Search NASA⌕ Search

SEARCH · Search NASA

Results for “normal distribution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19

Comparison of two methods for minimizing the effect of delayed charge on the dose delivered with a synchrotron based discrete spot scanning proton beam

Purpose: Delayed charge is a small amount of charge that is delivered to the patient after the planned irradiation is halted, which may degrade the quality of the treatment by delivering unwarranted dose to the patient. This study compares two methods for minimizing the effect of delayed charge on the dose delivered with a synchrotron based discrete spot scanning proton beam. Methods: The delivery of several treatment plans was simulated by applying a normally distributed value of delayed charge, with a mean of 0.001(SD 0.00025) MU, to each spot. Two correction methods were used to account for the delayed charge. Method one (CM1), which is in active clinical use, accounts for the delayed charge by adjusting the MU of the current spot based on the cumulative MU. Method two (CM2) in addition reduces the planned MU by a predicted value. Every fraction of a treatment was simulated using each method and then recomputed in the treatment planning system. The dose difference between the original plan and the sum of the simulated fractions was evaluated. Both methods were tested in a water phantom with a single beam and simple target geometry. Two separate phantom tests were performed. In one test the dose per fraction was varied from 0.5 to 2 Gy using 25 fractions per plan. In the other test the number fractions were varied from 1 to 25, using 2 Gy per fraction. Three patient plans were used to determine the effect of delayed charge on the delivered dose under realistic clinical conditions. The order of spot delivery using CM1 was investigated by randomly selecting the starting spot for each layer, and by alternating per layer the starting spot from first to last. Only discrete spot scanning was considered in this study. Results: Using the phantom setup and varying the dose per fraction, the maximum dose difference for each plan of 25 fractions was 0.37–0.39 Gy and 0.03–0.05 Gy for CM1 and CM2, respectively. While varying the total number of fractions, the maximum dose difference increased at a rate of 0.015 Gy and 0.0018 Gy per fraction for CM1 and CM2, respectively. For CM1, the largest dose difference was found at the location of the first spot in each energy layer, whereas for CM2 the difference in dose was small and showed no dependence on location. For CM1, all of the fields in the patient plans had an area where their excess dose overlapped. No such correlation was found when using CM2. Randomly selecting the starting spot reduces the maximum dose difference from 0.708 to 0.15 Gy. Alternating between first and last spot reduces the maximum dose difference from 0.708 to 0.37 Gy. In the patient plans the excess dose scaled linearly at 0.014 Gy per field per fraction for CM1 and standard delivery order. Conclusions: The predictive model CM2 is superior to a cumulative irradiation model CM1 for minimizing the effects of delayed charge, particularly when considering maximal dose discrepancies and the potential for unplanned hot-spots. This study shows that the dose discrepancy potentially scales at 0.014 Gy per field per fraction for CM1.

60 APPLIED LIFE SCIENCES↗

SU-C-18A-04: 3D Markerless Registration of Lung Based On Coherent Point Drift: Application in Image Guided Radiotherapy

Purpose: This study evaluated a new probabilistic non-rigid registration method called coherent point drift for real time 3D markerless registration of the lung motion during radiotherapy. Method: 4DCT image datasets Dir-lab (www.dir-lab.com) have been used for creating 3D boundary element model of the lungs. For the first step, the 3D surface of the lungs in respiration phases T0 and T50 were segmented and divided into a finite number of linear triangular elements. Each triangle is a two dimensional object which has three vertices (each vertex has three degree of freedom). One of the main features of the lungs motion is velocity coherence so the vertices that creating the mesh of the lungs should also have features and degree of freedom of lung structure. This means that the vertices close to each other tend to move coherently. In the next step, we implemented a probabilistic non-rigid registration method called coherent point drift to calculate nonlinear displacement of vertices between different expiratory phases. Results: The method has been applied to images of 10-patients in Dir-lab dataset. The normal distribution of vertices to the origin for each expiratory stage were calculated. The results shows that the maximum error of registration between different expiratory phases is less than 0.4 mm (0.38 SI, 0.33 mm AP, 0.29 mm RL direction). This method is a reliable method for calculating the vector of displacement, and the degrees of freedom (DOFs) of lung structure in radiotherapy. Conclusions: We evaluated a new 3D registration method for distribution set of vertices inside lungs mesh. In this technique, lungs motion considering velocity coherence are inserted as a penalty in regularization function. The results indicate that high registration accuracy is achievable with CPD. This method is helpful for calculating of displacement vector and analyzing possible physiological and anatomical changes during treatment.

