Sampling Strategy Research Articles

Dual-wavelength sub-Nyquist sampling scheme for clipping-avoidance photonic ADC

We propose a dual-wavelength scheme for a clipping-avoidance photonic analog-to-digital converter (PADC) operating at the sub-Nyquist sampling rate. The scheme utilizes two characteristics, the phase-wrapping feature of a PADC and the wavelength-sensitive feature of a phase modulator, equivalently performing a dual-modulus (DM) modulo operation to avoid clipping. Coupled with an unwrapping algorithm based on the Chinese remainder theorem (CRT), the proposed scheme enables signal reconstruction from the processed signals independent of the sampling rate. We demonstrated proof-of-concept experiments on a PADC chip fabricated on an LNOI platform. Experimental results show that 1G/2G/4G-baud 10-level pulse amplitude modulation (PAM-10) waveforms were successfully reconstructed at the sub-Nyquist sampling rate of 1/2/4Gs/s, respectively. Our work provides a potential solution to achieve on-chip clipping-avoidance PADCs operating at the sub-Nyquist sampling.

Nonparametric estimation of the cumulative incidence function for doubly-truncated and interval-censored competing risks data.

Interval sampling is widely used for collection of disease registry data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated data if the failure time can be observed exactly and doubly truncated and interval censored (DTIC) data if the failure time is known only to lie within an interval. In this article, we consider nonparametric estimation of the cumulative incidence functions (CIF) using doubly-truncated and interval-censored competing risks (DTIC-C) data obtained from interval sampling scheme. Using the approach of Shen (Stat Methods Med Res 31:1157-1170, 2022b), we first obtain the nonparametric maximum likelihood estimator (NPMLE) of the distribution function of failure time ignoring failure types. Using the NPMLE, we proposed nonparametric estimators of the CIF with DTIC-C data and establish consistency of the proposed estimators. Simulation studies show that the proposed estimator performs well for finite sample size.

Limited Sampling Strategy for Predicting the Area under Plasma Concentration–Time Curve of Nadolol in Healthy Subjects

AbstractNadolol is a hydrophilic β‐adrenoceptor blocker with a relatively long half‐life and negligible metabolism. It is a substrate of P‐glycoprotein and organic anion transporting polypeptide 1A2, and may serve as an in vivo probe drug for the assessment of drug–drug and food–drug interactions mediated by these transporters. In the present study, we aimed to develop limited sampling strategy (LSS) models for predicting the area under the plasma concentration–time curve (AUC0‐∞) of nadolol. Plasma concentration data (Ct) in healthy volunteers reported in four previous studies were randomly divided into a training dataset for model development (n = 15) and a test dataset for model validation (n = 16). By multiple linear regression analysis, we confirmed that four out of the eight models using two time points and all models using three time points met the acceptable criteria. In particular, the three time point models using (C3, C6, and C24) and (C4, C8, and C24) showed better predictive performances with r2 values of 0.983 and 0.980, respectively. In drug interaction studies of nadolol with itraconazole, rifampicin, grapefruit juice, and green tea extract, both LSS models accurately predicted the AUC0‐∞ with percent mean absolute error ≤11% and percent root mean square error ≤12%. In addition, using digitized pharmacokinetic data of nadolol, both LSS models were further validated by predicting the AUC0‐∞ in different doses. The results suggest that the LSS models using three time points allow a reliable prediction of AUC0‐∞ of nadolol in healthy individuals.

Statistical Quality Control on Bread Production using Process Control Chart

In this study, the researchers analyze quality control of bread using attributes P-chart to meet in quality control statistics. The population of this study consisted of all types of bread created by My-Food bakery industry (chocolate bread, butter bread, and round bread), with a manufacturing capacity of 500 packs each day, resulting in a total population of 15000 packages for 30 days. The sampling strategy used in this study was a withdrawal of bread type samples based on judgment sampling and random sampling. Although My-Food bakery created five varieties of bread, the researchers only took three. We may deduce from the SPSS test normalcy that these three types of bread are still within a company's standard limit. Despite the fact that production is under control, the corporation must investigate the manufacturing machinery in order to avoid further faulty products.

Novel sampling strategy for regular nucleic acid testing in low risk areas during epidemics.

