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There is nothing wrong with the NAEP reading exercises, the sampling design, or the NAEP Reading Proficiency Scale, these authors maintain. But adding a rich criterion-based frame of reference to the scale should yield an even more useful tool for shaping U.S. educational policy.

Does the reader comprehend the text because the reader is able or because the text is easy? Localizing the cause of comprehension in either the reader or the text is fraught with contradictions. A proposed solution uses a Rasch equation to models comprehension as the difference between a reader measure and text measure. Computing such a difference requires that reader and text are measured on a common scale. Thus, the puzzle is solved by positing a single continuum along which texts and readers can be conjointly ordered. A reader’s comprehension of a text is a function of the difference between reader ability and text readability. This solution forces recognition that generalizations about reader performance can be text independent (reader ability) or text dependent (comprehension). The article explores how reader ability and text readability can be measured on a single continuum, and the implications that this formulation holds for reading theory, the teaching of reading, and the testing of reading.

Rasch’s unidimensional models for measurement show how to connect object measures (e.g., reader abilities), measurement mechanisms (e.g., machine-generated cloze reading items), and observational outcomes (e.g., counts correct on reading instruments). Substantive theory shows what interventions or manipulations to the measurement mechanism can be traded off against a change to the object measure to hold the observed outcome constant. A Rasch model integrated with a substantive theory dictates the form and substance of permissible interventions. Rasch analysis, absent construct theory and an associated specification equation, is a black box in which understanding may be more illusory than not. Finally, the quantitative hypothesis can be tested by comparing theory-based trade-off relations with observed trade-off relations. Only quantitative variables (as measured) support such trade-offs. Note that to test the quantitative hypothesis requires more than manipulation of the algebraic equivalencies in the Rasch model or descriptively fitting data to the model. A causal Rasch model involves experimental intervention/manipulation on either reader ability or text complexity or a conjoint intervention on both simultaneously to yield a successful prediction of the resultant observed outcome (count correct). We conjecture that when this type of manipulation is introduced for individual reader text encounters and model predictions are consistent with observations, the quantitative hypothesis is sustained.

One must provide information about the conditions under which [the measurement outcome] would change or be different. It follows that the generalizations that figure in explanations [of measurement outcomes] must be change-relating… Both explainers [e.g., person parameters and item parameters] and what is explained [measurement outcomes] must be capable of change, and such changes must be connected in the right way (Woodward, 2003). Rasch’s unidimensional models for measurement tell us how to connect object measures, instrument calibrations, and measurement outcomes. Substantive theory tells us what interventions or changes to the instrument must offset a change to the measure for an object of measurement to hold the measurement outcome constant. Integrating a Rasch model with a substantive theory dictates the form and substance of permissible conjoint interventions. Rasch analysis absent construct theory and an associated specification equation is a black box in which understanding may be more illusory than not. The mere availability of numbers to analyze and statistics to report is often accepted as methodologically satisfactory in the social sciences, but falls far short of what is needed for a science.

Several concepts from Georg Rasch's last papers are discussed. The key one is comparison because Rasch considered the method of comparison fundamental to science. From the role of comparison stems scientific inference made operational by a properly developed frame of reference producing specific objectivity. The exact specifications Rasch outlined for making comparisons are explicated from quotes, and the role of causality derived from making comparisons is also examined. Understanding causality has implications for what can and cannot be produced via Rasch measurement. His simple examples were instructive, but the implications are far reaching upon first establishing the key role of comparison.

The field of career education measurement is in disarray. Evidence mounts that today’s career education instruments are verbal ability measures in disguise. A plethora of trait names such as career maturity, career development, career planning, career awareness, and career decision making have, in the last decade, appeared as labels to scales comprised of multiple choice items. Many of these scales appear to be measuring similar underlying traits and certainly the labels have a similar sound or “jingle” to them. Other scale names are attached to clusters of items that appear to measure different traits and at first glance appear deserving of their unique trait names, e.g., occupational information, resources for exploration, work conditions, personal economics. The items of these scales look different and the labels correspondingly are dissimilar or have a different “jangle” to them.

The process of ascribing meaning to scores produced by a measurement procedure is generally recognized as the most important task in developing an educational or psychological measure, be it an achievement test, interest inventory, or personality scale. This process, which is commonly referred to as construct validation (Cronbach, 1971; Cronbach & Meehl, 1955; ETS, 1979; Messick, 1975, 1980), involves a family of methods and procedures for assessing the degree to which a test measures a trait or theoretical construct.