60 APPLIED LIFE SCIENCES↗

SU-E-QI-21: Iodinated Contrast Agent Time Course In Human Brain Metastasis: A Study For Stereotactic Synchrotron Radiotherapy Clinical Trials

Purpose: Synchrotron stereotactic radiotherapy (SSRT) is an innovative treatment combining the selective accumulation of heavy elements in tumors with stereotactic irradiations using monochromatic medium energy x-rays from a synchrotron source. Phase I/II clinical trials on brain metastasis are underway using venous infusion of iodinated contrast agents. The radiation dose enhancement depends on the amount of iodine in the tumor and its time course. In the present study, the reproducibility of iodine concentrations between the CT planning scan day (Day 0) and the treatment day (Day 10) was assessed in order to predict dose errors. Methods: For each of days 0 and 10, three patients received a biphasic intravenous injection of iodinated contrast agent (40 ml, 4 ml/s, followed by 160 ml, 0.5 ml/s) in order to ensure stable intra-tumoral amounts of iodine during the treatment. Two volumetric CT scans (before and after iodine injection) and a multi-slice dynamic CT of the brain were performed using conventional radiotherapy CT (Day 0) or quantitative synchrotron radiation CT (Day 10). A 3D rigid registration was processed between images. The absolute and relative differences of absolute iodine concentrations and their corresponding dose errors were evaluated in the GTV and PTV used for treatment planning. Results: The differences in iodine concentrations remained within the standard deviation limits. The 3D absolute differences followed a normal distribution centered at zero mg/ml with a variance (∼1 mg/ml) which is related to the image noise. Conclusion: The results suggest that dose errors depend only on the image noise. This study shows that stable amounts of iodine are achievable in brain metastasis for SSRT treatment in a 10 days interval.

60 APPLIED LIFE SCIENCES↗

Sci—Fri PM: Topics — 04: What if bystander effects influence cell kill within a target volume? Potential consequences of dose heterogeneity on TCP and EUD on intermediate risk prostate patients

In vitro evidence has suggested that radiation induced bystander effects may enhance non-local cell killing which may influence radiotherapy treatment planning paradigms. This work applies a bystander effect model, which has been derived from published in vitro data, to calculate equivalent uniform dose (EUD) and tumour control probability (TCP) and compare them with predictions from standard linear quadratic (LQ) models that assume a response due only to local absorbed dose. Comparisons between the models were made under increasing dose heterogeneity scenarios. Dose throughout the CTV was modeled with normal distributions, where the degree of heterogeneity was then dictated by changing the standard deviation (SD). The broad assumptions applied in the bystander effect model are intended to place an upper limit on the extent of the results in a clinical context. The bystander model suggests a moderate degree of dose heterogeneity yields as good or better outcome compared to a uniform dose in terms of EUD and TCP. Intermediate risk prostate prescriptions of 78 Gy over 39 fractions had maximum EUD and TCP values at SD of around 5Gy. The plots only dropped below the uniform dose values for SD ∼ 10 Gy, almost 13% of the prescribed dose. The bystander model demonstrates the potential to deviate from the common local LQ model predictions as dose heterogeneity through a prostate CTV is varies. The results suggest the potential for allowing some degree of dose heterogeneity within a CTV, although further investigations of the assumptions of the bystander model are warranted.

60 APPLIED LIFE SCIENCES↗

SU-E-I-71: Quality Assessment of Surrogate Metrics in Multi-Atlas-Based Image Segmentation