Large-scale regular nucleic acid testing (NAT) such as Regular-1/7, played a crucial role in the successful and sustained containment of COVID-19 in China, enabling rapid case detection in low-risk areas. However, Regular-1/7 strategies are extremely costly and time-consuming. To address these challenges and facilitate the broader implementation of large-scale NAT during outbreaks of highly contagious diseases with long incubation periods, we propose a novel sampling strategy called Weighted Hub and Time Sampling (WHTS). This strategy considers the intensity of social activity, the degree of social overlap, and the time interval since the last NAT for each individual. Based on a scale-free contact network model, we simulated the spread of scenario in a community and compared the performance of the WHTS strategy to the Regular-1/7 strategy in terms of cost reduction and shorter alert time. The results show that WHTS-1/14 strategy can save half of the cost, and WHTS-1/7 strategy can alert 1.0 days in advance, compared to Regular-1/7 strategy. Additionally, The WHTS-1/14 strategy also achieves promising results under various scenarios, even though it samples half as many people as the Regular-1/7 strategy. Our study offers a valuable reference for large-scale testing in future efforts to manage emerging infectious diseases.

Multilevel importance sampling for rare events associated with the McKean–Vlasov equation

AbstractThis work combines multilevel Monte Carlo with importance sampling to estimate rare-event quantities that can be expressed as the expectation of a Lipschitz observable of the solution to a broad class of McKean–Vlasov stochastic differential equations. We extend the double loop Monte Carlo (DLMC) estimator introduced in this context in Ben Rached et al. (Stat Comput, 2024. https://doi.org/10.1007/s11222-024-10497-3) to the multilevel setting. We formulate a novel multilevel DLMC estimator and perform a comprehensive cost-error analysis yielding new and improved complexity results. Crucially, we devise an antithetic sampler to estimate level differences guaranteeing reduced computational complexity for the multilevel DLMC estimator compared with the single-level DLMC estimator. To address rare events, we apply the importance sampling scheme, obtained via stochastic optimal control in Ben Rached et al. (2024), over all levels of the multilevel DLMC estimator. Combining importance sampling and multilevel DLMC reduces computational complexity by one order and drastically reduces the associated constant compared to the single-level DLMC estimator without importance sampling. We illustrate the effectiveness of the proposed multilevel DLMC estimator on the Kuramoto model from statistical physics with Lipschitz observables, confirming the reduced complexity from $${\mathcal {O}(\textrm{TOL}_{\textrm{r}}^{-4})}$$ O ( TOL r - 4 ) for the single-level DLMC estimator to $${\mathcal {O}(\textrm{TOL}_{\textrm{r}}^{-3})}$$ O ( TOL r - 3 ) while providing a feasible estimate of rare-event quantities up to prescribed relative error tolerance $$\textrm{TOL}_{\textrm{r}}$$ TOL r .

External evaluation of neonatal vancomycin population pharmacokinetic models: Moving from first-order equations to Bayesian-guided therapeutic monitoring.

Guidelines for vancomycin therapeutic monitoring recommend using a Bayesian approach with a population pharmacokinetic model to estimate the 24 h area under the concentration-time curve over first-order equations. Thus, we performed an external evaluation of population pharmacokinetic models of vancomycin in neonates and compared Bayesian results with those observed in clinical practice via pharmacokinetic equations to improve therapeutic monitoring by proposing optimized initial dosing nomograms and assessing the feasibility of reduced blood sampling strategies using the most predictive models. Models were identified from the literature and evaluated via an external neonatal population. A priori predictive performance was first assessed by prediction-based diagnostics, then by simulation-based diagnostics and a posteriori analyses only if deemed satisfactory; model-informed vancomycin exposure was also compared with reference first-order pharmacokinetic equations. The best-performing models were ultimately subjected to Monte Carlo simulations to develop new initial dosing nomograms offering the highest probability of achieving therapeutic target. A total of 28 population pharmacokinetic models were evaluated in the external dataset, which includes 72 neonates and 380 vancomycin concentrations. Eleven models had an adequate predictive performance with bias ≤ ± 15% and imprecision 30%, while the Bayesian approach yielded over 75% agreement with reference exposure values in most cases. Nonetheless, Capparelli etal. and Mehrotra etal. models performed the best overall, showing the lowest imprecisions of 16.8% and 16.9%, respectively; both models recommended higher dosage regimens than the theoretical nomogram currently applied to favor therapeutic target attainment. We externally evaluated numerous neonatal population pharmacokinetic models of vancomycin and used the most predictive ones to advocate new initial dosing nomograms. Clinical implementation of the Bayesian approach could reduce the time needed to reach therapeutic target and limit the number of blood samples in newborns compared with traditional pharmacokinetic equations.

