Many ethical frameworks require artificial intelligence (AI) systems to be explainable. Explainable AI (XAI) models are frequently tested for their adequacy in user studies. Since different people may have different explanatory needs, it is important that participant samples in user studies are large enough to represent the target population to enable generalizations. However, it is unclear to what extent XAI researchers reflect on and justify their sample sizes or avoid broad generalizations across people. We analyzed XAI user studies (N (...) = 220) published between 2012 and 2022. Most studies did not offer rationales for their sample sizes. Moreover, most papers generalized their conclusions beyond their target population, and there was no evidence that broader conclusions in quantitative studies were correlated with larger samples. These methodological problems can impede evaluations of whether XAI systems implement the explainability called for in ethical frameworks. We outline principles for more inclusive XAI user studies. (shrink)

To date researchers planning experiments have always lived by the mantra that 'using equal sample sizes gives the best results' and although unequal groups are also used in experimentation, it is not the preferred method of many and indeed actively discouraged in literature. However, during live study planning there are other considerations that we must take into account such as availability of study participants, statistical power and, indeed, the cost of the study. These can all make allocating equal (...) class='Hi'>sample sizes difficult, and sometimes near impossible. This, some might say, means that the study would not adhere to rigorous statistical standard (Rosenbaum and Rubin, 1985). However, here we present evidence that, not only is this a false assumption, but that we may actually gain more power in the study by actually using unequal groups. Here, data from a Sepsis Biomarker study is used, in which the aim is to predict, by biomarker level and presence, whether the patient would go on to develop sepsis. It was found that larger control groups may give more power to studies looking for an effect in the mid range but not for large or small effects. This study shows merit in the hypothesis that more power can be achieved when a larger control group is used. Published by the Ministry of Defence at dstl - Reference DSTLTR92592 P2PP2R-2016-02-23T13:39:45. (shrink)

Results of a comprehensive simulation study are reported investigating the effects of sample size, test length, number of attributes and base rate of mastery on item parameter recovery and classification accuracy of four DCMs. Effects were evaluated using bias and RMSE computed between true parameters and estimated parameters. Effects of simulated factors on attribute assignment were also evaluated using the percentage of classification accuracy. More precise estimates of item parameters were obtained with larger sample size and (...) longer test length. Recovery of item parameters decreased as the number of attributes increased from three to five but base rate of mastery had a varying effect on the item recovery. Item parameter and classification accuracy were higher for DINA and DINO models. (shrink)

With small to modest sample sizes and complex models, maximum likelihood estimation of confirmatory factor analysis models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood estimation, and the mean, median, or mode of the marginal posterior distribution that (...) are calculated by using Markov Chain Monte Carlo methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error. We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research. (shrink)

The persistent pervasiveness of inappropriately small studies in empirical fields is regu-larly deplored in scientific discussions. Consensually, taken individually, higher-powered studies are more likely to be truth-conducive. However, are they also beneficial for the wider performance of truth-seeking communities? We study the impact of sample sizes on collective exploration dynamics under ordinary conditions of resource limita-tion. We find that large collaborative studies, because they decrease diversity, can have detrimental effects in certain realistic circumstances that we characterize precisely. We show (...) how limited inertia mechanisms may partially solve this pooling dilemma and dis-cuss our findings briefly in terms of editorial policies. (shrink)

“Decisions from experience” (DFE) refers to a body of work that emerged in research on behavioral decision making over the last decade. One of the major experimental paradigms employed to study experienced-based choice is the “sampling paradigm”, which serves as a model of decision making under limited knowledge about the statistical structure of the world. In this paradigm respondents are presented with two payoff distributions, which, in contrast to standard approaches in behavioral economics, are specified not in terms of explicit (...) outcome-probability information, but by the opportunity to sample outcomes from each distribution without economic consequences. Participants are encouraged to explore the distributions until they feel confident enough to decide from which they would prefer to draw from in a final trial involving real monetary payoffs. One commonly employed measure to characterize the behavior of participants in the sampling paradigm is the sample size, that is, the number of outcome draws which participants choose to obtain from each distribution prior to terminating sampling. A natural question that arises in this context concerns the “optimal” sample size, which could be used as a normative benchmark to evaluate human sampling behavior in DFE. In this theoretical manuscript, we relate the DFE sampling paradigm to the classical statistical decision theoretic literature and, under a probabilistic inference assumption, evaluate optimal sample sizes for decisions from experience. In our treatment we go beyond analytically established results by showing how the classical statistical decision theoretic framework can be used to derive optimal sample sizes under arbitrary, but numerically evaluable, constraints. Finally, we critically evaluate the value of deriving optimal sample sizes under this framework as testable predictions for the experimental study of sampling behavior in DFE. (shrink)