Purpose: With the ever-growing data of heterogeneous quality, relevance assessment of atlases becomes increasingly critical for multi-atlas-based image segmentation. However, there is no universally recognized best relevance metric and even a standard to compare amongst candidates remains elusive. This study, for the first time, designs a quantification to assess relevance metrics’ quality, based on a novel perspective of the metric as surrogate for inferring the inaccessible oracle geometric agreement. Methods: We first develop an inference model to relate surrogate metrics in image space to the underlying oracle relevance metric in segmentation label space, with a monotonically non-decreasing function subject to random perturbations. Subsequently, we investigate model parameters to reveal key contributing factors to surrogates’ ability in prognosticating the oracle relevance value, for the specific task of atlas selection. Finally, we design an effective contract-to-noise ratio (eCNR) to quantify surrogates’ quality based on insights from these analyses and empirical observations. Results: The inference model was specialized to a linear function with normally distributed perturbations, with surrogate metric exemplified by several widely-used image similarity metrics, i.e., MSD/NCC/(N)MI. Surrogates’ behaviors in selecting the most relevant atlases were assessed under varying eCNR, showing that surrogates with high eCNR dominated those with low eCNR in retaining the most relevant atlases. In an end-to-end validation, NCC/(N)MI with eCNR of 0.12 compared to MSD with eCNR of 0.10 resulted in statistically better segmentation with mean DSC of about 0.85 and the first and third quartiles of (0.83, 0.89), compared to MSD with mean DSC of 0.84 and the first and third quartiles of (0.81, 0.89). Conclusion: The designed eCNR is capable of characterizing surrogate metrics’ quality in prognosticating the oracle relevance value. It has been demonstrated to be correlated with the performance of relevant atlas selection and ultimate label fusion.

60 APPLIED LIFE SCIENCES↗

SU-E-J-03: Characterization of the Precision and Accuracy of a New, Preclinical, MRI-Guided Focused Ultrasound System for Image-Guided Interventions in Small-Bore, High-Field Magnets

Purpose: MRI-guided focused ultrasound (MRgFUS) has many potential and realized applications including controlled heating and localized drug delivery. The development of many of these applications requires extensive preclinical work, much of it in small animal models. The goal of this study is to characterize the spatial targeting accuracy and reproducibility of a preclinical high field MRgFUS system for thermal ablation and drug delivery applications. Methods: The RK300 (FUS Instruments, Toronto, Canada) is a motorized, 2-axis FUS positioning system suitable for small bore (72 mm), high-field MRI systems. The accuracy of the system was assessed in three ways. First, the precision of the system was assessed by sonicating regular grids of 5 mm squares on polystyrene plates and comparing the resulting focal dimples to the intended pattern, thereby assessing the reproducibility and precision of the motion control alone. Second, the targeting accuracy was assessed by imaging a polystyrene plate with randomly drilled holes and replicating the hole pattern by sonicating the observed hole locations on intact polystyrene plates and comparing the results. Third, the practicallyrealizable accuracy and precision were assessed by comparing the locations of transcranial, FUS-induced blood-brain-barrier disruption (BBBD) (observed through Gadolinium enhancement) to the intended targets in a retrospective analysis of animals sonicated for other experiments. Results: The evenly-spaced grids indicated that the precision was 0.11 +/− 0.05 mm. When image-guidance was included by targeting random locations, the accuracy was 0.5 +/− 0.2 mm. The effective accuracy in the four rodent brains assessed was 0.8 +/− 0.6 mm. In all cases, the error appeared normally distributed (p<0.05) in both orthogonal axes, though the left/right error was systematically greater than the superior/inferior error. Conclusions: The targeting accuracy of this device is sub-millimeter, suitable for many preclinical applications including focused drug delivery and thermal therapy. Funding support provided by Philips Healthcare.

60 APPLIED LIFE SCIENCES↗

TU-CD-BRA-05: Atlas Selection for Multi-Atlas-Based Image Segmentation Using Surrogate Modeling

Purpose: The growing size and heterogeneity in training atlas necessitates sophisticated schemes to identify only the most relevant atlases for the specific multi-atlas-based image segmentation problem. This study aims to develop a model to infer the inaccessible oracle geometric relevance metric from surrogate image similarity metrics, and based on such model, provide guidance to atlas selection in multi-atlas-based image segmentation. Methods: We relate the oracle geometric relevance metric in label space to the surrogate metric in image space, by a monotonically non-decreasing function with additive random perturbations. Subsequently, a surrogate’s ability to prognosticate the oracle order for atlas subset selection is quantified probabilistically. Finally, important insights and guidance are provided for the design of fusion set size, balancing the competing demands to include the most relevant atlases and to exclude the most irrelevant ones. A systematic solution is derived based on an optimization framework. Model verification and performance assessment is performed based on clinical prostate MR images. Results: The proposed surrogate model was exemplified by a linear map with normally distributed perturbation, and verified with several commonly-used surrogates, including MSD, NCC and (N)MI. The derived behaviors of different surrogates in atlas selection and their corresponding performance in ultimate label estimate were validated. The performance of NCC and (N)MI was similarly superior to MSD, with a 10% higher atlas selection probability and a segmentation performance increase in DSC by 0.10 with the first and third quartiles of (0.83, 0.89), compared to (0.81, 0.89). The derived optimal fusion set size, valued at 7/8/8/7 for MSD/NCC/MI/NMI, agreed well with the appropriate range [4, 9] from empirical observation. Conclusion: This work has developed an efficacious probabilistic model to characterize the image-based surrogate metric on atlas selection. Analytical insights lead to valid guiding principles on fusion set size design.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