A metrological infrastructure for the social, behavioral, and economic sciences has foundational and transformative potentials relating to education, health care, human and natural resource management, organizational performance assessment, and the economy at large. The traceability of universally uniform metrics to reference standard metrics is a taken-for-granted essential component of the infrastructure of the natural sciences and engineering. Advanced measurement methods and models capable of supporting similar metrics, standards, and traceability for intangible forms of capital have been available for decades but have yet to be implemented in ways that take full advantage of their capacities. The economy, education, health care reform, and the environment are all now top national priorities. There is nothing more essential to succeeding in these efforts than the quality of the measures we develop and deploy. Even so, few, if any, of these efforts are taking systematic advantage of longstanding, proven measurement technologies that may be crucial to the scientific and economic successes we seek. Bringing these technologies to the attention of the academic and business communities for use, further testing, and development in new directions is an area of critical national need.

Huge resources are invested in metrology and standards in the natural sciences, engineering, and across a wide range of commercial technologies. Significant positive returns of human, social, environmental, and economic value on these investments have been sustained for decades. Proven methods for calibrating test and survey instruments in linear units are readily available, as are data- and theory-based methods for equating those instruments to a shared unit. Using these methods, metrological traceability is obtained in a variety of commercially available elementary and secondary English and Spanish language reading education programs in the U.S., Canada, Mexico, and Australia. Given established historical patterns, widespread routine reproduction of predicted text-based and instructional effects expressed in a common language and shared frame of reference may lead to significant developments in theory and practice. Opportunities for systematic implementations of teacher-driven lean thinking and continuous quality improvement methods may be of particular interest and value.

A construct theory is the story we tell about what it means to move up and down the scale for a variable of interest (e.g., temperature, reading ability, short term memory). Why is it, for example, that items are ordered as they are on the item map? The story evolves as knowledge regarding the construct increases. We call both the process and the product of this evolutionary unfolding "construct definition" (Stenner et al., Journal of Educational Measurement 20:305–316, 1983). Advanced stages of construct definition are characterized by calibration equations (or specification equations) that operationalize and formalize a construct theory. These equations, make point predictions about item behavior or item ensemble distributions. The more closely theoretical calibrations coincide with empirical item difficulties, the more useful the construct theory and the more interesting the story. Twenty-five years of experience in developing the Lexile Framework for Reading enable us to distinguish five stages of thinking. Each subsequent stage can be characterized by an increasingly sophisticated use of substantive theory. Evidence that a construct theory and its associated technologies have reached a given stage or level can be found in the artifacts, instruments, and social networks that are realized at each level.

Implicit in the idea of measurement is the concept of objectivity. When we measure the temperature using a thermometer, we assume that the measurement we obtain is not dependent on the conditions of measurement, such as which thermometer we use. Any functioning thermometer should give us the same reading of, for example, 75 °F. If one thermometer measured 40 °, another 250 and a third 150, then the lack of objectivity would invalidate the very idea of accurately measuring temperature.

We argue that a goal of measurement is general objectivity: point estimates of a person’s measure (height, temperature, and reader ability) should be independent of the instrument and independent of the sample in which the person happens to find herself. In contrast, Rasch’s concept of specific objectivity requires only differences (i.e., comparisons) between person measures to be independent of the instrument. We present a canonical case in which there is no overlap between instruments and persons: each person is measured by a unique instrument. We then show what is required to estimate measures in this degenerate case. The canonical case encourages a simplification and reconceptualization of validity and reliability. Not surprisingly, this reconceptualization looks a lot like the way physicists and chemometricians think about validity and measurement error. We animate this presentation with a technology that blurs the distinction between instruction, assessment, and generally objective measurement of reader ability. We encourage adaptation of this model to health outcomes measurement.

Teachers make use of these two premises to match readers to text. Knowing a lot about text is helpful because “text matters” (Hiebert, 1998). But ordering or leveling text is only half the equation. We must also assess the level of the readers. These two activities are necessary so that the right books can be matched to the right reader at the right time. When teachers achieve this match intuitively, they are rewarded with students choosing to read more.

