schizoaffective disorder, or bipolar disorder diagnosed in a large case register database in Southeast London. Data were retrieved from the South London and Maudsley NHS Foundation Trust Biomedical Research Centre (SLaM BRC) register using Clinical Record Interactive Search (CRIS) system, a platform allowing research on full but de-identified electronic health records for secondary and tertiary mental healthcare services. Information of schizophrenia, schizoaffective disorder, bipolar disorder diagnosis and OCS/OCD status was ascertained from structural or free-text fields through natural language processing (NLP) algorithms based on artificial intelligence techniques during the observation window of January 2007 to December 2016. Associations between comorbid OCS/OCD and recorded Health of the Nation Outcome Scales (HoNOS) for problems with activities of daily living (ADLs), living conditions, occupational and recreational activities, and relationships were estimated by logistic regression with socio-demographic confounders controlled. Of 15,412 subjects diagnosed with schizophrenia, schizoaffective disorder, or bipolar disorder, 2,358 (15.3%) experienced OCS without OCD, and 2,586 (16.8%) had OCD recorded. The presence of OCS/OCD was associated with more problems with relationships (adj.OR = 1.34, 95% CI: 1.25–1.44), ADLs (adj.OR = 1.31, 95%CI: 1.22–1.41), and living conditions (adj.OR = 1.31, 95% CI: 1.22–1.41). Sensitivity analysis revealed similar outcomes. Comorbid OCS/OCD was associated with poorer psychosocial functioning in people with schizophrenia, schizoaffective disorder, or bipolar disorder. This finding highlights the importance of identification and treatment of comorbid OCS among this vulnerable patient group.

COVID-19 vaccine uptake in healthcare personnel (HCP) is poor. A cross-sectional survey study of behavioral health HCP was performed. Commonly identified reasons for vaccination were protecting others and oneself. Reasons against were a lack of perceived protection, dosing intervals, and side effects. Assessing vaccination attitudes can assist in uptake strategy.

Lithofacies and biostratigraphical analysis has enabled the establishment of a stratigraphic event framework for Ludfordian and Pridoli strata in south Wales and the Welsh Borderland. In SW Wales, the Golden Grove Axis acted as a structural hinge separating the shallow marine storm-influenced Cae’r mynach Seaway from a pediment surface above which Ludfordian colluvium (Abercyfor Formation) was deposited. The Axis seeded four NW-derived river-influenced delta progrades of Leintwardinian to early Pridoli age (Tilestones Formation). A NE-sourced early Pridoli wave-influenced delta deposited the Downton Castle Sandstone Formation (DCSF), coeval to the youngest Tilestones prograde, with a lateral interface existing between Mynydd Epynt and the Clun Forest area. Except for the Malverns area, the DCSF is no longer recognized south of the Neath Disturbance. Early Pridoli forced regression promoted widespread subaerial exposure north of the Neath Disturbance, with incision into tracts close to the Welsh Borderland Fault System. The basinward-shift in facies belts resulted in marine erosion and deposition of a phosphatic ravinement pebble lag. The wave-influenced Clifford’s Mesne Sandstone Formation delta subsequently seeded on the Gorsley Axis with tidally influenced Rushall Formation accumulating in a back-barrier setting. The Pwll-Mawr Formation records the easterly advance of coeval coastal deposits on the western side of the remnant Cae’r mynach Seaway. Behind migrating delta coastlines, green muds accumulated on coastal plains (Temeside Mudstone Formation) with better drained red dryland alluvium (Moor Cliffs Formation) charting expansion of Old Red Sandstone lithofacies. Mid-Pridoli incision preserves the Pont ar Llechau Formation estuarine valley fill.