Archive for the ‘evidence’ Category

A Second Simple Example of Measurement’s Role in Reducing Transaction Costs, Enhancing Market Efficiency, and Enables the Pricing of Intangible Assets

March 9, 2011

The prior post here showed why we should not confuse counts of things with measures of amounts, though counts are the natural starting place to begin constructing measures. That first simple example focused on an analogy between counting oranges and measuring the weight of oranges, versus counting correct answers on tests and measuring amounts of ability. This second example extends the first by, in effect, showing what happens when we want to aggregate value not just across different counts of some one thing but across different counts of different things. The point will be, in effect, to show how the relative values of apples, oranges, grapes, and bananas can be put into a common frame of reference and compared in a practical and convenient way.

For instance, you may go into a grocery store to buy raspberries and blackberries, and I go in to buy cantaloupe and watermelon. Your cost per individual fruit will be very low, and mine will be very high, but neither of us will find this annoying, confusing, or inconvenient because your fruits are very small, and mine, very large. Conversely, your cost per kilogram will be much higher than mine, but this won’t cause either of us any distress because we both recognize the differences in the labor, handling, nutritional, and culinary value of our purchases.

But what happens when we try to purchase something as complex as a unit of socioeconomic development? The eight UN Millennium Development Goals (MDGs) represent a start at a systematic effort to bring human, social, and natural capital together into the same economic and accountability framework as liquid and manufactured capital, and property. But that effort is stymied by the inefficiency and cost of making and using measures of the goals achieved. The existing MDG databases (http://data.un.org/Browse.aspx?d=MDG), and summary reports present overwhelming numbers of numbers. Individual indicators are presented for each year, each country, each region, and each program, goal by goal, target by target, indicator by indicator, and series by series, in an indigestible volume of data.

Though there are no doubt complex mathematical methods by which a philanthropic, governmental, or NGO investor might determine how much development is gained per million dollars invested, the cost of obtaining impact measures is so high that most funding decisions are made with little information concerning expected returns (Goldberg, 2009). Further, the percentages of various needs met by leading social enterprises typically range from 0.07% to 3.30%, and needs are growing, not diminishing. Progress at current rates means that it would take thousands of years to solve today’s problems of human suffering, social disparity, and environmental quality. The inefficiency of human, social, and natural capital markets is so overwhelming that there is little hope for significant improvements without the introduction of fundamental infrastructural supports, such as an Intangible Assets Metric System.

A basic question that needs to be asked of the MDG system is, how can anyone make any sense out of so much data? Most of the indicators are evaluated in terms of counts of the number of times something happens, the number of people affected, or the number of things observed to be present. These counts are usually then divided by the maximum possible (the count of the total population) and are expressed as percentages or rates.

As previously explained in various posts in this blog, counts and percentages are not measures in any meaningful sense. They are notoriously difficult to interpret, since the quantitative meaning of any given unit difference varies depending on the size of what is counted, or where the percentage falls in the 0-100 continuum. And because counts and percentages are interpreted one at a time, it is very difficult to know if and when any number included in the sheer mass of data is reasonable, all else considered, or if it is inconsistent with other available facts.

A study of the MDG data must focus on these three potential areas of data quality improvement: consistency evaluation, volume reduction, and interpretability. Each builds on the others. With consistent data lending themselves to summarization in sufficient statistics, data volume can be drastically reduced with no loss of information (Andersen, 1977, 1999; Wright, 1977, 1997), data quality can be readily assessed in terms of sufficiency violations (Smith, 2000; Smith & Plackner, 2009), and quantitative measures can be made interpretable in terms of a calibrated ruler’s repeatedly reproducible hierarchy of indicators (Bond & Fox, 2007; Masters, Lokan, & Doig, 1994).

The primary data quality criteria are qualitative relevance and meaningfulness, on the one hand, and mathematical rigor, on the other. The point here is one of following through on the maxim that we manage what we measure, with the goal of measuring in such a way that management is better focused on the program mission and not distracted by accounting irrelevancies.

Method

As written and deployed, each of the MDG indicators has the face and content validity of providing information on each respective substantive area of interest. But, as has been the focus of repeated emphases in this blog, counting something is not the same thing as measuring it.

Counts or rates of literacy or unemployment are not, in and of themselves, measures of development. Their capacity to serve as contributing indications of developmental progress is an empirical question that must be evaluated experimentally against the observable evidence. The measurement of progress toward an overarching developmental goal requires inferences made from a conceptual order of magnitude above and beyond that provided in the individual indicators. The calibration of an instrument for assessing progress toward the realization of the Millennium Development Goals requires, first, a reorganization of the existing data, and then an analysis that tests explicitly the relevant hypotheses as to the potential for quantification, before inferences supporting the comparison of measures can be scientifically supported.

