Measurement error is omnipresent in psychological data. However, the vast majority of applications of autoregressive time series analyses in psychology do not take measurement error into account. Disregarding measurement error when it is present in the data results in a bias of the autoregressive parameters. We discuss two models that take measurement error into account: An autoregressive model with a white noise term (AR+WN), and an autoregressive moving average (ARMA) model. In a simulation study we compare (...) the parameter recovery performance of these models, and compare this performance for both a Bayesian and frequentist approach. We find that overall, the AR+WN model performs better. Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models. Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women. We find that, depending on the person, approximately 30–50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters. (shrink)

In the last few decades the role played by models and modeling activities has become a central topic in the scientific enterprise. In particular, it has been highlighted both that the development of models constitutes a crucial step for understanding the world and that the developed models operate as mediators between theories and the world. Such perspective is exploited here to cope with the issue as to whether error-based and uncertainty-based modeling of measurement are incompatible, and thus alternative with (...) one another, as sometimes claimed nowadays. The crucial problem is whether assuming this standpoint implies definitely renouncing to maintain a role for truth and the related concepts, particularly accuracy, in measurement. It is argued here that the well known objections against true values in measurement, which would lead to refuse the concept of accuracy as non-operational, or to maintain it as only qualitative, derive from a not clear distinction between three distinct processes: the metrological characterization of measuring systems, their calibration, and finally measurement. Under the hypotheses that (1) the concept of true value is related to the model of a measurement process, (2) the concept of uncertainty is related to the connection between such model and the world, and (3) accuracy is a property of measuring systems (and not of measurement results) and uncertainty is a property of measurement results (and not of measuring systems), not only the compatibility but actually the conjoint need of error-based and uncertainty-based modeling emerges. (shrink)

In the United States, the racial and ethnic statistics published by the National Center for Health Statistics (NCHS) assume that each member of the U.S. population has a race and ethnicity and that if a member is black or white with respect to his risk of one disease, he is the same race with respect to his risk of another. Such an assumption is mistaken. Race and ethnicity are taken by the NCHS to be an intrinsic property of members of (...) a population, when they should be taken to depend on interest. The actual or underlying race or ethnicity of members of a population depends on the risk whose variation within the population we wish to describe or explain. (shrink)

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling (SEM), where latent variables are approximated by weighted composites of indicators. It has no formal mechanism to incorporate errors in indicators, which in turn renders components prone to the errors as well. We propose to extend GSCA to account for errors in indicators explicitly. This extension, called GSCA_M, considers both common and unique parts of indicators, as postulated in common factor analysis, and estimates a (...) weighted composite of indicators with their unique parts removed. Adding such unique parts or uniqueness terms serves to account for measurement errors in indicators in a manner similar to common factor analysis. Simulation studies are conducted to compare parameter recovery of GSCA_M and existing methods. These methods are also applied to fit a substantively well-established model to real data. (shrink)

The definition and measurement of the quality audit work has been the subject of many studies. Since the quality of auditors' work could not be observed directly except in ex post audit failures, prior researches adapted different proxies for measuring it. These proxies include firm size, reputation, auditor tenure, audit fees and other measures. This article reviews empirical studies over the past decades from all over the world in order to assess what researchers have done about measuring the quality (...) of auditors' work. Prior measurements are classified into two main groups; direct and indirect measure of quality audit and actual quality audit versus perceptions. This article contributes to the quality audit literature by proposing new measurement, which is developed based on the quality of auditors' work definition and theory of planned behaviour. (shrink)

Articulated arm coordinate measuring machine is a specific robotic structural instrument, which uses D-H method for the purpose of kinematic modeling and error compensation. However, it is difficult for the existing error compensation models to describe various factors, which affects the accuracy of AACMM. In this paper, a modeling and error compensation method for AACMM is proposed based on BP Neural Networks. According to the available measurements, the poses of the AACMM are used as the input, and the coordinates of (...) the probe are used as the output of neural network. To avoid tedious training and improve the training efficiency and prediction accuracy, a data acquisition strategy is developed according to the actual measurement behavior in the joint space. A neural network model is proposed and analyzed by using the data generated via Monte-Carlo method in simulations. The structure and parameter settings of neural network are optimized to improve the prediction accuracy and training speed. Experimental studies have been conducted to verify the proposed algorithm with neural network compensation, which shows that 97% error of the AACMM can be eliminated after compensation. These experimental results have revealed the effectiveness of the proposed modeling and compensation method for AACMM. (shrink)

