Reasonable Sample Size Research Articles

Sensitivity analysis and probability modelling of the structural response of a single-layer reticulated dome subjected to an external blast loading

The structural response of a single-layer reticulated dome to external explosions is shaped by many variables, and the associated uncertainties imply non-deterministic results. Existing deterministic methods for predicting the consequences of specific explosions do not account for these uncertainties. Therefore, the impact of the uncertainties associated with these input variables on the structures’ response needs to be studied and quantified. In this study, a parametric uncertainty analysis was conducted first. Then, local and global sensitivity analyses were carried out to identify the drivers of the structural dynamic response. A probabilistic structural response model was established based on sensitive variables and a reasonable sample size. Furthermore, some deterministic empirical methods for explosion-resistance design, including the plane blast load model of CONWEP, the curved blast load model under the 50% assurance level, and the 20% mass-increased method, were used for evaluating their reliability. The results of the analyses revealed that the structural response of a single-layer reticulated dome to an external blast loading is lognormally distributed. Evidently, the MB0.5 method based on the curved reflector load model yielded results with a relatively stable assurance rate and reliability, but CONWEP did not; thus, the 1.2MB0.5 method can be used for making high-confidence simple predictions. In addition, the results indicated that the structural response is very sensitive to the explosion parameters. Based on these results, it is suggested that for explosion proofing, setting up a defensive barrier is more effective than structural strengthening.

Constrained Adjusted Maximum a Posteriori Estimation of Bayesian Network Parameters.

Maximum a posteriori estimation (MAP) with Dirichlet prior has been shown to be effective in improving the parameter learning of Bayesian networks when the available data are insufficient. Given no extra domain knowledge, uniform prior is often considered for regularization. However, when the underlying parameter distribution is non-uniform or skewed, uniform prior does not work well, and a more informative prior is required. In reality, unless the domain experts are extremely unfamiliar with the network, they would be able to provide some reliable knowledge on the studied network. With that knowledge, we can automatically refine informative priors and select reasonable equivalent sample size (ESS). In this paper, considering the parameter constraints that are transformed from the domain knowledge, we propose a Constrained adjusted Maximum a Posteriori (CaMAP) estimation method, which is featured by two novel techniques. First, to draw an informative prior distribution (or prior shape), we present a novel sampling method that can construct the prior distribution from the constraints. Then, to find the optimal ESS (or prior strength), we derive constraints on the ESS from the parameter constraints and select the optimal ESS by cross-validation. Numerical experiments show that the proposed method is superior to other learning algorithms.

When is enough, enough? Questions of sampling in vertebrate ichnology

AbstractSample size is a challenge for most field scientists determined not by the statistically ideal, but by the available. In vertebrate ichnology, track length is an important variable correlating well with the track‐maker’s biology. It is also key to estimating the minimum number of individuals (MNI) present on a trampled horizon. Broad assumptions on biometrics of the track‐makers are often made based on a few prints without consideration for intra‐trackway variability. In this study we use a simple bootstrapping algorithm to explore variance within sample size for a range of trackways with fossil and experimental examples to determine the minimum sample size required to extract linear measurements. Predictably, experimentation shows that inter‐step variability changes with track‐maker and substrate, but the degree of variance is not as marked as previously anticipated. Change‐point modelling suggests that a maximum sample size of 22–25 captures most of the variance present in track length at least; another threshold at 7–10 has been identified, which represents the reasonable sample size minimum. Samples of fewer than seven tracks are subject to large amounts of potential variance and are unlikely to provide reliable and consistent measurements. These sampling thresholds hold across a wide range of depositional environments and track‐makers. We calculate generic standard errors for human track‐makers which may assist the practitioner with small samples to estimate the likely errors, especially when making MNI estimates. The challenge is placed to the wider vertebrate ichnology to explore this issue for other track‐makers and develop similar guidance.

Detection of significant antiviral drug effects on COVID-19 with reasonable sample sizes in randomized controlled trials: A modeling study.