A subset of the MDG data was selected from the MDG database available at http://data.un.org/Browse.aspx?d=MDG, recoded, and analyzed using Winsteps (Linacre, 2011). At least one indicator was selected from each of the eight goals, with 22 in total. All available data from these 22 indicators were recorded for each of 64 countries.

The reorganization of the data is nothing but a way of making the interpretation of the percentages explicit. The meaning of any one country’s percentage or rate of youth unemployment, cell phone users, or literacy has to be kept in context relative to expectations formed from other countries’ experiences. It would be nonsense to interpret any single indicator as good or bad in isolation. Sometimes 30% represents an excellent state of affairs, other times, a terrible one.

Therefore, the distributions of each indicator’s percentages across the 64 countries were divided into ranges and converted to ratings. A lower rating uniformly indicates a status further away from the goal than a higher rating. The ratings were devised by dividing the frequency distribution of each indicator roughly into thirds.

For instance, the youth unemployment rate was found to vary such that the countries furthest from the desired goal had rates of 25% and more(rated 1), and those closest to or exceeding the goal had rates of 0-10% (rated 3), leaving the middle range (10-25%) rated 2. In contrast, percentages of the population that are undernourished were rated 1 for 35% or more, 2 for 15-35%, and 3 for less than 15%.

Thirds of the distributions were decided upon only on the basis of the investigator’s prior experience with data of this kind. A more thorough approach to the data would begin from a finer-grained rating system, like that structuring the MDG table at http://mdgs.un.org/unsd/mdg/Resources/Static/Products/Progress2008/MDG_Report_2008_Progress_Chart_En.pdf. This greater detail would be sought in order to determine empirically just how many distinctions each indicator can support and contribute to the overall measurement system.

Sixty-four of the available 336 data points were selected for their representativeness, with no duplications of values and with a proportionate distribution along the entire continuum of observed values.

Data from the same 64 countries and the same years were then sought for the subsequent indicators. It turned out that the years in which data were available varied across data sets. Data within one or two years of the target year were sometimes substituted for missing data.

The data were analyzed twice, first with each indicator allowed its own rating scale, parameterizing each of the category difficulties separately for each item, and then with the full rating scale model, as the results of the first analysis showed all indicators shared strong consistency in the rating structure.

Results

Data were 65.2% complete. Countries were assessed on an average of 14.3 of the 22 indicators, and each indicator was applied on average to 41.7 of the 64 country cases. Measurement reliability was .89-.90, depending on how measurement error is estimated. Cronbach’s alpha for the by-country scores was .94. Calibration reliability was .93-.95. The rating scale worked well (see Linacre, 2002, for criteria). The data fit the measurement model reasonably well, with satisfactory data consistency, meaning that the hypothesis of a measurable developmental construct was not falsified.

The main result for our purposes here concerns how satisfactory data consistency makes it possible to dramatically reduce data volume and improve data interpretability. The figure below illustrates how. What does it mean for data volume to be drastically reduced with no loss of information? Let’s see exactly how much the data volume is reduced for the ten item data subset shown in the figure below.

The horizontal continuum from -100 to 1300 in the figure is the metric, the ruler or yardstick. The number of countries at various locations along that ruler is shown across the bottom of the figure. The mean (M), first standard deviation (S), and second standard deviation (T) are shown beneath the numbers of countries. There are ten countries with a measure of just below 400, just to the left of the mean (M).

The MDG indicators are listed on the right of the figure, with the indicator most often found being achieved relative to the goals at the bottom, and the indicator least often being achieved at the top. The ratings in the middle of the figure increase from 1 to 3 left to right as the probability of goal achievement increases as the measures go from low to high. The position of the ratings in the middle of the figure shifts from left to right as one reads up the list of indicators because the difficulty of achieving the goals is increasing.

Because the ratings of the 64 countries relative to these ten goals are internally consistent, nothing but the developmental level of the country and the developmental challenge of the indicator affects the probability that a given rating will be attained. It is this relation that defines fit to a measurement model, the sufficiency of the summed ratings, and the interpretability of the scores. Given sufficient fit and consistency, any country’s measure implies a given rating on each of the ten indicators.

For instance, imagine a vertical line drawn through the figure at a measure of 500, just above the mean (M). This measure is interpreted relative to the places at which the vertical line crosses the ratings in each row associated with each of the ten items. A measure of 500 is read as implying, within a given range of error, uncertainty, or confidence, a rating of

  • 3 on debt service and female-to-male parity in literacy,
  • 2 or 3 on how much of the population is undernourished and how many children under five years of age are moderately or severely underweight,
  • 2 on infant mortality, the percent of the population aged 15 to 49 with HIV, and the youth unemployment rate,
  • 1 or 2 the poor’s share of the national income, and
  • 1 on CO2 emissions and the rate of personal computers per 100 inhabitants.