By using the concept of a uniformity, the Structuralists have given us a most useful means of representing approximations. In the second section of this paper, I have made use of this technique to show how we can deal with errors of measurement — imprecise explananda — in the context of theoretical explanation. As well as (I hope) providing further demonstration of the power of the Structuralist approach, this also serves to support the ontic conception of explanation by (...) showing that it can help us resolve substantial problems in the theory of explanation. (shrink)

Measurement is said to be the basis of exact sciences as the process of assigning numbers to matter (things or their attributes), thus making it possible to apply the mathematically formulated laws of nature to the empirical world. Mathematics and empiria are best accorded to each other in laboratory experiments which function as what Nancy Cartwright calls nomological machine: an arrangement generating (mathematical) regularities. On the basis of accounts of measurement errors and uncertainties, I will argue for (...) two claims: 1) Both fundamental laws of physics, corresponding to ideal nomological machine, and phenomenological laws, corresponding to material nomological machine, lie, being highly idealised relative to the empirical reality; and also laboratory measurement data do not describe properties inherent to the world independently of human understanding of it. 2) Therefore the naive, representational view of measurement and experimentation should be replaced with a more pragmatic or practice-based view. (shrink)

The measurement of sensory intensity has had a long history, attracting the attention of investigators from many disciplines including physiology, psychology, physics, mathematics, philosophy, and even chemistry. While there has been a continuing doubt by some that sensation has the properties necessary for measurement, experiments designed to obtain estimates of sensory intensity have found that a general rule applies: Equal stimulus ratios produce equal sensory ratios. Theories concerning the basis for this simple psychophysical rule are discussed, with emphasis (...) given to the physical correlate theory, which considers judgments of subjective magnitudes to be based upon estimates of physical dimensions that vary regularly with changes in degree of stimulation. For the most thoroughly investigated sensory scales, brightness and loudness, the physical correlate is considered to be distance. Our “tacit knowledge” of the sensory effects of changing distance plays an essential role in matching motor activities to environmental conditions and in ensuring accurate perceptual evaluations through brightness and loudness constancies. In psychophysical experiments, subjects apparently use this same tacit knowledge when required to estimate relative subjective magnitudes. The evidence related to the physical correlate theory is summarized, and it is concluded that, while under appropriate conditions we demonstrate considerable skill in evaluating environmental relationships, we are quite unable to estimate the neurophysiological nature or quantity of sensory response. A psychophysics devoted to studying conditions required for accuracy and conditions producing errors in the perception of environmental relationships would seem to be more valuable than one devoted to subjective magnitudes. (shrink)

The error statistical account of testing uses statistical considerations, not to provide a measure of probability of hypotheses, but to model patterns of irregularity that are useful for controlling, distinguishing, and learning from errors. The aim of this paper is (1) to explain the main points of contrast between the error statistical and the subjective Bayesian approach and (2) to elucidate the key errors that underlie the central objection raised by Colin Howson at our PSA 96 Symposium.

The way metrologists conceive of measurement has undergone a major shift in the last two decades. This shift can in great part be traced to a change in the statistical methods used to deal with the expression of measurement results, and, more particularly, with the calculation of measurement uncertainties. Indeed, as we show, the incapacity of the frequentist approach to the calculus of uncertainty to deal with systematic errors has prompted the replacement of the customary frequentist (...) methods by fully Bayesian procedures. The epistemological ramifications of the Bayesian approach merge with a deep empiricist mood tantamount to an “epistemic turn”: measurement results are analysed in terms of degrees of belief, and central concepts such as error and accuracy are called into question. We challenge the perspective entailed by this epistemic turn: we insist on the centrality of the concepts of error and accuracy by underlining the intentional character of measurement that is intimately linked to the process of correction of experimental data. We further circumvent the difficulties posed by the classical analysis of measurement by stressing the social rather than the epistemic dimension of measurement activities. (shrink)