Participants attempted to solve a modified version of Wason's selection task. Variables were: sizes of the sets referenced by a specified assertion, form of the assertion, thematic content of the assertion, and the need for sampling or not. In Experiment 1, participants were given enough information to determine the truth or falsity of the specified assertion with certainty; in Experiment 2, they had to rely on sampling and could not determine the assertion's truth or falsity with certainty. Performance was better (...) in Experiment 1 than in Experiment 2, but in both cases much better than what is typically obtained with the conventional selection task. The results support the hypothesis that performance of the selection task is sensitive to the sizes of the sets involved, add credence to the conclusion that framing the task in a thematically meaningful way can facilitate performance, and demonstrate that facilitation does not require deontic reasoning or a well-known convention being involved. The relationship between expressed confidence and level of performance is consistent with other studies showing the former to be a good predictor of the latter. (shrink)

Several studies have shown that our visual system may construct a “summary statistical representation” over groups of visual objects. Although there is a general understanding that human observers can accurately represent sets of a variety of features, many questions on how summary statistics, such as an average, are computed remain unanswered. This study investigated sampling properties of visual information used by human observers to extract two types of summary statistics of item sets, average and variance. We presented three models of (...) ideal observers to extract the summary statistics: a global sampling model without sampling noise, global sampling model with sampling noise, and limited sampling model. We compared the performance of an ideal observer of each model with that of human observers using statistical efficiency analysis. Results suggest that summary statistics of items in a set may be computed without representing individual items, which makes it possible to discard the limited sampling account. Moreover, the extraction of summary statistics may not necessarily require the representation of individual objects with focused attention when the sets of items are larger than 4. (shrink)

Group size is a function of relative neocortical volume in nonhuman primates. Extrapolation from this regression equation yields a predicted group size for modern humans very similar to that of certain hunter-gatherer and traditional horticulturalist societies. Groups of similar size are also found in other large-scale forms of contemporary and historical society. Among primates, the cohesion of groups is maintained by social grooming; the time devoted to social grooming is linearly related to group size among the (...) Old World monkeys and apes. To maintain the stability of the large groups characteristic of humans by grooming alone would place intolerable demands on time budgets. It is suggested that (1) the evolution of large groups in the human lineage depended on the development of a more efficient method for time-sharing the processes of social bonding and that (2) language uniquely fulfills this requirement. Data on the size of conversational and other small interacting groups of humans are in line with the predictions for the relative efficiency of conversation compared to grooming as a bonding process. Analysis of a sample of human conversations shows that about 60% of time is spent gossiping about relationships and personal experiences. It is suggested that language evolved to allow individuals to learn about the behavioural characteristics of other group members more rapidly than is possible by direct observation alone. (shrink)

This study focuses on the prediction of the engagement of small- and medium-sized enterprises (SMEs) in environmental management practices, based on a random sample of 689 SMEs. The study finds that several endogenous factors, including tangibility of sector, firm size, innovative orientation, family influence and perceived financial benefits from energy conservation, predict an SME’s level of engagement in selected environmental management practices. For family influence, this effect is found only in interaction with the number of owners. In addition (...) to empirical research on SMEs’ environmental behavior, this article draws on the ecological modernization literature as well as the theory of planned behavior. (shrink)

My aim in this paper is to show how the problem of inflated effect sizes corrupts the severity measure of evidence. This has never been done. In fact, the Winner’s Curse is barely mentioned in the philosophical literature. Since the severity score is the predominant measure of evidence for frequentist tests in the philosophical literature, it is important to underscore its flaws. It is also crucial to bring the philosophical literature up to speed with the limits of classical testing. The (...) Winner’s Curse is one of them. The problem is that when a significant result is obtained by using an underpowered test, the severity score becomes particularly high for large discrepancies from the null-hypothesis. This means that such discrepancies are very well supported by the evidence according to that measure. However, it is now well documented that significant tests with low power display inflated effect sizes. They systematically show departures from the null hypothesis H0 that are much greater than they really are. From an epistemological point of view this means that a significant result produced by an underpowered test does not provide evidence for large discrepancies from H0. Therefore, the severity score is an inadequate measure of evidence. Given that we are now aware of the phenomenon of inflated effect sizes, it would be irresponsible to rely on the severity score to measure the strength of the evidence against the null. Instead, one must take appropriate measures to try and avoid using underpowered tests by setting a threshold for the sample size or by replicating the results of the experiment. (shrink)

