Stephen Woodcock

Improvements in international assessment scores are typically reported as aggregate national gains, yet whether such gains are shared equitably across a system’s structural features is less understood. Adopting a school-composition perspective, this study treated gender, socioeconomic composition, and early literacy and numeracy readiness as structural features of Saudi Arabia’s gender-segregated schooling system and examined how their associations with Grade 4 mathematics achievement changed across the Trends in International Mathematics and Science Study (TIMSS) 2015, 2019, and 2023 cycles, spanning the Vision 2030 reform period. Data from 15,305 students were aggregated into 84 structural groups and analysed using a survey-design-corrected Weighted Least Squares General Linear Model. Achievement rose across the period, and the difference favouring girls’ school groups narrowed from approximately 60 scale points in 2015 to a non-significant 13.14 points in 2023, driven predominantly by faster improvement in boys’ school groups; this was the most robust finding. The socioeconomic gradient was widest in 2019, although the magnitude of this estimate was sensitive to influential groups. Early literacy and numeracy readiness showed a positive association that did not survive the exclusion of influential observations. These patterns describe changes during the reform period and cannot be attributed to the reform itself.

Empirical researchers who draw conclusions from statistical hypothesis tests have long been urged to be more thoughtful about their statistical designs, and to provide more modest interpretations of their findings. To support such behavioral change, we present a novel visualization tool for setting sample sizes and analyzing summary data. The core idea is to present multiple test options in the design phase of research, and to present alternative interpretations of summary data in the analysis phase. Our interactive tool is underpinned by a mathematically rigorous multiple testing procedure featuring one-sided t-tests against margins of material significance (i.e., practically meaningful effect sizes). Its presentations resemble the funnel plots developed for statistical meta-analyses. The tool is applied to studies from three different fields to illustrate how it might encourage better statistical design and more nuanced analysis and reporting.

Deployment of coral nurseries by stakeholder-led coral propagation practices has been increasingly adopted on Australia’s Great Barrier Reef (GBR) to meet an urgent need for enhanced ecological resilience at targeted reef sites. While coral propagation techniques using various nursery designs have been established for decades, limited research has explored how these structures interact with reef fish assemblages that perform key ecological functions. To examine fish responses to nursery coral structures widely used on the northern GBR, 48 floating mid-water nurseries with varying coral compositions were evaluated across 7 moorings at 4 reefs using short-format video (9 min) surveys benchmarked against long-format video (60 min) surveys. Across surveys, we explored the extent to which nurseries have developed into novel habitats that support diverse fish assemblages. GoPro® surveys recorded over 2333 fishes from 24 families, with Acanthuridae observed in 72% of all surveys, Scarinae in 69%, and Pomacentridae in 53%. Nursery coral cover ranged from 0-75% and was the main determinant of fish abundance, which also increased with greater coral and morphological richness. However, fish diversity and richness showed no clear pattern with coral composition on nursery structures. These findings suggest that maintaining higher coral cover and a diversity of coral morphologies may enhance fish abundance on nurseries; however, further research is needed to determine how fish diversity influences nursery outcomes, particularly in relation to coral growth and survival. We consider these findings alongside long-standing coral reef ecological research to discuss the potential functional value and broader appreciation of fish assemblages in coral nursery propagation practices.

Quantifying phenotypic plasticity, the capacity of organisms to adjust phenotypes in response to environmental changes, is essential for understanding ecological and physiological resilience under climate stress. However, existing methods often lack flexibility and precision, especially under multi‐dimensional environmental conditions. Here, we introduce a novel statistical approach, the Environmentally Standardized Plasticity Index (*ESPI), which integrates Hedges' g for effect size quantification and Euclidean distance for characterizing environmental variability. We validated this method using both simulated datasets and empirical data from the marine diatom Thalassiosira weissflogii , investigating five key phenotypic traits over 7 days under varying temperature, irradiance, and nutrient conditions. Our findings indicate distinct temporal patterns of plasticity: certain traits, such as photosynthetic efficiency (alpha) and saturation irradiance ( E _k ), demonstrated high initial plasticity followed by gradual acclimation, whereas others, like pigment composition, exhibited delayed phenotypic responses. This temporal dimension highlights the critical role of the growth phase in shaping plasticity responses. The proposed *ESPI method provides a robust, intuitive, and versatile framework for quantifying phenotypic plasticity, offering significant advances in predicting organismal adaptation to environmental change.