Maternal exposure to violence and early child behavioural development in Tirana, Albania: Methods, challenges, and fieldwork reflections

This article delineates the methods of the author's PhD in Criminology, carried out at the University of Cambridge from 2019 to 2023. The main aim of the PhD was to explore the pathways between maternal exposure to violence and the behavioural development of two-to-three-year-old children in Tirana, Albania. To achieve this, the author spent 10 months in Tirana collecting data from a sample of 328 mothers and 59 nursery teachers in eight diverse socio-economic research sites. The purpose of this article is to reveal the details of the methodological approach, the meticulous planning, as well as the obstacles faced when implementing the PhD project. It provides a thorough description of the research design, sampling strategy, measurement tools, ethical considerations, data collection challenges, and fieldwork experiences.

Racial Discrimination and Mental Health: Analyzing the Impact of Discrimination, Stress, Depressive Symptoms and Self-Esteem on Anxiety Experiences

ABSTRACT Background Existing research demonstrates that racial inequity influences mental health outcomes. However, few studies simultaneously analyze the multiple factors influencing racial disparities regarding these outcomes. Our study addresses this gap by analyzing the impact of discrimination, stress, self-esteem, racial identity, depressive symptoms, and demographic factors on anxiety symptoms. Methods Participants were adults recruited from a primary care clinic in the Southeastern region of the United States. We utilized a stratified random sampling strategy to select 383 participants. Participants completed a survey designed to assess levels of anxiety, depression, perceived stress, self-esteem, racial identity, experiences with discrimination, and demographic information. A hierarchical regression analyzed which factors most impact symptoms of anxiety. Results Of the 363 participants in our study, the majority were female (71.3%), 57% were White identifying, 43% were Black identifying, and the average age was 54.4 (SD = 12.3). Model 4 accounted for 58% of the variance of anxiety symptoms and included a combination of depressive symptoms, perceived stress, self-esteem, experiences of everyday discrimination, and interaction terms. Within this model, perceived stress (t = 3.81, p < .01), experiences of everyday discrimination, (t = 2.33, p < .01), and income (t = -1.96, p < .01) were significantly associated with increased anxiety. Conclusions and implications Multiple contextual factors influence the relationship between race and anxiety. In particular, anxiety increases with lower rates of self-esteem and income. Conversely, anxiety increases with higher rates of stress, discrimination, and depressive symptoms. Social workers should consider each of these factors when treating patients presenting with symptoms of anxiety.

HCA-RFLA: A SAR Remote Sensing Ship Detection Based on Hierarchical Collaborative Attention Method and Gaussian Receptive Field-Driven Label Assignment Strategy

Ensuring safety at sea has become a primary focus of marine monitoring, driving the increasing adoption of ship detection technology in the maritime industry. Detecting small ship targets in SAR images presents challenges, as they occupy only a small portion of the image and exhibit subtle features, reducing detection efficiency. To address these challenges, we propose the HCA-RFLA algorithm for ship detection in SAR remote sensing. To better capture small targets, we design a hierarchical collaborative attention (HCA) mechanism that enhances feature representation by integrating multi-level features with contextual information. Additionally, due to the scarcity of positive samples for small targets under IoU and center sampling strategies, we propose a label assignment strategy based on Gaussian receptive fields, known as RFLA. RFLA assigns positive samples to small targets based on the Gaussian distribution between feature points and ground truth, increasing the model’s sensitivity to small samples. The HCA-RFLA was experimentally validated using the SSDD, HRSID, and SSD datasets. Compared to other state-of-the-art methods, HCA-RFLA improves detection accuracy by 6.2%, 4.4%, and 3.6%, respectively. These results demonstrate that HCA-RFLA outperforms existing algorithms in SAR remote sensing ship detection.