Recently Díaz, Hössjer and Marks (DHM) presented a Bayesian framework to measure cosmological tuning (either fine or coarse) that uses maximum entropy (maxent) distributions on unbounded sample spaces as priors for the parameters of the physical models (https://doi.org/10.1088/1475-7516/2021/07/020). The DHM framework stands in contrast to previous attempts to measure tuning that rely on a uniform prior assumption. However, since the parameters of the models often take values in spaces of infinite size, the uniformity assumption is unwarranted. This is (...) known as the normalization problem. In this paper we explain why and how the DHM framework not only evades the normalization problem but also circumvents other objections to the tuning measurement like the so called weak anthropic principle, the selection of a single maxent distribution and, importantly, the lack of invariance of maxent distributions with respect to data transformations. We also propose to treat fine-tuning as an emergence problem to avoid infinite loops in the prior distribution of hyperparameters (common to all Bayesian analysis), and explain that previous attempts to measure tuning using uniform priors are particular cases of the DHM framework. Finally, we prove a theorem, explaining when tuning is fine or coarse for different families of distributions. The theorem is summarized in a table for ease of reference, and the tuning of three physical parameters is analyzed using the conclusions of the theorem. (shrink)

There has been some theoretical and empirical debate that the positive relationship between corporate social performance (CSP) and firm financial performance (FFP) is spurious and in fact caused by a third factor, namely large firm size. This study examines this question by integrating three meta-analyses of more than two decades of research on (1) CSP and FFP, (2) firm size and CSP, and (3) firm size and FFP into one path-analytic model. The present study does not confirm (...) size as a third factor which would confound the relationship between CSP and FFP. That is, even if firm size is controlled for across studies (comprising, on average, over 15 000 observations), CSP and FFP remain positively correlated, showing a "true-score" corrected path coefficient p of 0.37. (shrink)

Our ability to rapidly distinguish new from already stored information is important for behavior and decision making, but the underlying processes remain unclear. Here, we tested the hypothesis that contextual cues lead to a preselection of information and, therefore, faster recognition. Specifically, on the basis of previous modeling work, we hypothesized that recognition time depends on the amount of relevant content stored in long-term memory, i.e., set size, and we explored possible age-related changes of this relationship in older humans. (...) In our paradigm, subjects learned by heart four different word lists written in different colors. On the day of testing, a color cue indicated with a probability of 50% that a subsequent word might be from the corresponding list or from a list of new words. The old/new status of the word had to be distinguished via button press. As a main finding, we can show in a sample of n = 49 subjects, including 26 younger and 23 older humans, that response times increased linearly and logarithmically as a function of set size in both age groups. Conversely, corrected hit rates decreased as a function of set size with no statistically significant differences between both age groups. As such, our findings provide empirical evidence that contextual information can lead to a preselection of relevant information stored in long-term memory to promote efficient recognition, possibly by cyclical top-down and bottom-up processing. (shrink)

Recent work by Kahan et al. (2017) on the psychology of motivated numeracy in the context of intracultural disagreement suggests that people are less likely to employ their capabilities when the evidence runs contrary to their political ideology. This research has so far been carried out primarily in the USA regarding the liberal–conservative divide over gun control regulation. In this paper, we present the results of a modified replication that included an active reasoning intervention with Western European participants regarding both (...) the hierarchy–egalitarianism and individualism–collectivism divides over immigration policy (n = 746; considerably less than the preregistration sample size). We reproduce the motivated numeracy effect, though we do not find evidence of increased polarization of high-numeracy participants. (shrink)

DOI: 10.1080/00031305.2018.1564697 When the editors of Basic and Applied Social Psychology effectively banned the use of null hypothesis significance testing (NHST) from articles published in their journal, it set off a fire-storm of discussions both supporting the decision and defending the utility of NHST in scientific research. At the heart of NHST is the p-value which is the probability of obtaining an effect equal to or more extreme than the one observed in the sample data, given the null hypothesis (...) and other model assumptions. Although this is conceptually different from the probability of the null hypothesis being true, given the sample, p-values nonetheless can provide evidential information, toward making an inference about a parameter. Applying a 10,000-case simulation described in this article, the authors found that p-values’ inferential signals to either reject or not reject a null hypothesis about the mean (α = 0.05) were consistent for almost 70% of the cases with the parameter’s true location for the sampled-from population. Success increases if a hybrid decision criterion, minimum effect size plus p-value (MESP), is used. Here, rejecting the null also requires the difference of the observed statistic from the exact null to be meaningfully large or practically significant, in the researcher’s judgment and experience. The simulation compares performances of several methods: from p-value and/or effect size-based, to confidence-interval based, under various conditions of true location of the mean, test power, and comparative sizes of the meaningful distance and population variability. For any inference procedure that outputs a binary indicator, like flagging whether a p-value is significant, the output of one single experiment is not sufficient evidence for a definitive conclusion. Yet, if a tool like MESP generates a relatively reliable signal and is used knowledgeably as part of a research process, it can provide useful information. (shrink)