This article discusses the ways in which nineteenth-century geodesists reflected on precision as an epistemic virtue in their measurement practice. Physical geodesy is often understood as a quintessential nineteenth-century precision science, stimulating advances in instrument making and statistics, and generating incredible quantities of data. Throughout most of the nineteenth century, geodesists indeed pursued their most prestigious research problem – the exact determination of the earth’s polar flattening – along those lines. Treating measurement errors as random, they assumed (...) that remaining discordances could be overcome by manufacturing better instruments and extending statistical analysis to a larger amount of data. In the second half of the nineteenth century, however, several German geodesists developed sophisticated methodological critiques of their discipline, in which they diagnosed a too-narrow focus on precision among their peers. On their account, geodesists urgently needed to identify and anticipate the causes of the remaining measurement errors that arose from the earth’s little understood interior constitution. While mostly overlooked in the literature, these critiques paved the way for many empirical successes in late nineteenth- and early twentieth-century geodesy, including the first convergent measurements of the earth’s polar flattening. (shrink)

Though he maintained a significant interest in theoretical aspects of measurement, Henry E. Kyburg, Jr. was critical of the representational theory that in many ways has come to dominate discussions concerning the foundations of measurement. In particular, Kyburg (in Savage and Ehrlich (eds) Philosophical and foundational issues in measurement theory, 1992 ) asserts that the representational theory of measurement, as introduced in (Scott and Suppes, Journal of Symbolic Logic, 23:113–128, 1958 ) and developed in (Krantz et (...) al., Foundations of measurment: additive and polynomial representations. Academic Press, 1971 ), cannot account for the measurement of error. The present work examines and responds to this charge. (shrink)

The chapter begins by explaining the concepts of quantity and magnitude. It then presents the method of measurement without using magnitude. This method of direct measurement can be achieved through the observation of the transitive relation among objects. A particular set of equivalence classes is selected to serve as a unit of measurement and is assigned magnitude. The concept of measurement error and approximation is then introduced. In some cases, such as temperature, indirect measurement, or (...) measurement in terms of a different quantity, yields less error and proves more accurate and convenient than direct measurement. In general, indirect measurements of different kinds are appropriate at different regions of the scale. (shrink)

Measures of algorithmic bias can be roughly classified into four categories, distinguished by the conditional probabilistic dependencies to which they are sensitive. First, measures of "procedural bias" diagnose bias when the score returned by an algorithm is probabilistically dependent on a sensitive class variable (e.g. race or sex). Second, measures of "outcome bias" capture probabilistic dependence between class variables and the outcome for each subject (e.g. parole granted or loan denied). Third, measures of "behavior-relative error bias" capture probabilistic dependence between (...) class variables and the algorithmic score, conditional on target behaviors (e.g. recidivism or loan default). Fourth, measures of "score-relative error bias" capture probabilistic dependence between class variables and behavior, conditional on score. Several recent discussions have demonstrated a tradeoff between these different measures of algorithmic bias, and at least one recent paper has suggested conditions under which tradeoffs may be minimized. -/- In this paper we use the machinery of causal graphical models to show that, under standard assumptions, the underlying causal relations among variables forces some tradeoffs. We delineate a number of normative considerations that are encoded in different measures of bias, with reference to the philosophical literature on the wrongfulness of disparate treatment and disparate impact. While both kinds of error bias are nominally motivated by concern to avoid disparate impact, we argue that consideration of causal structures shows that these measures are better understood as complicated and unreliable measures of procedural biases (i.e. disparate treatment). Moreover, while procedural bias is indicative of disparate treatment, we show that the measure of procedural bias one ought to adopt is dependent on the account of the wrongfulness of disparate treatment one endorses. Finally, given that neither score-relative nor behavior-relative measures of error bias capture the relevant normative considerations, we suggest that error bias proper is best measured by score-based measures of accuracy, such as the Brier score. (shrink)

Abstract In Myth & Measurement: The New Economics of the Minimum Wage, David Card and Alan Krueger assemble a variety of evidence purporting to weaken the case that minimum wages lead to unemployment among low?wage workers. Although the authors succeed in casting doubt on some previous studies that supported the standard view, they fail to provide compelling evidence for their alternative model. The methodological errors in their showcase study of minimum wages in New Jersey and Pennsylvania render it (...) nearly worthless, and the remainder of the book's arguments are not weighty enough to reverse the conventional economic wisdom on minimum wages. (shrink)