Trainability barriers and opportunities in quantum generative modeling

AbstractQuantum generative models provide inherently efficient sampling strategies and thus show promise for achieving an advantage using quantum hardware. In this work, we investigate the barriers to the trainability of quantum generative models posed by barren plateaus and exponential loss concentration. We explore the interplay between explicit and implicit models and losses, and show that using quantum generative models with explicit losses such as the KL divergence leads to a new flavor of barren plateaus. In contrast, the implicit Maximum Mean Discrepancy loss can be viewed as the expectation value of an observable that is either low-bodied and provably trainable, or global and untrainable depending on the choice of kernel. In parallel, we find that solely low-bodied implicit losses cannot in general distinguish high-order correlations in the target data, while some quantum loss estimation strategies can. We validate our findings by comparing different loss functions for modeling data from High-Energy-Physics.

Anti-Black racism in Canadian health care: a qualitative study of diverse perceptions of racism and racial discrimination among Black adults in Montreal, Quebec.

Racism has been shown to impact the health of Black persons through its influence on health care, including its expression through implicit biases in provider training, attitudes, and behaviours. Less is known about the experiences of racism in contexts outside of the USA, and how race and racism interact with other social locations and systems of discrimination to shape Black patients' experiences of racism in health care encounters. To help address this gap, this study examined diverse Black individuals' perceived experiences of, and attitudes towards, anti-Black racism and racial discrimination in Canadian health care, specifically in Montreal, Quebec. This descriptive qualitative study adopted a social constructionist approach. Employing purposive maximal variation and snowball sampling strategies, eligible study participants were: self-identified Black persons aged 18 years and older who lived in Montreal during the COVID-19 pandemic, who could speak English or French, and who were registered with the Quebec medical insurance program. In-depth interviews were conducted, and a Framework Analysis approach guided the systematic exploration and interpretation of data using an intersectionality lens. We interviewed 32 participants, the majority of whom were women (59%), university educated (69%), and modestly comfortable financially (41%), but diverse in terms of age (22 to 79 years), country of origin, and self-defined ethnicity. We identified five major themes demonstrating substantial variations in perceived racism in health care that are influenced by unique social locations such as gender identity, age, and immigration history: (1) no perceptions of racism in health care, (2) ambiguous perceptions of racism in health care, (3) perceptions of overt interpersonal racism in health care, (4) perceptions of covert interpersonal racism in health care (including the downplaying of health concerns, stereotyping, and racial microaggressions), and (5) perceptions of systemic racism in health care. Perceptions of anti-Black racism and racial discrimination in Canadian health care are complex and may include intra-racial group differences. This study begins to address the dearth of empirical research documenting experiences of anti-Black racism in health care in Quebec, highlighting a continued need for serious consideration of the ways in which racism may manifest in the province, as well as a need for anti-racist advocacy. Advancing racial health equity requires greater sensitivity from providers and decision makers to variations in Black patients' health care experiences, towards ensuring that they have access to high quality and equitable health care services.

Pengembangan Sumber Daya Manusia pada Produktivitas Kerja di Puskesmas

All individuals who operate actively and professionally in the health sector are considered health human resources, regardless of whether they have earned formal health education or not. The purpose of this study is to ascertain the Health Center's HR management implementation strategy. This study employed a descriptive qualitative methodology. Purposive sampling, nonprobability sampling, or a sampling strategy based on particular criteria were used to choose the study participants. Documentation, interviews, and observation are some of the data collection techniques. The study's findings show that the HR development management communication components and the recommendations for the Health Center HR development policy have been successfully applied. Even with the improvement in quality, there are still a number of barriers preventing resources from being used efficiently.

Comparative study of sampling strategies for machine learning-based landslide susceptibility assessment

Comparative study of sampling strategies for machine learning-based landslide susceptibility assessment

Students’ ratings to evaluate effective teaching practices of secondary schools in Bangladesh