SU-F-T-147: An Alternative Parameterization of Scatter Behavior Allows Significant Reduction of Beam Characterization for Pencil Beam Proton Therapy

Purpose: 1) To describe the characteristics of pencil beam proton dose deposition kernels in a homogenous medium using a novel parameterization. 2) To propose a method utilizing this novel parametrization to reduce the measurements and pre-computation required in commissioning a pencil beam proton therapy system. Methods: Using beam data from a clinical, pencil beam proton therapy center, Monte Carlo simulations were performed to characterize the dose depositions at a range of energies from 100.32 to 226.08 MeV in 3.6MeV steps. At each energy, the beam is defined at the surface of the phantom by a two-dimensional Normal distribution. Using FLUKA, the in-medium dose distribution is calculated in 200×200×350 mm cube with 1 mm{sup 3} tally volumes. The calculated dose distribution in each 200×200 slice perpendicular to the beam axis is then characterized using a symmetric alpha-stable distribution centered on the beam axis. This results in two parameters, α and γ, that completely describe shape of the distribution. In addition, the total dose deposited on each slice is calculated. The alpha-stable parameters are plotted as function of the depth in-medium, providing a representation of dose deposition along the pencil beam. We observed that these graphs are isometric through a scaling of both abscissa and ordinate map the curves. Results: Using interpolation of the scaling factors of two source curves representative of different beam energies, we predicted the parameters of a third curve at an intermediate energy. The errors are quantified by the maximal difference and provide a fit better than previous methods. The maximal energy difference between the source curves generating identical curves was 21.14MeV. Conclusion: We have introduced a novel method to parameterize the in-phantom properties of pencil beam proton dose depositions. For the case of the Knoxville IBA system, no more than nine pencil beams have to be fully characterized.

60 APPLIED LIFE SCIENCES↗

Sci-Thur AM: YIS – 06: A Monte Carlo study of macro- and microscopic dose descriptors and the microdosimetric spread using detailed cellular models

Purpose: To develop Monte Carlo models of cell clusters to investigate the relationships between macro- and microscopic dose descriptors, quantify the microdosimetric spread in energy deposition for subcellular targets, and determine how these results depend on the computational model. Methods: Microscopic tissue structure is modelled as clusters of 13 to 150 cells, with cell (nuclear) radii between 5 and 10 microns (2 and 9 microns). Energy imparted per unit mass (specific energy or dose) is scored in the nucleus (D{sub nuc}) and cytoplasm (D{sub cyt}) for incident photon energies from 20 to 370 keV. Dose-to-water (D{sub w,m}) and dose-to-medium (D{sub m,m}) are compared to D{sub nuc} and D{sub cyt}. Single cells and single nuclear cavities are also simulated. Results: D{sub nuc} and D{sub cyt} are sensitive to the surrounding environment with deviations of up to 13% for a single nucleus/cell compared with a multicellular cluster. These dose descriptors vary with cell and nucleus size by up to 10%. D{sub nuc} and D{sub cyt} differ from D{sub w,m} and D{sub m,m} by up to 32%. The microdosimetric spread is sensitive to whether cells are arranged randomly or in a hexagonal lattice, and whether subcellular compartment sizes are sampled from a normal distribution or are constant throughout the cluster. Conclusions: D{sub nuc} and D{sub cyt} are sensitive to cell morphology, elemental composition and the presence of surrounding cells. The microdosimetric spread was investigated using realistic elemental compositions for the nucleus and cytoplasm, and depends strongly on subcellular compartment size, source energy and dose.