What is the correct concept behind measures of inflation? Does money cause business activity or is it the other way around? Shall we stimulate growth by raising aggregate demand or rather by lowering taxes and thereby providing incentives to produce? Policy-relevant questions such as these are of immediate and obvious importance to the welfare of societies. The standard approach in dealing with them is to build a model, based on economic theory, answer the question for the model world and then (...) apply the results to economic phenomena outside. Data come in, if at all, only in testing a limited number of the model's consequences. Despite some critical voices, economic methodology too has by and large subscribed to a "theory first" approach to applied economics. Error in Economics systematically develops an alternative to the theory-based orthodoxy. It places the methodical study of evidence at the centre of the scientific enterprise and thus provides a foundation for a methodology of evidence-based economics. But the book does not stop at the truism that claims should be based on the best available evidence. Rather, detailed studies in the areas of measurement, causal inference and policy analysis show what it means for a claim to be evidence-based in the context of a concrete case. The examples discussed concern topics as diverse as consumer price indices, radio spectrum auctions, the transmission mechanism, natural experiments on minimum wages and the evaluation of counterfactuals for policy. Error in Economics is essential reading for economic methodologists, philosophers of science and anyone interested in how claims about socio-economic matters are validated. (shrink)

In this chapter I explicate and evaluate the concept of medical error. Unlike standard philosophical approaches to analyzing medical phenom- ena in the abstract, I instead address medical error specifi cally within the context of an embodied social world. I illustrate how, as a deeply contex- tual concept, medical error is inextricably tied to the social conditions— and concrete, powerful interests—of the particulars in which it is found. -/- I begin with an analysis that demonstrates the relational quality of medi- (...) cal error, as a functional, outcome-oriented concept, evaluating the origin and context of the term’s emergence, and connecting it to a similarly contextual concept, “standard of care.” I move on to note the concern- ing implications of medical error identifi cation and measurement when viewed through an intersectional standpoint. To do so, I discuss what intersectional approaches can help reveal about our contemporary social world of medicine and public health. Intersectional approaches, as I will explain, focus on how intersections of social identity can unmask social structures that negatively impact groups and individuals. It appears, as -/- I will suggest, that disparities in social goods (e.g., social standing, edu- cation, wealth) complicate our identification of medical error, itself, and compound concerns of equity and access to medical goods for those who have diminished expectations for health. (shrink)

Recent research shows that in reasoning tasks, subjects usually produce an initial intuitive answer, accompanied by a metacognitive experience, which has been called feeling of rightness. This paper is aimed at exploring the complimentary experience of feeling of error, that is, the spontaneous, subtle sensation of cognitive uneasiness arising from conflict detection during thinking. We investigate FOE in two studies with the “bat-and-ball” reasoning task, in its standard and isomorphic control versions. Study 1 is a generation study, in which participants (...) are asked to generate their own response. Study 2 is an evaluation study, in which participants are asked to choose between two conflicting answers. In each study, the FOE is measured by the FOE questionnaire. Results show that the FOE is significantly present in the standard B&B task when participants give a wrong answer, that our questionnaire can measure it, and furthermore, that it is diagnostic of genuine error. (shrink)

This paper considers two subjective measures of the existence of unconscious mental states - the guessing criterion, and the zero correlation criterion - and considers the assumptions underlying their application in experimental paradigms. Using higher order thought theory the impact of different types of biases on the zero correlation and guessing criteria are considered. It is argued that subjective measures of consciousness can be biased in various specified ways, some of which involve the relation between first order states and second (...) order thoughts, and hence are not errors in measurement of the conscious status of mental states; but other sorts of biases are measurement errors, involving the relation between higher order thoughts and their expression. Nonetheless, it is argued this type of bias does not preclude subjective measures - both the guessing criterion and the zero correlation criterion - as being amongst the most appropriate and useful tools for measuring the conscious status of mental states. (shrink)