For any one country with a measure of 500 on this scale, ten percentages or rates that appear completely incommensurable and incomparable are found to contribute consistently to a single valued function, developmental goal achievement. Instead of managing each separate indicator as a universe unto itself, this scale makes it possible to manage development itself at its own level of complexity. This ten-to-one ratio of reduced data volume is more than doubled when the total of 22 items included in the scale is taken into account.

This reduction is conceptually and practically important because it focuses attention on the actual object of management, development. When the individual indicators are the focus of attention, the forest is lost for the trees. Those who disparage the validity of the maxim, you manage what you measure, are often discouraged by the the feeling of being pulled in too many directions at once. But a measure of the HIV infection rate is not in itself a measure of anything but the HIV infection rate. Interpreting it in terms of broader developmental goals requires evidence that it in fact takes a place in that larger context.

And once a connection with that larger context is established, the consistency of individual data points remains a matter of interest. As the world turns, the order of things may change, but, more likely, data entry errors, temporary data blips, and other factors will alter data quality. Such changes cannot be detected outside of the context defined by an explicit interpretive framework that requires consistent observations.

-100  100     300     500     700     900    1100    1300
|-------+-------+-------+-------+-------+-------+-------|  NUM   INDCTR
1                                 1  :    2    :  3     3    9  PcsPer100
1                         1   :   2    :   3            3    8  CO2Emissions
1                    1  :    2    :   3                 3   10  PoorShareNatInc
1                 1  :    2    :  3                     3   19  YouthUnempRatMF
1              1   :    2   :   3                       3    1  %HIV15-49
1            1   :   2    :   3                         3    7  InfantMortality
1          1  :    2    :  3                            3    4  ChildrenUnder5ModSevUndWgt
1         1   :    2    :  3                            3   12  PopUndernourished
1    1   :    2   :   3                                 3    6  F2MParityLit
1   :    2    :  3                                      3    5  DebtServExpInc
|-------+-------+-------+-------+-------+-------+-------|  NUM   INDCTR
-100  100     300     500     700     900    1100    1300
                   1
       1   1 13445403312323 41 221    2   1   1            COUNTRIES
       T      S       M      S       T

Discussion

A key element in the results obtained here concerns the fact that the data were about 35% missing. Whether or not any given indicator was actually rated for any given country, the measure can still be interpreted as implying the expected rating. This capacity to take missing data into account can be taken advantage of systematically by calibrating a large bank of indicators. With this in hand, it becomes possible to gather only the amount of data needed to make a specific determination, or to adaptively administer the indicators so as to obtain the lowest-error (most reliable) measure at the lowest cost (with the fewest indicators administered). Perhaps most importantly, different collections of indicators can then be equated to measure in the same unit, so that impacts may be compared more efficiently.

Instead of an international developmental aid market that is so inefficient as to preclude any expectation of measured returns on investment, setting up a calibrated bank of indicators to which all measures are traceable opens up numerous desirable possibilities. The cost of assessing and interpreting the data informing aid transactions could be reduced to negligible amounts, and the management of the processes and outcomes in which that aid is invested would be made much more efficient by reduced data volume and enhanced information content. Because capital would flow more efficiently to where supply is meeting demand, nonproducers would be cut out of the market, and the effectiveness of the aid provided would be multiplied many times over.

The capacity to harmonize counts of different but related events into a single measurement system presents the possibility that there may be a bright future for outcomes-based budgeting in education, health care, human resource management, environmental management, housing, corrections, social services, philanthropy, and international development. It may seem wildly unrealistic to imagine such a thing, but the return on the investment would be so monumental that not checking it out would be even crazier.

A full report on the MDG data, with the other references cited, is available on my SSRN page at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1739386.

Goldberg, S. H. (2009). Billions of drops in millions of buckets: Why philanthropy doesn’t advance social progress. New York: Wiley.

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How Evidence-Based Decision Making Suffers in the Absence of Theory and Instrument: The Power of a More Balanced Approach

January 28, 2010

The Basis of Evidence in Theory and Instrument

The ostensible point of basing decisions in evidence is to have reasons for proceeding in one direction versus any other. We want to be able to say why we are proceeding as we are. When we give evidence-based reasons for our decisions, we typically couch them in terms of what worked in past experience. That experience might have been accrued over time in practical applications, or it might have been deliberately arranged in one or more experimental comparisons and tests of concisely stated hypotheses.

At its best, generalizing from past experience to as yet unmet future experiences enables us to navigate life and succeed in ways that would not be possible if we could not learn and had no memories. The application of a lesson learned from particular past events to particular future events involves a very specific inferential process. To be able to recognize repeated iterations of the same things requires the accumulation of patterns of evidence. Experience in observing such patterns allows us to develop confidence in our understanding of what that pattern represents in terms of pleasant or painful consequences. When we are able to conceptualize and articulate an idea of a pattern, and when we are then able to recognize a new occurrence of that pattern, we have an idea of it.