Development of an effective antiviral drug for Coronavirus Disease 2019 (COVID-19) is a global health priority. Although several candidate drugs have been identified through in vitro and in vivo models, consistent and compelling evidence from clinical studies is limited. The lack of evidence from clinical trials may stem in part from the imperfect design of the trials. We investigated how clinical trials for antivirals need to be designed, especially focusing on the sample size in randomized controlled trials. A modeling study was conducted to help understand the reasons behind inconsistent clinical trial findings and to design better clinical trials. We first analyzed longitudinal viral load data for Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) without antiviral treatment by use of a within-host virus dynamics model. The fitted viral load was categorized into 3 different groups by a clustering approach. Comparison of the estimated parameters showed that the 3 distinct groups were characterized by different virus decay rates (p-value < 0.001). The mean decay rates were 1.17 d-1 (95% CI: 1.06 to 1.27 d-1), 0.777 d-1 (0.716 to 0.838 d-1), and 0.450 d-1 (0.378 to 0.522 d-1) for the 3 groups, respectively. Such heterogeneity in virus dynamics could be a confounding variable if it is associated with treatment allocation in compassionate use programs (i.e., observational studies). Subsequently, we mimicked randomized controlled trials of antivirals by simulation. An antiviral effect causing a 95% to 99% reduction in viral replication was added to the model. To be realistic, we assumed that randomization and treatment are initiated with some time lag after symptom onset. Using the duration of virus shedding as an outcome, the sample size to detect a statistically significant mean difference between the treatment and placebo groups (1:1 allocation) was 13,603 and 11,670 (when the antiviral effect was 95% and 99%, respectively) per group if all patients are enrolled regardless of timing of randomization. The sample size was reduced to 584 and 458 (when the antiviral effect was 95% and 99%, respectively) if only patients who are treated within 1 day of symptom onset are enrolled. We confirmed the sample size was similarly reduced when using cumulative viral load in log scale as an outcome. We used a conventional virus dynamics model, which may not fully reflect the detailed mechanisms of viral dynamics of SARS-CoV-2. The model needs to be calibrated in terms of both parameter settings and model structure, which would yield more reliable sample size calculation. In this study, we found that estimated association in observational studies can be biased due to large heterogeneity in viral dynamics among infected individuals, and statistically significant effect in randomized controlled trials may be difficult to be detected due to small sample size. The sample size can be dramatically reduced by recruiting patients immediately after developing symptoms. We believe this is the first study investigated the study design of clinical trials for antiviral treatment using the viral dynamics model.

Endogenous fluctuations in demand and distribution: An empirical investigation

This paper empirically investigates the possibility of self-sustained oscillations at business cycle frequency. The theoretical model considers aggregate economic activity and the functional income distribution in the spirit of Goodwin (1967). In the empirical investigation, we utilize four measures each of economic activity and the labor share for the US post-war macroeconomy. Using Schuster’s periodogram, we first show that these time series have an important frequency peak at about forty quarters. We therefore detrend them with wavelet methods. To allow for nonlinear dynamic interaction, we introduce a feedforward neural network (FNN). This method is first shown to correctly identify stability or a limit cycle in simulations of the theoretical model with reasonable noise and sample size. Estimation results provide some support for a limit cycle in the post-war US, but this evidence is not independent of detrending methods used.

Theoretical basis for reduction of number of survey units of MARSSIM final status survey at decommissioning facilities

To investigate the effects of combining two survey units quantitatively in the final status survey of MARSSIM for a decommissioning facility, an expression for the sample size of combined survey unit was developed, which consists exclusively of related parameters of the two survey units. The simulation results using the expression showed that all combining cases considered always result in a decrease in the overall sample size and that it is beneficial to combine two survey units whose radiological characteristics are similar or not significantly different from each other to obtain more decrease in the overall sample size. The results also show that it is necessary to check the practicability of a specific combining case since not all the combined survey units have reasonable sample sizes to obtain. The results also implied that dividing a single survey unit into two separate survey units would result in an increase in the overall sample size.

Sample size calculation for active-arm trial with counterfactual incidence based on recency assay.

The past decade has seen tremendous progress in the development of biomedical agents that are effective as pre-exposure prophylaxis (PrEP) for HIV prevention. To expand the choice of products and delivery methods, new medications and delivery methods are under development. Future trials of non-inferiority, given the high efficacy of ARV-based PrEP products as they become current or future standard of care, would require a large number of participants and long follow-up time that may not be feasible. This motivates the construction of a counterfactual estimate that approximates incidence for a randomized concurrent control group receiving no PrEP. We propose an approach that is to enroll a cohort of prospective PrEP users and aug-ment screening for HIV with laboratory markers of duration of HIV infection to indicate recent infections. We discuss the assumptions under which these data would yield an estimate of the counterfactual HIV incidence and develop sample size and power calculations for comparisons to incidence observed on an investigational PrEP agent. We consider two hypothetical trials for men who have sex with men (MSM) and transgender women (TGW) from different regions and young women in sub-Saharan Africa. The calculated sample sizes are reasonable and yield desirable power in simulation studies. Future one-arm trials with counterfactual placebo incidence based on a recency assay can be conducted with reasonable total screening sample sizes and adequate power to determine treatment efficacy.