A postcompletion error is a type of procedural error that occurs after the main goal of a task has been accomplished. There is a strong theoretical foundation accounting for postcompletion errors (Altmann & Trafton, 2002; Byrne & Bovair, 1997). This theoretical foundation has been leveraged to develop a logistic regression model of postcompletion errors based on reaction time and eye movement measures (Ratwani, McCurry, & Trafton, 2008). This study further develops and extends this predictive model by (a) validating (...) the model and the general set of predictors on a new task to test the robustness of the model, and (b) determining which specific theoretical components are most important to postcompletion error prediction. (shrink)

Organizational membership seems to be linked to a more participatory and informed political culture, to foster electoral participation, and to promote positive feelings toward democracy. More recently, the social capital and associative democracy debates have introduced new arguments about the positive effects of associational involvement. However, little attention has been paid to the problems of measuring associational involvement and to their consequences for our theories. This article discusses the various problems of validity and reliability of our measurements of associational membership. (...) It is shown that different questionnaire formats produce substantially different results. The article also addresses the issue of measurement errors and emphasizes the problems they introduce when doing cross-national comparisons. (shrink)

Climate change will cause large numbers of casualties, perhaps extending over thousands of years. Casualties have a clear moral significance that economic and other technical measures of harm tend to mask. They are, moreover, universally understood, whereas other measures of harm are not. Therefore, the harms of climate change should regularly be expressed in terms of casualties by such agencies such as IPCC’s Working Group III, in addition to whatever other measures are used. Casualty estimates should, furthermore, be used to (...) derive estimates of casualties per emission source up to a given date. Such estimates would have wide margins of error, but they would add substantially to humanity’s grasp of the moral costs of particular greenhouse gas emissions. (shrink)

Motor proficiency reflects the ability to perform precise and coordinated movements in different contexts. Previous research suggests that different profiles of motor proficiency may be associated with different cognitive functioning characteristics thus suggesting an interaction between cognitive and motor processes. The current study investigated this interaction in the general population of healthy adults with different profiles of motor proficiency by focusing on error-related cognitive control and behavioral adaptation mechanisms. In addition, the impact of these processes was assessed in terms of (...) trait anxiety and worries. Forty healthy adults were divided into high and low motor proficiency groups based on an assessment of their motor skills. Using electroencephalography during a flanker task, error-related negativity was measured as the neural indicator of cognitive control. Post-error slowing was measured to represent behavioral adaptation. Participants also completed an anxiety assessment questionnaire. Participants in the high motor proficiency group achieved better task accuracy and showed relatively enhanced cognitive control through increased ERN. Contrastingly, individuals in the lower motor proficiency group achieved poorer accuracy whilst showing some evidence of compensation through increased PES. Trait anxiety reflecting general worries was found to be correlated with motor functioning, but the study could not provide evidence that this was related to cognitive or behavioral control mechanisms. The interaction between cognitive and motor processes observed in this study is unique for healthy and sub-clinical populations and provides a baseline for the interpretation of similar investigations in individuals with motor disorders. (shrink)

This paper is based on ethnographic research of data practices in a public health project called Weather Health and Air Pollution. I examine two different kinds of practices that make air pollution data, focusing on how they relate to particular modes of sensing and articulating air pollution. I begin by describing the interstitial spaces involved in making measurements of air pollution at monitoring sites and in the running of a computer simulation. Specifically, I attend to a shared dimension of these (...) practices, the checking of a numerical reading for error. Checking a measurement for error is routine practice and a fundamental component of making data, yet these are also moments of interpretation, where the form and meaning of numbers are ambiguous. Through two case studies of modelling and monitoring data practices, I show that making a ‘good’ measurement requires developing a feeling for the instrument–air pollution interaction in terms of the intended functionality of the measurements made. These affective dimensions of practice are useful analytically, making explicit the interaction of standardised ways of knowing and embodied skill in stabilising data. I suggest that environmental data practices can be studied through researchers’ materialisation of error, which complicate normative accounts of Big Data and highlight the non-linear and entangled relations that are at work in the making of stable, accurate data. (shrink)