This article investigates the effects of firm size, profitability, industry affiliation, and the business cycle on retailer philanthropy. The importance of industry and firm effects on giving was analyzed with regression models using industry-fixed effects as well as firm strategy variables. The analysis included instrumental variables methodology to account for simultaneity in the charitable giving–profits relationship. Data were gathered from the IRS Corporate Statistics of Income Sourcebook, data that provide firm size class measures covering the entire firm (...) class='Hi'>size distribution ranging from small retailers up to large multi-national retail firms. Retailer philanthropy was measured as the ratio of charitable contributions to total receipts. Important findings include a cubic relationship between retailer philanthropy and firm size; industry effects stronger than those observed for retail profit; and the absence of business cycle effects. The empirical research relating retail charitable giving to firm attributes including firm size and advertising, industry and business cycle factors are unique in the business ethics literature. Prior studies regarding the importance of industry on charitable giving utilized data across broad sectors of the economy. Firms from different sectors could be expected to differ in philanthropic approach due to differences in public contact as well as differences in public relations exposure. The strong industry effects reported for this sample of exclusively retail firms, with similar public contact, provide strong evidence for the importance of industry in determining firms’ charitable strategies. (shrink)

I discuss the behavior of the Akaike Information Criterion in the limit when the sample size grows. I show the falsity of the claim made recently by Stanley Mulaik in Philosophy of Science that AIC would not distinguish between saturated and other correct factor analytic models in this limit. I explain the meaning and demonstrate the validity of the familiar, more moderate criticism that AIC is not a consistent estimator of the number of parameters of the smallest correct (...) model. I also give a short explanation why this feature of AIC is compatible with the motives of using it. (shrink)

I discuss the behavior of the Akaike Information Criterion in the limit when the sample size grows. I show the falsity of the claim made recently by Stanley Mulaik in Philosophy of Science that AIC would not distinguish between saturated and other correct factor analytic models in this limit. I explain the meaning and demonstrate the validity of the familiar, more moderate criticism that AIC is not a consistent estimator of the number of parameters of the smallest correct (...) model. I also give a short explanation why this feature of AIC is compatible with the motives for using it. (shrink)

Objectives:Social isolation is increasing in aging societies and several studies have shown a relation with worse cognition in old age. However, less is known about the association in the oldest-old (85+); the group that is at highest risk for both social isolation and dementia. Methods:Analyses were based on follow-up 5 to 9 of the longitudinal German study on aging, cognition, and dementia in primary care patients (AgeCoDe) and the study on needs, health service use, costs, and health-related quality of life (...) in a large sample of oldest-old primary care patients (AgeQualiDe), a multi-center population-based prospective cohort study. Measurements included the Lubben Social Network Scale (LSNS-6), with a score below 12 indicating social isolation, as well as the Mini-Mental Status Examination (MMSE) as an indicator of cognitive function. Results:Dementia-free study participants (n = 942) were M = 86.4 (SD = 3.0) years old at observation onset, 68.2% were women. One third (32.3%) of them were socially isolated. Adjusted linear hybrid mixed effects models revealed significantly lower cognitive function in individuals with smaller social networks (β = 0.5, 95% CI = 0.3-0.7, p <.001). Moreover, changes in an individual's social network size were significantly associated with cognitive changes over time (β = 0.2, 95% CI = 0.1-0.4, p =.003), indicating worse cognitive function with shrinking social networks. Conclusion:Social isolation is highly prevalent among oldest-old individuals, being a risk factor for decreases in cognitive function. Consequently, it is important to maintain a socially active lifestyle into very old age. Likewise, this calls for effective ways to prevent social isolation. (shrink)

Recent research on corporate social responsibility (CSR) suggests the need for further exploration into the relationship between small and medium-sized enterprises (SMEs) and CSR. SMEs rarely use the language of CSR to describe their activities, but informal CSR strategies play a large part in them. The goal of this article is to investigate whether differences exist between the formal and informal CSR strategies through which firms manage relations with and the claims of their stakeholders. In this context, formal CSR strategies (...) seem to characterize large firms while informal CSR strategies prevail among micro, small, and medium-sized enterprises. We use a sample of 3,626 Italian firms to investigate our research questions. Based on a multistakeholder framework, the analysis provides evidence that small businesses* use of CSR, involving strategies with an important impact on the bottom line, reflects an attempt to secure their license to operate in the communities; while large firms rarely make attempts to integrate their CSR strategies into explicit management systems. (shrink)