The last 50 years of human and social science measurement theory and practice have witnessed a steady retreat from physical science as the canonical model. Humphry (2011) unapologetically draws on metrology and physical science analogies to reformulate the relationship between discrimination and the unit. This brief note focuses on why this reformulation is important and on how these ideas can improve measurement theory and practice.

Psychometric models typically represent encounters between persons and dichotomous items as a random variable with two possible outcomes, one of which can be labeled success. For a given item, the stipulation that each person has a probability of success defines a construct on persons. This model specification defines the construct, but measurement is not yet achieved. The path to measurement must involve replication; unlike coin-tossing, this cannot be attained by repeating the encounter between the same person and the same item. Such replication can only be achieved with more items whose features are included in the model specifications. That is, the model must incorporate multiple items. This chapter examines multi-item model specifications that support the goal of measurement. The objective is to select the model that best facilitates the development of reliable measuring instruments. From this perspective, the Rasch model has important features compared to other models.

Measurement plays a vital role in the creation of markets, one that hinges on efficiencies gained via universal availability of precise and accurate information on product quantity and quality. Fulfilling the potential of these ideals requires close attention to measurement and the role of technology in science and the economy. The practical value of a strong theory of instrument calibration and metrological traceability stems from the capacity to mediate relationships in ways that align, coordinate, and integrate different firms’ expectations, investments, and capital budgeting decisions over the long term. Improvements in the measurement of reading ability exhibit patterns analogous to Moore’s Law, which has guided expectations in the micro-processor industry for almost 50 years. The state of the art in reading measurement serves as a model for generalizing the mediating role of instruments in making markets for other forms of intangible assets. These remarks provide only a preliminary sketch of the kinds of information that are both available and needed for making more efficient markets for human, social, and natural capital. Nevertheless, these initial steps project new horizons in the arts and sciences of measuring and managing intangible assets.

The purpose of this paper is to review some assumptions underlying the use of norm-referenced tests in educational evaluations and to provide a prospectus for research on these assumptions as well as other questions related to norm-referenced tests. Specifically, the assumptions which will be examined are (1) expressing treatment effects in a standard score metric permits aggregation of effects across grades, (2) commonly used standardized tests are sufficiently comparable to permit aggregation of results across tests, and (3) the summer loss observed in Title I projects is due to an actual loss in achievement skills and knowledge. We wish to emphasize at the outset that our intent in this paper is to raise questions and not to present a coherent set of answers.

In an argument whereby, “… individual-centered statistical techniques require models in which each individual is characterized separately and from which, given adequate data, the individual parameters can be estimated”.

In his classic paper entitled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Eugene Wigner addresses the question of why the language of Mathematics should prove so remarkably effective in the physical [natural] sciences. He marvels that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it.” We have been similarly struck by the outsized benefits that theory based instrument calibrations convey on the natural sciences, in contrast with the almost universal practice in the social sciences of using data to calibrate instrumentation.

This paper presents and illustrates a novel methodology, construct-specification equations, for examining the construct validity of a psychological instrument. Whereas traditional approaches have focused on the study of between-person variation on the construct, the suggested methodology emphasizes study of the relationships between item characteristics and item scores. The major thesis of the construct-specification-equation approach is that until developers of a psychological instrument understand what item characteristics are determining the item difficulties, the understanding of what is being measured is unsatisfyingly primitive. This method is illustrated with data from the Knox Cube Test which purports to be a measure of visual attention and short-term memory.

This paper describes Mapping Variables, the principal technique for planning and constructing a test or rating instrument. A variable map is also useful for interpreting results. Modest reference is made to the history of mapping leading to its importance in psychometrics. Several maps are given to show the importance and value of mapping a variable by person and item data. The need for critical appraisal of maps is also stressed.

The researchers explored the conceptual complexity of vocabulary in contemporary elementary-grades core science program textbooks to address two research questions: (1) Can a progression of concepts’ complexity level be described across grades? (2) Was there gradual developmental growth of the most complex concepts’ networks of associated concepts from the beginning of a program to the end? That is, for the most complex concepts, did associated concepts begin to appear in the early grades, with gradual cumulative addition of associated concepts throughout the elementary grades? Gradual accumulation of associated concepts could enable students to progressively construct a mental network of concepts within which a more complex concept could be situated, a network that could facilitate learning of most complex concepts. Two best-selling, contemporary elementary-grades core science programs constituted the data source. The researchers employed two measures: a conceptual complexity measure and the number of associated concepts (called nodes in concept networks) for each of the most complex concepts. The researchers conducted multilevel modeling and found that, on the whole, the programs exposed students to increasingly complex concepts with the rise of grades. Few highly complex concepts appeared in the earliest grades. Similarly, few associated concepts for the most complex concepts appeared in the earliest grades. Instead, associated concepts tended to be introduced simultaneously with the most complex concepts in the later grades. That is, on the whole, the programs did not expose students to the opportunity to construct strong affiliated concept networks (clusters of associated constructs) prior to introduction of the most complex concepts.