PurposeInternational studies have emphasised the importance of effective teaching for student learning. However, few studies have investigated teaching practices in Bangladesh. The purpose of the study set out to explore the mathematics teaching behaviour of secondary school level of Bangladesh.Design/methodology/approachA convenient sampling strategy was used to collect 502 grade nine students’ perceptions from 15 mathematics classes within Dhaka Metropolitan City (DMC). A valid and reliable student questionnaire was used where the students rated their mathematics teachers' teaching behaviours identified in the dynamic model of educational effectiveness (DMEE).FindingsThe findings from the quantitative analysis of the student evaluations revealed that the mathematics teachers demonstrated structuring, modelling, questioning, teacher–student interactions and teacher dealing with misbehaviours in their daily classroom teaching.Research limitations/implicationsA small sample of mathematics classes were chosen in the study; hence, the findings may not be totally representative nor generalisable to the population of secondary mathematics teachers within Dhaka, Bangladesh.Practical implicationsThe study conducted in Bangladesh contributes to the international dimension to educational effectiveness research. The findings from the study provide partial support for teaching factors and dimensions in DMEE (Creemers and Kyriakides, 2008), and emphasise the need for further studies, particularly in cross-cultural contexts.Originality/valueThis is the first study to evaluate teaching behaviours of secondary mathematics teachers through students’ perceptions in Bangladesh. It contributes important insights about teaching behaviours to inform the development of evidence-based policy and practice on quality teaching in the region.

Kawí Tamiruyé: a permanent research forest plot in the Sierra Tarahumara

This study characterizes the dasometric and structural parameters of a permanent research plot in northern Mexico. From a total census, 2165 trees (n) were recorded in an area of 1.4 ha-1 and, through the application of various sampling schemes, dasometric variables, and diversity indices were estimated for comparison with the census of a reference plot. We calculated the following dasometric measurements, Quadratic Mean Diameter (QMD)= 12.16 cm, Crown Area (CA)= 61.6%, Reineke's Stand Density Index (SDI)= 668 individuals, Basal Area (BA)= 25.16 m2, Total Volume (Vol)= 158.83 m3 ha-1, aboveground biomass (AGB= 142.78 Mg ha-1) and Carbon (C= 71.39 Mg ha-1). Ecologically, the species with the highest importance value index (IVI) were P. engelmannii and J. deppeana (50.8% and 35%, respectively). The Simpson's dominance index (δ)= 0.39 and diversity (λ)= 0.61 were low, as was the Shannon-Weaver index of diversity (H'= 1.3), which is in agreement with the Margalef index (DMg= 1.04). The value of Pielou's evenness (J'= 0.53) confirmed low abundance. Equidistant systematic sampling at 40 m was closer to the reference census, presenting lower values in the mean and variance estimators compared to the other sampling methods. The results can be included in management portfolios to improve decision-making. Although further studies on site size, inclusion of additive indices, and operational costs are required.

A Quantitative Risk Assessment Model for Listeria monocytogenes in Non-Ready-to-Eat Frozen Vegetables

A quantitative risk assessment (QRA) model was developed to evaluate the risk of invasive listeriosis from the consumption of non-ready-to-eat (non-RTE) frozen vegetables. On a lot basis, the QRA model simulates Listeria monocytogenes concentration and prevalence in a “Processing module” that comprises blanching, potential recontamination and packaging, any post-packaging inactivation treatment, and within-lot end-product testing and in a subsequent “Consumer’s handling module” that encompasses portioning of frozen vegetables, defrosting, and cooking. Based on available published data, the model was coded in nine sequential R functions designed to assess the effectiveness of blanching, the improvement in processing environment hygiene, the implementation of sampling schemes at the end of processing, and improved consumer instructions on the product’s package. In a reference scenario, the model estimated that 9.4% of 500 g packages of frozen vegetables would be contaminated, although at mean levels lower than 10 CFU/g, and assuming that 20% of the portions of frozen vegetables would be left to thaw at room temperature for 2 h, the lot-level mean risk of listeriosis in the susceptible population would be 2.935 × 10−14 (median 5.446 × 10−15) for uncooked 50 g servings and 2.765 × 10−17 (median 5.184 × 10−18) for cooked 50 g servings. Analysis of selected scenarios suggested that not cooking the non-RTE product contributes to the risk to a greater extent than the level of contamination in the incoming raw vegetables, the latter in turn being more influential than the level of contamination in the processing environment. The QRA model is freely available as an R package with full documentation and can be used as a tool to inform the consideration of strengthened risk management measures in view of the current changes in consumer behavior and new diet trends.

Spectrally selective and interleaved water imaging and fat imaging (siWIFI).