The Monty Hall problem and the Sleeping Beauty paradox are two of the best-known problems in probability theory and information theory. The essence of both is asking what credence a player should give to one of two options, when the options presented have been informed by a decision made by another intelligent agent, based on information unavailable to the player. The solution to the Monty Hall problem is largely well established, but there is no such consensus for Sleeping Beauty. While most commenters advocate for the so-called thirder solution, there remains a robust defence of the dissenting halfer viewpoint. Here, we demonstrate that these two famous problems can be simulated from the same simple experiment and thus are, in fact, entirely equivalent. As such, we also advocate for the thirder solution to Sleeping Beauty, in line with the equivalent result for Monty Hall. Despite this defence of the thirder position, we argue that many of the published statements made in favour of this conclusion are either misleading or incorrect, owing to ambiguous notation regarding frames of reference and knowledge. Similar issues have led to flawed attempts at resolving other paradoxes, including the Two Envelope paradox and the Absent-Minded Driver paradox.

Oxygen (O₂) availability is essential for healthy coral reef functioning, yet how continued loss of dissolved O₂ via ocean deoxygenation impacts performance of reef building corals remains unclear. Here, we examine how intra‐colony spatial geometry of important Great Barrier Reef (GBR) coral species Acropora may influence variation in hypoxic thresholds for upregulation, to better understand capacity to tolerate future reductions in O₂ availability. We first evaluate the application of more streamlined models used to parameterise Hypoxia Response Curve data, models that have been used historically to identify variable oxyregulatory capacity. Using closed‐system respirometry to analyse O₂ drawdown rate, we show that a two‐parameter model returns similar outputs as previous 12th‐order models for descriptive statistics such as the average oxyregulation capacity (T_pos) and the ambient O₂ level at which the coral exerts maximum regulation effort (P_cmax), for diverse Acropora species. Following an experiment to evaluate whether stress induced by coral fragmentation for respirometry affected O₂ drawdown rate, we subsequently identify differences in hypoxic response for the interior and exterior colony locations for the species Acropora abrotanoides, Acropora cf. microphthalma and Acropora elseyi. Average regulation capacity across species was greater (0.78–1.03 ± SE 0.08) at the colony interior compared with exterior (0.60–0.85 ± SE 0.08). Moreover, P_cmax occurred at relatively low pO₂ of 2 availability, these factors corresponded to differences in mean intra‐colony oxyregulation, suggesting that lower variation in dissolved O₂ corresponds with higher capacity for oxyregulation. Collectively, our data show that intra‐colony spatial variation affects coral oxyregulation hypoxic thresholds, potentially driving differences in Acropora oxyregulatory capacity.

Researchers across many fields routinely analyze trial data using Null Hypothesis Significance Tests with zero null and p < 0.05. To promote thoughtful statistical testing, we propose a visualization tool that highlights practically meaningful effects when calculating sample sizes. The tool re-purposes and adapts funnel plots, originally developed for meta-analyses, after generalizing them to cater for meaningful effects. As with traditional sample size calculators, researchers must nominate anticipated effect sizes and variability alongside the desired power. The advantage of our tool is that it simultaneously presents sample sizes needed to adequately power tests for equivalence, for non-inferiority and for superiority, each considered at up to three alpha levels and in positive and negative directions. The tool thus encourages researchers at the design stage to think about the type and level of test in terms of their research goals, costs of errors, meaningful effect sizes and feasible sample sizes. An R-implementation of the tool is available on-line.

In this paper, we propose a six-dimensional nonlinear system of differential equations for the human immunodeficiency virus (HIV) including the B-cell functions with a general nonlinear incidence rate. The compartment of infected cells was subdivided into three classes representing the latently infected cells, the short-lived productively infected cells, and the long-lived productively infected cells. The basic reproduction number was established, and the local and global stability of the equilibria of the model were studied. A sensitivity analysis with respect to the model parameters was undertaken. Based on this study, an optimal strategy is proposed to decrease the number of infected cells. Finally, some numerical simulations are presented to illustrate the theoretical findings.