Loevinger's specifications for a unidimensional test are discussed. The implications are reviewed using commentary from Guttman's and Rasch's specification for specific objectivity. A large population is sampled to evaluate the implications of this approach in light of Wright's early presentation regarding data analysis. The results of this analysis show the sample follows the specifications of Loevinger and those of Rasch for a unidimensional test.

Patient-reported outcome measures (PROMs) are used to collect information directly from patients. They may cover several different types of outcomes ranging from symptoms, functioning, utility, satisfaction, through to quality-of-life (QoL). They generally consist of self-completed questionnaires that can be administered by means of hard copies or in a range of electronic formats. PROMs vary considerably in terms of the constructs they assess, the care with which they are developed, and their scientific quality. However, none of the PROMs available approach the quality of measurement achieved by measures/instruments used in physics. PROs are examples of latent variables. These are not directly observable, but can be inferred from, for example, responses to a questionnaire. The only measure of a latent variable that approaches the quality of measurement achieved by the physical sciences is the Lexile Framework for Reading. This framework is based on a construct theory that grew out of an analysis of several available reading measures. A specification equation was generated that was able to link the construct theory to scores obtained with the Lexile measure. A fundamental requirement of this quality of measurement is that the data collected with the model fit Rasch Measurement Theory (RMT). It is argued that PROM developers should aspire to match this level of measurement sophistication if their instruments are to provide valid insights into the impacts of disease and its treatment.

The Common Core raises the stature of texts to new heights, creating a hubbub. The fuss is especially messy at the early grades, where children are expected to read more complex texts than in the past. But early-grades teachers have been given little actionable guidance about text complexity. The authors recently examined early-grades texts to discover what makes them complex and now report that there is a lot that can help teachers, specifically, young children’s texts are special, a handful of text characteristics can signal text-complexity level, sometimes the interplay of text characteristics modulates text-complexity level, and knowing why a text is complex can facilitate text selection.

Educational Psychology (see record 2015-17975-001). Figures 5 and 8 were inadvertently printed in greyscale through a production related error. The correct color figures appear in this record.] The Common Core set a standard for all children to read increasingly complex texts throughout schooling. The purpose of the present study was to explore text characteristics specifically in relation to early-grades text complexity. Three hundred fifty primary-grades texts were selected and digitized. Twenty-two text characteristics were identified at 4 linguistic levels, and multiple computerized operationalizations were created for each of the 22 text characteristics. A researcher-devised text-complexity outcome measure was based on teacher judgment of text complexity in the 350 texts as well as on student judgment of text complexity as gauged by their responses in a maze task for a subset of the 350 texts. Analyses were conducted using a logical analytical progression typically used in machine-learning research. Random forest regression was the primary statistical modeling technique. Nine text characteristics were most important for early-grades text complexity including word structure (decoding demand and number of syllables in words), word meaning (age of acquisition, abstractness, and word rareness), and sentence and discourse-level characteristics (intersentential complexity, phrase diversity, text density/information load, and noncompressibility). Notably, interplay among text characteristics was important to explanation of text complexity, particularly for subsets of texts.

The purpose of the present cross-age study with South Korean students was to investigate the relationship of age and years of English-as-a-foreign-language (EFL) exposure with English-reading ability. The main research question was, “Do individuals’ age and number of years of English exposure interact in relation to English-reading ability?” The study also revealed the cross-age comparative status of South Korean students’ EFL reading ability.

The purpose of the study was to explore the validity of a novel computer-analytic developmental scale, the Writing Ability Developmental Scale. On the whole, collective results supported the validity of the scale. It was sensitive to writing ability differences across grades and sensitive to within-grade variability as compared to human-rated sensitivity. It predicted scores on the human-rated continuous scale very well. As compared to the human-rated continuous scale, it demonstrated similarly constant mean differences across ethnicity and socioeconomic status—although not for all rising grade differences or for gender. There was no genre differential across the two scales, and measurement precision was highly similar for the two scales.

