Another reason why normalized gain should continue to be used to analyze concept inventories (and estimate learning rates)

Jairo Navarrete; Valentina Giaconi; Gonzalo Contador; Mariano Vazquez

Home/Archive/arXiv

arXiv · 2407.07730

Another reason why normalized gain should continue to be used to analyze concept inventories (and estimate learning rates)

Jairo Navarrete·Valentina Giaconi·Gonzalo Contador·Mariano Vazquez

View original source ↗Read source document ↗Export metadata ↓

Abstract

A transformation called normalized gain (ngain) has been acknowledged as one of the most common measures of knowledge growth in pretest-posttest contexts in physics education research. Recent studies in math education have shown that ngains can also be applied to assess learners' ability to acquire unfamiliar knowledge, that is, to estimate their "learning rate". This quantity is estimated from learning data through two well-known methods: computing the average ngain of the group or computing the ngain of the average learner. These two methods commonly yield different results, and prior research has concluded that the difference between them is associated with a pretest-ngains correlation. Such a correlation would suggest a bias of this learning measurement because it implies its favoring of certain subgroups of students according to their performance in pretest measurements. The present study analyzes these two estimation methods by drawing on statistical models. Our results show that the two estimation methods are equivalent when no measurement errors exist. In contrast, when there are measurement errors, the first method provides a biased estimator, whereas the second one provides an unbiased estimator. Furthermore, these measurement errors induce a spurious correlation between the pretest and ngain scores. Our results seem consistent with prior research, except they show that measurement errors in pretest and posttest scores are the source of a spurious pretest-ngain correlation. Consequently, estimating learning rates might effectively provide unbiased estimates of knowledge change that control for the effect of prior knowledge even in the presence of pretest-ngain correlations.

Explore related subjects

stat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Jairo Navarrete, Valentina Giaconi, Gonzalo Contador, Mariano Vazquez. 2024-07-10. Another reason why normalized gain should continue to be used to analyze concept inventories (and estimate learning rates). https://arxiv.org/abs/2407.07730

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Privacy-Preserving Causal Meta-Mediation Analysis with Survival Outcomes

Privacy and data-governance constraints often prevent pooling individual-level data across studies, limiting the use of conventional approaches for causal media- tion analysis in multicenter settings. We propose a federated causal meta-mediation framework for right-censored time-to-event outcomes that enables collaborative es- timation without sharing individual-level data. Our framework targets natural indirect effects in a prespecified population by combining information on mediator and outcome mechanisms across distributed data sources. A site-by-site identifi- cation strategy further allows heterogeneity across data sources to be character- ized, with a variance decomposition separating outcome-related, mediator-related, and interaction components. We develop federated one-step and targeted maxi- mum likelihood estimators that accommodate data-adaptive and machine-learning methods for nuisance-function estimation. The finite-sample performance of the proposed estimators is evaluated through numerical simulations. To illustrate the practical utility of the framework, we apply it on data from the French National Health Data System to evaluate the role of methotrexate coprescription in explain- ing the effect of TNFi versus IL-12/23 inhibitor therapy on treatment persistence among psoriatic patients.

stat.AP↗

arXiv2026

Geospatial Foundation Models Capture Health-Relevant Dimensions of Place Beyond Conventional Social Risk Indices

Area-based social risk indices summarize residents' socioeconomic conditions but incompletely capture physical features of place that may affect health. We evaluated whether numerical representations of physical place produced by four geospatial foundation model families from 2022 satellite data explained residual variance in tract-level associations between the Area Deprivation Index, Social Deprivation Index, and Social Vulnerability Index with health outcomes. We used LightGBM to predict variables from the American Community Survey and 40 chronic disease and health-behavior outcomes from CDC PLACES across 82,646 census tracts in the contiguous United States, evaluating performance across 10 held-out states. Among survey variables, models were moderately predictive of some variables including housing type (R-squared up to 0.54) but weak for disability, unemployment, and income disparity. For health outcomes, models explained up to 54% of variance left unexplained by social risk indices, with the largest gains for annual checkups, arthritis, and high blood pressure. Mean total variance explained by geospatial foundation models across the 40 health-related outcomes increased from 0.31 in the smallest tract-size decile to 0.39 in the largest. Geospatial foundation models capture health-relevant features of place not represented by conventional social risk indices and may usefully augment them in epidemiological analyses.

stat.AP↗

arXiv2026

A spatiotemporal negative binomial model with dynamic dispersion: An application to Tuberculosis infections

Tuberculosis (TB) remains a critical public health concern in Brazil, characterized by pronounced spatial heterogeneity and fluctuating temporal volatility. In this paper, we study monthly TB notifications across 61 microregions of Sao Paulo state from 2001 to 2024. To do this, we introduce a negative binomial spatial integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) model featuring jointly dynamic conditional means and time-varying dispersion. To capture inter-regional spillovers, we incorporate both discrete adjacency structures and a novel continuous distance-based formulation leveraging the Matern correlation function. Parameter estimation via conditional maximum likelihood employs a two-step profile-likelihood iterative scheme, demonstrating solid finite-sample performance in simulation studies. Applied to the Sao Paulo TB surveillance data, the framework substantially outperforms standard Poisson and fixed-dispersion spatiotemporal baselines in empirical fit and uncertainty quantification, maintaining nominal 95% predictive coverage across both dense metropolitan centers and rural microregions. Our results reveal marked spatial heterogeneity in baseline incidence, dynamic overdispersion driven by localized outbreaks, and short-range spatial interaction decay. By accurately modeling spatiotemporal volatility, the proposed methodology provides a robust statistical tool to support public health surveillance, policy-making, and resource allocation.

stat.AP↗