Calibration errors are inevitable and should not be ignored during the estimation of item parameters. Items with calibration error can affect the measurement results of tests. One of the purposes of the current study is to investigate the impacts of the calibration errors during the estimation of item parameters on the measurement accuracy, average test length, and test efficiency for variable-length cognitive diagnostic computerized adaptive testing. The other purpose is to examine the methods for reducing the (...) adverse effects of calibration errors. Simulation results show that calibration error has negative effect on the measurement accuracy for the deterministic input, noisy “and” gate model, and the reduced reparameterized unified model; the average test lengths is shorter, and the test efficiency is overestimated for items with calibration errors; the compensatory reparameterized unified model is less affected by the calibration errors, and the classification accuracy, average test length, and test efficiency are slightly stable in the CRUM framework; methods such as improving the quality of items, using large calibration sample to calibrate the parameters of items, as well as using cross-validation method can reduce the adverse effects of calibration errors on CD-CAT. (shrink)

This investigation sought to find the relationships among multiple dimensions of personality and multiple features of language style. Unlike previous investigations, after controlling for such other moderators as culture and socio-demographics, the current investigation explored those dimensions of naturalistic spoken language that most closely align with communication. In groups of five to eight players, participants from eight international locales completed hour-long competitive games consisting of a series of ostensible missions. Composite measures of quantity, lexical diversity, sentiment, immediacy and negations were (...) measured with an automated tool called SPLICE and with Linguistic Inquiry and Word Count. We also investigated style dynamics over the course of an interaction. We found predictors of extraversion, agreeableness, and neuroticism, but overall fewer significant associations than prior studies, suggesting greater heterogeneity in language style in contexts entailing interactivity, conversation rather than solitary message production, oral rather than written discourse, and groups rather than dyads. Extraverts were found to maintain greater linguistic style consistency over the course of an interaction. The discussion addresses the potential for Type I error when studying the relationship between language and personality. (shrink)

This paper addresses the doubts voiced by Wigner about the physical relevance of the concept of geometrical points by exploiting some facts known to all but honored by none: Almost all real numbers are transcendental; the explicit representation of any one will require an infinite amount of physical resources. An instrument devised to measure a continuous real variable will need a continuum of internal states to achieve perfect resolution. Consequently, a laboratory instrument for measuring a continuous variable in a finite (...) time can report only a finite number of values, each of which is constrained to be a rational number. It does not matter whether the variable is classical or quantum-mechanical. Now, in von Neumann’s measurement theory (von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, [1955]), an operator A with a continuous spectrum—which has no eigenvectors—cannot be measured, but it can be approximated by operators with discrete spectra which are measurable. The measurable approximant F(A) is not canonically determined; it has to be chosen by the experimentalist. It is argued that this operator can always be chosen in such a way that Sewell’s results (Sewell in Rep. Math. Phys. 56: 271, [2005]; Sewell, Lecture given at the J.T. Lewis Memorial Conference, Dublin, [2005]) on the measurement of a hermitian operator on a finite-dimensional vector space (described in Sect. 3.2) constitute an adequate resolution of the measurement problem in this theory. From this follows our major conclusion, which is that the notion of a geometrical point is as meaningful in nonrelativistic quantum mechanics as it is in classical physics. It is necessary to be sensitive to the fact that there is a gap between theoretical and experimental physics, which reveals itself tellingly as an error inherent in the measurement of a continuous variable. (shrink)

This paper examines how people assess inequality of income distribution and how inequality could be measured. We start from the philosophical analysis of Temkin, who distinguishes nine plausible aspects of inequality. His approach is based on the concept of ‘complaints’ or distances between incomes. We examine the Temkin approach by means of the questionnaire-experimental method pioneered by Amiel and Cowell to find out whether the aspects of equality have any plausibility for student respondents and, if so, whether there are aspects (...) which are more appealing than others. Both the numerical and verbal responses show that a considerable majority of the respondents might be influenced by the intuitions included in the combination of the Weighted Additive Principle and the Average view of complaints. The questionnaire results also shed some empirical light on the acceptance of the Transfer Principle and the attitudes towards the Sequence. Footnotes I would like to thank Erik Schokkaert, Frank Cowell, and Liema Davidovitz for various suggestions which have led to improvements in this paper. I am very grateful for helpful comments from seminar participants and an anonymous referee. I remain responsible for any remaining error. This paper was written while the author enjoyed the hospitality of Sticerd, LSE, London and he acknowledges the financial support provided by the Training and Mobility of Researchers Program of the European Communities, grant #ERBFMRXCT980248. (shrink)