Investigating country image influences after a product-harm crisis

PurposeAlthough international product-harm crises have become more common, the influence of the country image (CI) associated with foreign goods in such crises remains under researched. This study aims to investigate the extent to which the CI of a foreign made product influences consumers’ attribution of blame and trust and, ultimately, their future purchase intentions after the product is involved in a crisis.Design/methodology/approachA 2 (country) × 3 (crisis type) quasi experimental design was used, with data collected from Australia (n = 375) and China (n = 401).FindingsCI can influence attribution of blame, subsequent levels of trust and likely purchase intentions. Australian and Chinese consumers have different views when it comes to trusting a company or placing blame, depending on the country of origin or the type of crisis. The direct and positive effect of CI on consumer purchase intentions following a product-harm crisis is sequentially mediated by attribution of blame and trust. Trust is the most powerful influence on future purchase intentions in both samples.Research limitations/implicationsIn this research, only one type of crisis response strategy (no comment) was used. Thus, the results of this study must be viewed with caution when considering outcomes relating to other response options. Additionally, the testing was limited to only two samples, focussing on three countries (England, China, Vietnam), and one product context using a hypothetical brand. Further, despite our reasonable sample size (N = 776), the number of respondents represented in each cell would still be considered a limitation overall.Practical implicationsWhen developing crisis response strategies, managers should take into account the influence of a positive/negative source CI in driving attribution and trust. To minimize the impact of crisis on future purchasing decisions, organizations can leverage positive biases and mitigate negative ones, aiming to maintain or restore trust as a priority.Originality/valueThe study provides cross-country understanding about the significant role of CI during a product-harm crisis in relation to subsequent consumers’ blame attribution, their trust in the focal organization and ultimately their future purchase intentions.

Laser Doppler vibrometry-based characterization of bending waves by rotating viscoelastic panel materials applied in wallboard systems

A low-cost, thin-panel form of viscoelastic materials has found potential applications as constrained damping layers integrated into gypsum wallboards. The standardized chamber-based random-incident tests demonstrate drastically increased sound transmission losses without significantly increasing the board thickness and weight when the viscoelastic thin panels are integrated into gypsum wallboards in sandwich structure. For better understanding of their excellent effect as constrained damping layers, this work applies a laser Doppler vibrometer-based method in characterizing bending wave properties of the viscoelastic panel materials. The method involves a time-domain broadband measurement technique which correlates impulse responses taken at two points radially away from a bending wave source. Using reasonable sample sizes, boundary reflections will still obscure measurement results, particularly towards low frequencies. By rotating the panel under test, the coherence of direct wave pulses measured equidistant from the source and the lack thereof disturbing boundary reflections enables largely removing the undesirable reflections. In this way the direct wave pulses can be extracted by angular averaging and windowing in the time-domain. This paper discusses experimental investigations on the characterization method of bending wave properties using a laser Doppler vibrometer.

A multimodal study of the effects of tDCS on dorsolateral prefrontal and temporo-parietal areas during dichotic listening.

The underlying neural mechanisms of transcranial direct current stimulation (tDCS), especially beyond the primary motor cortex, remain unclear. Several studies examined tDCS effects on either functional activity, neurotransmitters or behavior but few investigated those aspects together to reveal how the brain responds to tDCS. The objective is to elucidate the underlying mechanisms of tDCS using a multimodal approach that extends from behavioral to neurotransmitter levels of explanation. Thirty-two healthy participants performed an auditory dichotic listening task at two visits, one session with sham and one session with real tDCS (2mA) while simultaneously undergoing functional magnetic resonance imaging (fMRI). The anode and cathode were placed over the left temporo-parietal cortex (TPC) and dorsolateral prefrontal cortex, respectively. Before and after simultaneous dichotic listening/fMRI/tDCS, combined glutamate and glutamine (Glx) and myo-inositol levels were assessed in the stimulated areas. While fMRI and dichotic listening showed expected functional activity and behavioral effects, neither method demonstrated differences between real and sham stimulation. Glx only showed a statistical trend towards higher levels after real tDCS in both stimulated brain areas. There were no significant correlations between behavior and Glx. Despite a reasonable sample size, electrical field strength, and replication of behavioral and functional activity results, tDCS had little to no effect on dichotic listening, Glx, and functional activity. The study emphasizes that findings about the underlying neural mechanisms of the primary motor cortex cannot simply be generalized to other brain areas. Particularly, the TPC might be less sensitive to tDCS. Moreover, the study demonstrates the general feasibility of multimodal approaches.