To develop a novel imaging sequence that independently acquires water and fat images while being inherently insensitive to motion. The new sequence, termed spectrally selective and interleaved water imaging and fat imaging (siWIFI), uses a narrow bandwidth RF pulse for selective excitation of water and fat separately. The interleaved acquisition method ensures that the obtained water and fat images are inherently coregistered. A radial sampling strategy further reduces motion-induced artifacts. Phantoms with lipid concentrations ranging from 0% to 50% were scanned to measure fat fraction. Moreover, healthy volunteers were scanned to assess the in vivo feasibility of fat fraction measurement at the hip, knee, and liver. In vivo fat fraction measurements were compared with those from vendor-provided iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) scans. Furthermore, a magnetization transfer (MT) preparation module was incorporated to demonstrate the feasibility of simultaneous measurement of fat fraction and MT ratio utilizing the siWIFI framework. The phantom fat fractions measured by siWIFI showed excellent correlation with lipid concentrations (R2 = 0.9995, p < 0.0001). In vivo studies demonstrated that the fat fractions obtained from siWIFI were comparable to those from IDEAL. Additionally, siWIFI demonstrates reduced motion artifacts from pulsatile flow in knee imaging compared to IDEAL scans and exhibits less sensitivity to respiratory motion in liver imaging compared to IDEAL scans without breath-hold. The knee imaging study demonstrated that MT-prepared siWIFI is capable of generating fat fraction and MT ratio maps simultaneously. The proposed siWIFI sequence allows selective water-fat imaging and quantification with reduced motion artifacts.

Mapping the prevalence and covariates associated with home delivery in Bangladesh: A multilevel regression analysis.

Bangladesh has made an intense effort to improve maternal healthcare facilities including facility delivery, but the number of home deliveries is still very high. Therefore, this study aims to find out district-wise prevalence and determine the individual and community-level predictors of home delivery among women in Bangladesh. Data were derived from the Multiple Indicator Cluster Survey (MICS) 2019, a nationwide cross-sectional survey in Bangladesh. A final sample of 9,166 (weighted) women who gave birth in the two years preceding the survey were included in this study. Considering the two-stage cluster sampling strategy adopted by MICS, we used multilevel (2-level) logistic regression analysis to find out the correlates of home delivery. The overall weighted prevalence of home delivery was 46.41% (95% confidence interval [CI]: 45.39-47.43). The highest prevalence was observed in Bandarban district (84.58%), while the lowest was found in Meherpur district (6.95%). The intercept-only regression model demonstrates that the likelihood of women from various clusters having home delivery varied significantly (variance: 1.47, standard error [SE]: 0.117), indicating the applicability of multilevel regression modeling. The multilevel regression analysis showed that women with higher education, wealth status and ANC visit, and those aged >18 years at first marriage/union were associated with lower odds of delivering child at home compared to their counterparts. While women from age group of 35-49 years, whose last pregnancy was unintended were more likely to deliver child at home. In addition, those respondents belonging to a community that had higher wealth status, women's education level, and exposure to media showed lower odds of having delivery at home. The finding indicates that delivery at home is still high in Bangladesh. Targeted interventions to reduce home delivery are urgently needed in Bangladesh to tackle adversities during deliveries and save mothers from the consequences.

Detection Probabilities of Flathead Catfish in Small Kansas Impoundments

Abstract A primary challenge of Flathead Catfish Pylodictis olivaris management is uncertainty associated with sampling strategies and resulting ambiguity in population-level information. Assessment of impoundment and environmental conditions that affect detection probability may aid in reducing sample variance and benefit inferences regarding changes to Flathead Catfish populations. We sampled eight small impoundments in Kansas (37 – 114 surface ha) using low frequency electrofishing in summer, 2021. We revisited sites nine times over three months using an occupancy modeling framework to estimate the influence of impoundment and environmental conditions on detection probability of Flathead Catfish. We employed an information theoretic approach and ranked models built with impoundment as a random effect and three environmental variables predicted to influence detection of Flathead Catfish in small impoundments. Detection probability across all populations was 0.526 (SE = 0.020) and was influenced by water temperature, mean depth of the impoundment, and proportion of impoundment sampled. Generally, detection probability increased with all measured variables. The inclusion of detection probability in assessments of Flathead Catfish in small impoundments can inform interpretation of catch-related metrics. Further, variable detection suggests collection of multiple samples during a defined sampling period might be more suitable for characterizing populations than a single sample.