In recent years, supply chain finance is exploited to solve the financing difficulties of small- and medium-sized enterprises. SME credit risk assessment is a critical part in the SCF system. The diffusion of SME credit risk may cause serious consequences, leading the whole supply chain finance system unstable and insecure. Compared with traditional credit risk assessment models, the supply chain relationship, credit condition of SME, and core enterprises should all be considered to rate SME credit risk in SCF. Traditional methods (...) mix all indicators from different index systems. They cannot give a quantitative result on how these index systems work. Furthermore, traditional credit risk assessment models are heavily dependent on the number of annotated SME data. However, it is implausible to accumulate enough credit risky SMEs in advance. In this paper, we propose an adaptive heterogenous multiview graph learning method to tackle the small sample size problem for SMEs’ credit risk forecasting. Three graphs are constructed by using indicators from supply chain operation, SME financial indicator, and nonfinancial indicator individually. All the graphs are integrated in an adaptive manner, providing a quantitative explanation on how the three parts cooperate. The experimental analysis shows that the proposed method has good performance for determining whether SME is risky or nonrisky in SCF. From the perspective of SCF, SME financing ability is still the main factor to determine the credit risk of SME. (shrink)

In this paper we will show how Qurashī patrilines and marriage records can be statistically analysed to generate an estimate of the tribe’s size at the time of Muḥammad. By extension this will also give us an estimate for the population size of Mecca. We will begin by using the marriage data preserved in a genealogical work to identify a cohort of adult Qurashī male contemporaries of Muḥammad. We will then divide this cohort into men who had brothers (...) versus those who did not. It will be shown that this ratio is exactly what we would expect if we were modelling a complete population and therefore it cannot be a sample. With this in place we can extrapolate the number of women and dependants that would have been linked to each man, giving us an estimate of the tribe’s size in the period. Supplementing this with selected historiographical data will give us the population size of Mecca. The resulting findings raise a series of questions concerning Qurashī origins that will then be addressed by applying a similar methodology to the eras before Muḥammad’s. This will illuminate the manner and timing of the emergence of the Quraysh as a distinct entity. (shrink)

: This work proposes the methodology to obtain a correlation between the particle size of the rock material and the point load test index, in order to characterize the materials, present in mining projects in terms of resistance. For a correct development of mining activities, both open pit and underground, it is important to determine the compressive strength of the rocks, since, through it, geomechanical classifications are obtained, and thus calculate safety factors to define stabilization and/or fortification systems for (...) mining operations. This work was developed on the basis of samples from a geological formation and subsequent preparation of specimens, then they were subjected to physical tests, which can be carried out without problem in the field, and finally, the respective relationships were obtained. The results are encouraging and the equations are proposed to characterize the rock and achieve the proposed objective. Keywords: Rock, Crushing, Classification, Compression. (shrink)

Reasons for the rapid appearance and growth of SWFs is contributed by increase in oil prices and the accumulation of large balance-of-payments surpluses. Purpose of the article is to investigate size of observed Sovereign Wealth Funds in 2013. Moreover, to describe what explain differences in the size of SWFs, on the other hand what determines the amount of foreign exchange reserves. Is the size of observed funds closely related to rate of growth of the countries? Is return (...) of observed funds is closely related to fund value bn USD, GDP growth and inflation rate of the country? Methodology/methods deployed in this paper has been done illustrations by using available data from official websites of funds, Sovereign Wealth Fund Institute, International Monetary Fund, CIA The World Factbook and author’s calculations due the fact that most of funds do not provide data to the public. In addition to this, we present the estimations by using regression analysis, transferring observed data using the least squares method, The two-sample t-test for mean value, ANOVA, TINV. Scientific aim is to examine whether AUM of SWFs, moreover the size of 14 observed funds is closely related to rate of growth of the countries at 90 percent of probability. Second, if return of 14 observed funds is closely related to fund value bn USD, GDP growth and inflation rate of the country at 95 percent of probability. Third, if there are significant differences between return in 2010 and 2013. Findings indicates that paper came to the conclusion that the return of 14 observed funds is closely related to fund value bn USD, GDP growth and inflation rate of the country at 95 percent of probability. Furthermore, there are significant differences between return in 2010 and 2013. Conclusions pointed out that the influence of SWFs has become undeniable, with total assets topping 6,585tn USD in June 2014, these investors have reached a size comparable to that of the entire alternative assets industry. (shrink)