The Counterfactual χ-GAN: Finding comparable cohorts in observational health data.

Causal inference often relies on the counterfactual framework, which requires that treatment assignment is independent of the outcome, known as strong ignorability. Approaches to enforcing strong ignorability in causal analyses of observational data include weighting and matching methods. Effect estimates, such as the average treatment effect (ATE), are then estimated as expectations under the re-weighted or matched distribution, P. The choice of P is important and can impact the interpretation of the effect estimate and the variance of effect estimates. In this work, instead of specifying P, we learn a distribution that simultaneously maximizes coverage and minimizes variance of ATE estimates. In order to learn this distribution, this research proposes a generative adversarial network (GAN)-based model called the Counterfactual χ-GAN (cGAN), which also learns feature-balancing weights and supports unbiased causal estimation in the absence of unobserved confounding. Our model minimizes the Pearson χ2-divergence, which we show simultaneously maximizes coverage and minimizes the variance of importance sampling estimates. To our knowledge, this is the first such application of the Pearson χ2-divergence. We demonstrate the effectiveness of cGAN in achieving feature balance relative to established weighting methods in simulation and with real-world medical data.

Assessing Cancer Patient Experience of Care in Outpatient Oncology Practices in the United States.

Cancer patients' experience of care is an important component of quality that has not previously been used for comparing performance. We administered a new patient experience survey to cancer patients receiving outpatient chemotherapy treatment. We examined its measures for sensitivity to adjustment for case-mix and response tendency (level of general optimism/pessimism) and reliability for making performance comparisons between practices. We surveyed 2304 cancer patients who received chemotherapy at 23 medical oncology practices in Southeastern Pennsylvania, receiving 715 responses (response rate 31%; 14 practices had 10 or more responses). We aggregated patient responses to calculate practice-level scores on 5 predefined composites: Affective Communication, Shared Decision-Making, Patient Self-Management, Exchanging Information, and Access. We then ranked the practices on each composite before and after adjustment for standard case-mix variables and supplemental adjustment for response tendency (measured via the Life Orientation Test-Revised). We calculated the reliability of practice scores on each composite using hierarchical linear models and calculated minimum sample sizes necessary to achieve reliabilities exceeding 0.7. After adjusting responses for case-mix and converting to a 0-100 scale, composite scores ranged from 77 for the Patient Self-Management composite to 92 for the Access composite. Adjustment for response tendency had an impact on practice rankings only for the Shared Decision-Making composite. The number of responses necessary to create reliable practice-level measurements ranged from 17 (Access composite) to 96 (Affective Communication composite). Patient experiences at oncology practices can be measured reliably using reasonable sample sizes. Standard case-mix adjustment is adequate for making comparisons on most composites.

Efficient dose-finding for drug combination studies involving a shift in study populations

This paper describes the design of an early phase, prospective trial evaluating the safety and tolerability of the combination of the histone deacetylase inhibitor, entinostat, in combination with capecitabine. The study consists of two parts; an initial phase evaluating the safety of the combination in participants with metastatic breast cancer, followed by a second phase assessing the safety of the combination in participants with residual disease after neo-adjuvant chemotherapy for breast cancer. We describe the adaptation of a model-based design for identifying the maximum tolerated dose combination that efficiently moves from the initial phase in an advanced disease population to the second phase in the target population. Operating characteristics demonstrate the ability of the method to accurately predict true maximum tolerated dose combinations in a high percentage of trials with reasonable sample sizes, while treating participants at and around desirable combinations. The proposed design is a practical, early-phase, adaptive method for use with drug combination dose finding in the presence of shifting patient populations. More challenging research questions are being investigated in early-phase trials, which has created the need to implement more flexible designs that can meet the objectives of current studies, such as those exploring drug combinations while addressing patient heterogeneity. Our goal is to facilitate acceptance and application of more novel designs in contemporary early-phase studies.