The Common Core State Standards (CCSS) set a controversial aspirational, quantitative trajectory for text complexity exposure for readers throughout the grades, aiming for all high school graduates to be able to independently read complex college and workplace texts. However, the trajectory standard is presented without reference to how the grade-by-grade complexity ranges were determined or rationalized, and little guidance is provided for educators to know how to apply the flexible quantitative text exposure standard in their local contexts. We extend and elaborate the CCSS presentation and discussion, proposing that decisions about shifting quantitative text complexity levels in schools requires more than implementation of a single, static standard. A rigorous two-part analytical strategy for decision making surrounding the quantitative trajectory standard is proposed, a strategy that can be used by state policy makers, district officials, and educators in general. First, borrowing methods from student growth modeling, we illustrate an analytical method for creation of multiple trajectories that can lead to the CCSS end-of-high-school target for text complexity exposure, resulting in trajectories that place greater burden for shifting text complexity levels on students in different grades. Second, we submit that knowledge of the multiple possibilities, in conjunction with a set of guiding principles for decision making, can support educators and policy makers in critiquing and using the CCSS quantitative standard for text complexity exposure to establish particular expectations for quantitative text complexity exposure for particular students in situ.

Rasch’s unidimensional models for measurement are conjoint models that make it possible to put both texts and readers on the same scale. Causal Rasch Models (Stenner et al. Frontiers in Psychology 4:1–14, 2013) for language testing fuse a theory of text complexity to a Rasch Model making it possible for a computer to response illustrate texts read by language learners during daily practice. Causal Rasch Models are doubly prescriptive. First, they are prescriptive as to data structure (e.s., non-intersecting item characteristic curves.) Second, they are prescriptive as to the requirements of a substantive theory. One consequence of this fusion of a Rasch Model with a substantive theory is that individual-centered growth trajectories can be estimated for each reader even though no two readers ever read the same article or respond to a single common item. Rather than common items or common persons being the connective tissue that makes comparisons of readers possible, common theory is the connective tissue just as is true in, say, human temperature measurement where each person is paired with a unique thermometer. Thus, although the instrument is unique for each person on each occasion, a text complexity theory makes it possible to convert counts correct to a common reading ability metric in each and every application.

Separated and mixed applications of qualitative and quantitative methods are typically encumbered by markedly different philosophical orientations. Multiple inefficiencies arise when mixed methods work at cross purposes with each other. The phenomenological method, however, has the potential to integrate qualitative and quantitative concerns in ways that orient research towards uniform criteria of substantive meaningfulness and mathematical rigour. Three characteristics of a qualitative-quantitative methodological pluralism are described: structural invariance, substantive interpretability and the display of anomaly. When combined with networked information technologies, new opportunities emerge for a qualitatively meaningful and quantitatively precise measurement framework in the research and practice of the health sciences.

The authors introduce readers to the research documenting racial and ethnic gaps in school readiness. They describe the key tests, including the Peabody Picture Vocabulary Test (PPVT), the Early Childhood Longitudinal Study (ECLS), and several intelligence tests, and describe how they have been administered to several important national samples of children. Next, the authors review the different estimates of the gaps and discuss how to interpret these differences. In interpreting test results, researchers use the statistical term "standard deviation" to compare scores across the tests. On average, the tests find a gap of about 1 standard deviation. The ECLS-K estimate is the lowest, about half a standard deviation. The PPVT estimate is the highest, sometimes more than 1 standard deviation. When researchers adjust those gaps statistically to take into account different outside factors that might affect children's test scores, such as family income or home environment, the gap narrows but does not disappear. Why such different estimates of the gap? The authors consider explanations such as differences in the samples, racial or ethnic bias in the tests, and whether the tests reflect different aspects of school "readiness," and conclude that none is likely to explain the varying estimates. Another possible explanation is the Spearman Hypothesis-that all tests are imperfect measures of a general ability construct, g; the more highly a given test correlates with g, the larger the gap will be. But the Spearman Hypothesis, too, leaves questions to be investigated. A gap of 1 standard deviation may not seem large, but the authors show clearly how it results in striking disparities in the performance of black and white students and why it should be of serious concern to policymakers.