60 APPLIED LIFE SCIENCES↗

Spectroscopy of a Cavitating Liquid in the Optical and X-ray Spectral Ranges

Results of spectroscopic investigation of a multibubble sonoluminescence and a hydrodynamic luminescence of glycerol in the optical range between 400 and 700 nm and in the X-ray spectral interval between 1 and 70 keV are presented. Continuous spectrum the shape of which is sufficiently well described by the normal distribution with respect to photon energy was obtained for both sono- and hydroluminescence in the optical spectral range. Based on the identity of the spectra, a conclusion can be drawn that the effects of the sono- and hydroluminescence are of the same physical nature. The shape of the obtained spectra suggests that the observed glow of a liquid under mechanical action represents fluorescence of only one type of centers in a condensed medium. X-ray radiation is absent in the specified energy range. Although an X-ray spectrometer detects some a signal of some kind, in reality, this turns out to be noise created by the magnetostrictive transducer of an ultrasonic generator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effect of the link lifetime in a dynamical lattice on the properties of the avalanche processes on it

The properties of the avalanche processes that develop on a dynamical lattice, the structure of links in which changes due to a specific characteristic of each lattice node, namely, its “activity,” which determines the probability of connection of a certain node with neighboring nodes in one step of lattice evolution. The statistics of the sizes of the avalanches appearing in the lattice system is studied as a function of the node activity and the link lifetime (the lifetime of the links formed in the system). It is analytically and numerically shows that the type of avalanche dynamics in the system changes as a function of these parameters. The following three regimes can take place in the system: (1) avalanches of any sizes, from small to catastrophic, can appear, which is reflected in the power-law behavior of the probability density function of the appearance of avalanches of certain sizes; (2) avalanches of a certain average size mainly appear in the system, and the probability density is close to that of a normal distribution; and (3) transient regime, where the probability density function of the appearance of avalanches of certain sizes is close to an exponential function. These results open up the possibilities of controlling the behavior of a complex system; in particular, they can be used to prevent catastrophic avalanches by changing the link lifetime and the average node activity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Defect specific luminescence dead layers in CdS and CdSe

CdS and CdSe are often used in optoelectronic devices whose effectiveness is may be dictated by defects in the near surface region. Luminescence is one of the main tools for studying such defects. The energy dependence of the x-ray excited optical luminescence (XEOL) spectra of these materials enables the extraction of the depth dependence of the defect distribution. Normal and time-gated XEOL spectra were obtained from these materials in the energy range 600 to 1500 eV. Here, we find that the results can best be understood in terms of a luminescence dead layer whose width depends on the position of the defect level in the band gap.

36 MATERIALS SCIENCE↗

Quantitative Evaluation of Top Coal Caving Methods at the Working Face of Extra‐Thick Coal Seams Based on the Random Medium Theory

Adopting an effective top coal caving method is the key to enhancing coal recovery and reducing gangue content for the fully mechanized top coal caving working face with extra‐thick coal seams. In this study, the movement of coal particles generated during top coal caving is considered to follow a normal distribution. Then, the caving body and coal‐rock settlement along the working face during the caving process are studied based on both the random media theory and probability theory. Accordingly, the optimal caving interval and caving sequences are determined, and a novel interval symmetrical coal caving method is proposed. The proposed method is systematically verified with results from physical similarity tests, and different caving methods are assessed by field tests. The results show the following: (1) The coal‐rock settlement and the caving body demonstrate clear axial symmetrical features along the working face; the size of the caving body increases as the caving height grows and its shape turns progressively from semicircular to semielliptical with a lower foot of the coal‐rock settlement. (2) The caving interval is derived using the sum of the radii of the coal‐rock settlement curves formed by the two largest caving bodies. (3) The symmetrical caving approach provides a symmetrical space for the subsequent movement of the broken top coal, which enables a uniform development of the caving body. (4) Compared with the traditional sequential coal caving method with the same number of supports, the interval symmetrical caving method results in a 21.7% of coal production increase, 17% caving rate promotion, and a shortened caving time by 23.4%. (5) The interval symmetrical caving method is found to improve the controllability of the caving process at the fully mechanized top coal caving working face. In general, this work presents a theoretical approach to select the optimal caving methods for the fully mechanized caving working face in extra‐thick coal seams for an improved production efficiency of the work face. The results of this study can also provide theoretical significance and referencing value for quantitative analyses of the coal caving methods for work faces with similar geological conditions.