The Status of the Quality Control in Neuroimaging Studies of Acupuncture Analgesia.

Neuroimaging technology is an important technology used to explore the neural mechanisms of acupuncture analgesia. In this study, we extracted original studies published in Chinese and English focusing on the use of neuroimaging technology to explore the mechanisms of acupuncture analgesia from PubMed, Cochrane Central Register of Controlled Trials (CENTRAL), EMBASE, Web of Science, and CNKI databases from January 1999 to August 2020. The extracted data were statistically analyzed in terms of year of publication, country, experimental design, and quality control approaches used, sample size, characteristics of participants, acupuncture operation, and other information. Analysis of the literature revealed that international cooperation promotes scientific research. Flexible experimental design can better explain the mechanism of acupuncture analgesia. Reasonable sample size, strict participant inclusion criteria, and standard acupuncture practices are essential for repeatability of conclusions. These findings show that attention should be paid to quality control in future research to improve the reliability of research on acupuncture analgesia.

A cross-region transfer learning method for classification of community service cases with small datasets

The precise classification of community service cases is the most fundamental aspect of intelligent community service systems. However, data imbalance makes it challenging to achieve the desired level of precise classification. Existing transfer learning methods use open Internet knowledge for identifying case features and mining potential feature relations. However, community service cases have the characteristics such as short text length and non-public content, which restrict the transfer learning modes. In this paper, a cross-region transfer learning method is proposed to solve the classification problem of cases with small datasets in data imbalance situation while considering the perspective of regional cooperation. First, an ontology modeling method is applied to standardize the case features, reducing the effect of semantic ambiguity on transfer results. Secondly, to improve the effectiveness of source domain classification, this paper utilizes an extended marginal fisher analysis where the distance is measured by the inner product between data. Next, the mapping matrix from target domain to source domain is learned through domain adaptation. Finally, the method is verified based on the empirical data from Lanzhou and Beidaihe in China. Experimental results on classifiers show the proposed method helps regions to improve case classification rates significantly through knowledge complementation. The proposed approach can be followed to build case-based community service systems of reasonable accuracy and limited sample sizes.

Gender differences in the impact of perceived or objectively measured residential green or blue space on self-rated health – a systematic review

TPS 702: Green space and population health, Exhibition Hall, Ground floor, August 28, 2019, 3:00 PM - 4:30 PM Background/Aim. Though gender is an important social determinant of health, gender inequalities have not been considered comprehensively in environmental health research so far. The project INGER intends to develop innovative methods for integration of gender in environmental health research. The aim of this systematic review was to clarify whether gender-theoretical concepts were addressed in studies on gender differences in the impact of residential green/blue space on self-rated health. Methods. Three electronic databases were searched to identify studies on residential green/blue space and self-rated health. Inclusion criteria were publication in 2000-2018, at least one keyword for gender/sex in title/abstract, adult study participants, and providing data on green or blue spaces and self-rated health. Green/blue spaces could be measured subjectively (e.g. perceived amount of or access to green space) or objectively (Normalized Difference Vegetation Index, landcover map). Sufficient for study inclusion were consideration of gender differences in the impact of green/blue space on self-rated health in the analysis and presentation of results on potential gender differences. Results. Out of 4230 potential eligible articles identified by the search seven cross-sectional studies met the inclusion criteria. Quality assessment gave fair results. All studies had a reasonable sample size and valid data collection. They presented an overall positive impact of green space on self-rated health. Only two studies reported on quality characteristics of green space. No or only weak evidence for gender differences in the impact of green space on self-rated health were found. However, all studies used a binary operationalisation male/female without further theoretical foundation. Interchangeable use of the terms ‘gender’ and ‘sex’ indicated a conceptual muddle. Due to the heterogeneity in approaches to assess green/blue spaces no meta-analysis was possible. Conclusion. Research quality could be enhanced by integrating gender-theoretical concepts into study design and interpretation of results.

Assessment of the Inter-Batch Variability of Microstructure Parameters in Topical Semisolids and Impact on the Demonstration of Equivalence.