Validity of specification equations used by auto-text processors to estimate theoretical text complexity have increased importance because of the Common Core State Standards. Theoretical estimates of text complexity will inform (a) setting standards for college and career readiness, (b) grade-level standards, matching readers to text, and (d) creating a daily diet of stretch and targeted text designed to grow reading ability and content knowledge. The purpose of this research was to investigate the specification equation used in the Lexile Framework for Reading to measure text complexity. The Lexile Reading Analyzer contains a specification equation that uses proxies for the semantic difficulty and syntactic complexity to estimate the theoretical complexity of professionally-edited text. Differences between theoretical and empirical estimates of text complexity were examined for a set of 446 professionally authored, previously published passages. Students in grades 2-12 read these passages using A Learning Oasis, a web-based technology, to ensure that most of the articles read were well-targeted to student ability (+100L). Each article was response illustrated using an auto-generated semantic cloze item type embedded into passages. Observed student performance on this item type was used to derive an empirical estimate of text complexity for each passage. Theoretical estimates of text complexity accounted for approximately 90 percent of the variance in empirical estimates of text complexity. These findings suggest that the specification equation contains powerful predictors of empirical text complexity, speculation remains on what additional variables might account for the 10 percent of unexplained variation.

Several concepts from Georg Rasch's last papers are discussed. The key one is comparison because Rasch considered the method of comparison fundamental to science. From the role of comparison stems scientific inference made operational by a properly developed frame of reference producing specific objectivity. The exact specifications Rasch outlined for making comparisons are explicated from quotes, and the role of causality derived from making comparisons is also examined. Understanding causality has implications for what can and cannot be produced via Rasch measurement. His simple examples were instructive, but the implications are far reaching upon first establishing the key role of comparison.

Rasch’s unidimensional models for measurement show how to connect object measures (e.g., reader abilities), measurement mechanisms (e.g., machine-generated cloze reading items), and observational outcomes (e.g., counts correct on reading instruments). Substantive theory shows what interventions or manipulations to the measurement mechanism can be traded off against a change to the object measure to hold the observed outcome constant. A Rasch model integrated with a substantive theory dictates the form and substance of permissible interventions. Rasch analysis, absent construct theory and an associated specification equation, is a black box in which understanding may be more illusory than not. Finally, the quantitative hypothesis can be tested by comparing theory-based trade-off relations with observed trade-off relations. Only quantitative variables (as measured) support such trade-offs. Note that to test the quantitative hypothesis requires more than manipulation of the algebraic equivalencies in the Rasch model or descriptively fitting data to the model. A causal Rasch model involves experimental intervention/manipulation on either reader ability or text complexity or a conjoint intervention on both simultaneously to yield a successful prediction of the resultant observed outcome (count correct). We conjecture that when this type of manipulation is introduced for individual reader text encounters and model predictions are consistent with observations, the quantitative hypothesis is sustained.

Geometry is the most ancient branch of physics. All linear measurement is essentially a form of practical geometry. Following Maxwell’s method of drawing analogies from geometry, Rasch conceptualized measurement models as analogous to scientific laws. Rasch likely absorbed Maxwell’s method via close and prolonged interactions with colleagues known for their use of it. Examination of the common form of the relationships posited in the Pythagorean theorem, multiplicative natural laws, and Rasch models leads to a new perspective on the potential unity of science. To be fully realized in the social sciences, Rasch’s measurement ideas need to be dissociated from statistics and IRT, and instead rooted in the Maxwellian sources Rasch actually drew from. Following through on the method of analogy from geometry may make human and social measurement more intuitive and useful.

Measurement plays a vital role in the crea- tion of markets, one that hinges on efficiencies gained via the universal availability of precise and accurate information on product quantity and quality. Fulfilling the potential of these ideals requires close attention to measurement and the role of technology in science and the economy. The practical value of a strong theory of instrument calibration and metro- logical traceability stems from the capacity to mediate rela- tionships in ways that align, coordinate, and integrate differ- ent firms' expectations, investments, and capital budgeting decisions over the long term. Improvements in the meas- urement of reading ability exhibit patterns analogous to Moore's Law, which has guided expectations in the micro- processor industry for almost 50 years. The state of the art in reading measurement serves as a model for generalizing the mediating role of instruments in making markets for other form s of intangible assets. These remarks provide only a preliminary sketch of the kinds of information that are both available and needed for making more efficient markets for human, social, and natural capital. Nevertheless, these initial steps project new horizons in the arts and sciences of meas- uring and managing intangible assets.