Jiulin, Shi (ORCID:0000000155819062)↗

JGCRI/fldgen

Generate random global temperature fields with spatial and temporal correlation derived from an ESM As of version 2.0, fldgen allows to emulate any climate variable, not just ones that are approximately normally distributed, and it allows us to emulate climate variables in combinations, such as temperature and precipitation. These new capabilities can be used for risk modeling in areas such as drought and it agricultural impacts, where both temperature and moisture play a role.

Link, Robert↗

Double Bootstrapping

This code performs a simulation experiment that involves (i) drawing random numbers from the normal distribution, (ii) resampling elements from arrays with replacement, and (iii) computing various quantities like mean, standard deviation, etc. Further information is available in section 4 of FERMILAB-FN-1273-ETD [https://inspirehep.net/literature/2925453].

Shyamsundar, Prasanth [Fermi National Accelerator ↗

Posterior propriety for hierarchical models with log-likelihoods that have norm bounds

Statisticians often use improper priors to express ignorance or to provide good frequency properties, requiring that posterior propriety be verified. Our paper addresses generalized linear mixed models, GLMMs, when Level I parameters have Normal distributions, with many commonly-used hyperpriors. It provides easy-to-verify sufficient posterior propriety conditions based on dimensions, matrix ranks, and exponentiated norm bounds, ENBs, for the Level I likelihood. Since many familiar likelihoods have ENBs, which is often verifiable via log-concavity and MLE finiteness, our novel use of ENBs permits unification of posterior propriety results and posterior MGF/moment results for many useful Level I distributions, including those commonly used with multilevel generalized linear models, e.g., GLMMs and hierarchical generalized linear models, HGLMs. Furthermore, those who need to verify existence of posterior distributions or of posterior MGFs/moments for a multilevel generalized linear model given a proper or improper multivariate F prior as in Section 1 should find the required results in Sections 1 and 2 and Theorem 3 (GLMMs), Theorem 4 (HGLMs), or Theorem 5 (posterior MGFs/moments).

97 MATHEMATICS AND COMPUTING↗

Joint emulation of Earth System Model temperature-precipitation realizations with internal variability and space-time and cross-variable correlation: fldgen v2.0 software description

Earth System Models (ESMs) are excellent tools for quantifying many aspects of future climate dynamics but are too computationally expensive to produce large collections of scenarios for downstream users of ESM data. In particular, many researchers focused on the impacts of climate change require large collections of ESM runs to rigorously study the impacts to both human and natural systems of low-frequency high-importance events, such as multi-year droughts. Climate model emulators provide an effective mechanism for filling this gap, reproducing many aspects of ESMs rapidly but with lower precision. The fldgen v1.0 R package quickly generates thousands of realizations of gridded temperature fields by randomizing the residuals of pattern scaling temperature output from any single ESM, retaining the spatial and temporal variance and covariance structures of the input data at a low computational cost. The fldgen v2.0 R package described here extends this capability to produce joint realizations of multiple variables, with a focus on temperature and precipitation in an open source software package available for community use (https://github.com/jgcri/fldgen). This substantially improves the fldgen package by removing the requirement that the ESM variables be normally distributed, and will enable researchers to quickly generate covarying temperature and precipitation data that are synthetic but faithful to the characteristics of the original ESM.

54 ENVIRONMENTAL SCIENCES↗

Toward the validation of crowdsourced experiments for lightness perception

Crowdsource platforms have been used to study a range of perceptual stimuli such as the graphical perception of scatterplots and various aspects of human color perception. Given the lack of control over a crowdsourced participant’s experimental setup, there are valid concerns on the use of crowdsourcing for color studies as the perception of the stimuli is highly dependent on the stimulus presentation. Here, we propose that the error due to a crowdsourced experimental design can be effectively averaged out because the crowdsourced experiment can be accommodated by the Thurstonian model as the convolution of two normal distributions, one that is perceptual in nature and one that captures the error due to variability in stimulus presentation. Based on this, we provide a mathematical estimate for the sample size needed to produce a crowdsourced experiment with the same power as the corresponding in-person study. We tested this claim by replicating a large-scale, crowdsourced study of human lightness perception with a diverse sample with a highly controlled, in-person study with a sample taken from psychology undergraduates. Our claim was supported by the replication of the results from the latter. These findings suggest that, with sufficient sample size, color vision studies may be completed online, giving access to a larger and more representative sample. With this framework at hand, experimentalists have the validation that choosing either many online participants or few in person participants will not sacrifice the impact of their results.

97 MATHEMATICS AND COMPUTING↗