Demonstration of similar microstructure is essential for demonstrating the equivalence of generic topical products since the microstructure of semisolids may affect the drug release. The objective of this study was to compare the microstructure-defining physical parameters of different batches of a reference ointment containing calcipotriol and betamethasone (Daivobet 50 µg/0.5 mg/g) in order to define the acceptance range that allows concluding equivalence between these batches. Being batches of the same reference product, they are expected to be clinically equivalent and possess similar microstructure. The 90% confidence intervals for the test/reference ratio of these physical parameters were calculated with parametric and non-parametric approaches. Both methods conclude that equivalent microstructure between batches cannot be demonstrated with a reasonable sample size when the acceptance range was set at ±10%, since several physical parameters exhibit inter-batch variability >10%. An acceptance range of ±10% is therefore too strict to conclude equivalence in the microstructure of semisolid dosage forms, given the inter-batch variability observed between batches of the reference product. A wider fixed acceptance range or an acceptance range widened based on the inter-batch variability of the reference product would be advisable.

Dynamic mechanical characterization of viscoelastic materials using bending wave correlation vibrometry

Direct solid-borne sound measurements allow incorporation of phase in characterizing viscoelastic materials. In the absence of excessively large samples, reflections from specimen boundaries obscure this valuable data. Circularly crested bending waves generated in plates provide a means of preserving phase information while maintaining reasonable sample sizes. The coherence of signals measured equidistant from the source and the lack thereof concerning reflections, enables isolation of the direct sound. This talk presents developments in a laser Doppler vibrometer based dynamic mechanical characterization method aimed at broadband classification of viscoelastic materials. The applicability of this technique to in-situ applications is demonstrated. Material properties are shown to correspond with results from existing methods.

A Vetting Protocol for the Analytical Procedures Platform for the AP-Phase of PCAOB Audits

Study Context AS5[2017], issued by the Public Company Accounting Oversight Board, requires the use of Analytical Procedures [AP] at the Planning and Substantive Phases of Assurance Audits of firms traded on active exchanges. Logically, an aspect of this requirement is satisfied by using a Panel of the Client’s data at the Planning Phase to forecast the Client’s YE-closing values and then at the Substantive Phase to dispose the directional difference between the: [Actual Client’s YE-value and the AP-Forecasted YE-value]—the Disposition Phase. Research Focus To date, neither the PCAOB nor the AICPA have suggested a pilot-test paradigm to vet the AP-forecasting Protocol under consideration. To address this lacuna, we detail an AP: Decision Support System [AP:DSS] that offers to the Audit InCharge a two-stage pre-analysis AP-vetting [Pilot-Test] platform that employs False Negative [FN] and False Positive [FP] Profilers. In inferential analyses, the FP-Risk is usually benchmarked using the FN-Risk. Deliverables A comprehensive AP-vetting model is offered and illustrated using: (i) a preliminary estimator of a reasonable sample size, (ii) two Standard Forecasting Models: The Excel versions of the OLS Linear Two-parameter and the Moving Average Models, and (iii) a Benchmarking protocol. Unique in this AP:DSS vetting protocol is that the FP-risk is contexted by the FN-risk from the independent benchmark domain. This duality enhances the inferential impact of the vetting protocol as it uses separate variable sets. The AP:DSS is available at no cost as an e-Download.

Robust spatial extent inference with a semiparametric bootstrap joint inference procedure.

Spatial extent inference (SEI) is widely used across neuroimaging modalities to adjust for multiple comparisons when studying brain-phenotype associations that inform our understanding of disease. Recent studies have shown that Gaussian random field (GRF)-based tools can have inflated family-wise error rates (FWERs). This has led to substantial controversy as to which processing choices are necessary to control the FWER using GRF-based SEI. The failure of GRF-based methods is due to unrealistic assumptions about the spatial covariance function of the imaging data. A permutation procedure is the most robust SEI tool because it estimates the spatial covariance function from the imaging data. However, the permutation procedure can fail because its assumption of exchangeability is violated in many imaging modalities. Here, we propose the (semi-) parametric bootstrap joint (PBJ; sPBJ) testing procedures that are designed for SEI of multilevel imaging data. The sPBJ procedure uses a robust estimate of the spatial covariance function, which yields consistent estimates of standard errors, even if the covariance model is misspecified. We use the methods to study the association between performance and executive functioning in a working memory functional magnetic resonance imaging study. The sPBJ has similar or greater power to the PBJ and permutation procedures while maintaining the nominal type 1 error rate in reasonable sample sizes. We provide an R package to perform inference using the PBJ and sPBJ procedures.