We argue that a goal of measurement is general objectivity: point estimates of a person's measure (height, temperature, and reader ability) should be independent of the instrument and independent of the sample in which the person happens to find herself. In contrast, Rasch's concept of specific objectivity requires only differences (i.e., comparisons) between person measures to be independent of the instrument. We present a canonical case in which there is no overlap between instruments and persons: each person is measured by a unique instrument. We then show what is required to estimate measures in this degenerate case. The canonical case encourages a simplification and reconceptualization of validity and reliability. Not surprisingly, this reconceptualization looks a lot like the way physicists and chemometricians think about validity and measurement error. We animate this presentation with a technology that blurs the distinction between instruction, assessment, and generally objective measurement of reader ability. We encourage adaptation of this model to health outcomes measurement.

The use of Rasch-derived latent trait measurement of outcomes for persons with chronic disease and disablement evolved from other fields, particularly education. Person-metrics is the measurement of how much chronic disease and disablement affects an individual's daily activities physically, cognitively, and through vocational and social role participation. The ability of the Rasch model to assume that the probability of a given person/item interaction is governed by the difficulty of the item and the ability of the person is invaluable to disability measurement. The difference between raw scores and true measures is illustrated by an example of a patient whose physical difficulty is rated on rising from a wheelchair and walking 100m (known to be more difficult), and then walking an additional 200m. Though number ratings of 0-1-2 are assigned to these tasks, they are not equidistant, and only a true measure shows the actual levels of physical difficulty.

Psychometric models typically represent encounters between persons and dichotomous items as a random variable with two possible outcomes, one of which can be labeled success. For a given item, the stipulation that each person has a probability of success defines a construct on persons. This model specification defines the construct, but measurement is not yet achieved. The path to measurement must involve replication; unlike coin-tossing, this cannot be attained by repeating the encounter between the same person and the same item. Such replication can only be achieved with more items whose features are included in the model specifications. That is, the model must incorporate multiple items. This chapter examines multi-item model specifications that support the goal of measurement. The objective is to select the model that best facilitates the development of reliable measuring instruments. From this perspective, the Rasch model has important features compared to other models.

The Lexile Framework for Reading models comprehension as the difference between a reader measure and a text measure. Uncertainty in comprehension rates results from unreliability in reader measures and inaccuracy in text readability measures. Whole-text processing eliminates sampling error in text measures. However, Lexile text measures are imperfect due to misspecification of the Lexile theory. The standard deviation component associated with theory misspecification is estimated at 64L for a standard-length passage (approximately 125 words). A consequence is that standard errors for longer texts (2,500 to 150,000 words) are measured on the Lexile scale with uncertainties in the single digits. Uncertainties in expected comprehension rates are largely due to imprecision in reader ability and not inaccuracies in text readabilities.

The last 50 years of human and social science measurement theory and practice have witnessed a steady retreat from physical science as the canonical model. Humphry (this issue) unapologetically dra...

The central importance of reading ability in learning makes it the natural place to start in formative and summative assessments in education. The Lexile Framework for Reading constitutes a commercial metrological traceability network linking books, test results, instructional materials, and students in elementary and secondary English and Spanish language reading education in the U.S., Canada, Mexico, and Australia.

The public and researchers in psychology and the social sciences are largely unaware of the huge resources invested in metrology and standards in science and commerce, for understandable reasons, but with unfortunate consequences. Measurement quality varies widely in fields lacking uniform standards, making it impossible to coordinate local behaviours and decisions in tune with individually observed instrument readings. However, recent developments in reading measurement have effectively instituted metrological traceability methods within elementary and secondary English and Spanish language reading education in the U.S., Canada, Mexico, and Australia. Given established patterns in the history of science, it may be reasonable to expect that widespread routine reproduction of controlled effects expressed in uniform units in the social sciences may lead to significant developments in theory and practice.

The problem of demonstrating the invariance of factor structures across criterion groups is addressed. Procedures are outlined which combine the replication of factor structures across four sex-race groups with the use of the coefficient of invariance to demonstrate the level of invariance associated with the factors identified in a self concept measure (the Self Observation Scales, Intermediate Form A). Implications for hypothesis testing are discussed.