Evidence-based decision making is then a matter of formulating expectations from repeatedly demonstrated and routinely reproducible patterns of observations that lend themselves to conceptual representations, as ideas expressed in words. Linguistic and cultural frameworks selectively focus attention by projecting expectations and filtering observations into meaningful patterns represented by words, numbers, and other symbols. The point of efforts aimed at basing decisions in evidence is to try to go with the flow of this inferential process more deliberately and effectively than might otherwise be the case.

None of this is new or controversial. However, the inferential step from evidence to decision always involves unexamined and unjustified assumptions. That is, there is always an element of metaphysical faith behind the expectation that any given symbol or word is going to work as a representation of something in the same way that it has in the past. We can never completely eliminate this leap of faith, since we cannot predict the future with 100% confidence. We can, however, do a lot to reduce the size of the leap, and the risks that go with it, by questioning our assumptions in experimental research that tests hypotheses as to the invariant stability and predictive utility of the representations we make.

Theoretical and Instrumental Assumptions Hidden Behind the Evidence

For instance, evidence as to the effectiveness of an intervention or treatment is often expressed in terms of measures commonly described as quantitative. But it is unusual for any evidence to be produced justifying that description in terms of something that really adds up in the way numbers do. So we often find ourselves in situations in which our evidence is much less meaningful, reliable, and valid than we suppose it to be.

Quantitative measures are often valued as the hallmark of rational science. But their capacity to live up to this billing depends on the quality of the inferences that can be supported. Very few researchers thoroughly investigate the quality of their measures and justify the inferences they make relative to that quality.

Measurement presumes a reproducible pattern of evidence that can serve as the basis for a decision concerning how much of something has been observed. It naturally follows that we often base measurement in counts of some kind—successes, failures, ratings, frequencies, etc. The counts, scores, or sums are then often transformed into percentages by dividing them into the maximum possible that could be obtained. Sometimes the scores are averaged for each person measured, and/or for each item or question on the test, assessment, or survey. These scores and percentages are then almost universally fed directly into decision processes or statistical analyses with no further consideration.

The reproducible pattern of evidence on which decisions are based is presumed to exist between the measures, not within them. In other words, the focus is on the group or population statistics, not on the individual measures. Attention is typically focused on the tip of the iceberg, the score or percentage, not on the much larger, but hidden, mass of information beneath it. Evidence is presumed to be sufficient to the task when the differences between groups of scores are of a consistent size or magnitude, but is this sufficient?

Going Past Assumptions to Testable Hypotheses

In other words, does not science require that evidence be explained by theory, and embodied in instrumentation that provides a shared medium of observation? As shown in the blue lines in the Figure below,

  • theory, whether or not it is explicitly articulated, inevitably influences both what counts as valid data and the configuration of the medium of its representation, the instrument;
  • data, whether or not it is systematically gathered and evaluated, inevitably influences both the medium of its representation, the instrument, and the implicit or explicit theory that explains its properties and justifies its applications; and
  • instruments, whether or not they are actually calibrated from a mapping of symbols and substantive amounts, inevitably influence data gathering and the image of the object explained by theory.

The rhetoric of evidence-based decision making skips over the roles of theory and instrumentation, drawing a direct line from data to decision. In leaving theory laxly formulated, we allow any story that makes a bit of sense and is communicated by someone with a bit of charm or power to carry the day. In not requiring calibrated instrumentation, we allow any data that cross the threshold into our awareness to serve as an acceptable basis for decisions.

What we want, however, is to require meaningful measures that really provide the evidence needed for instruments that exhibit invariant calibrations and for theories that provide predictive explanatory control over the variable. As shown in the Figure, we want data that push theory away from the instrument, theory that separates the data and instrument, and instruments that get in between the theory and data.

We all know to distrust too close a correspondence between theory and data, but we too rarely understand or capitalize on the role of the instrument in mediating the theory-data relation. Similarly, when the questions used as a medium for making observations are obviously biased to produce responses conforming overly closely with a predetermined result, we see that the theory and the instrument are too close for the data to serve as an effective mediator.

Finally, the situation predominating in the social sciences is one in which both construct and measurement theories are nearly nonexistent, which leaves data completely dependent on the instrument it came from. In other words, because counts of correct answers or sums of ratings are mistakenly treated as measures, instruments fully determine and restrict the range of measurement to that defined by the numbers of items and rating categories. Once the instrument is put in play, changes to it would make new data incommensurable with old, so, to retain at least the appearance of comparability, the data structure then fully determines and restricts the instrument.

What we want, though, is a situation in which construct and measurement theories work together to make the data autonomous of the particular instrument it came from. We want a theory that explains what is measured well enough for us to be able to modify existing instruments, or create entirely new ones, that give the same measures for the same amounts as the old instruments. We want to be able to predict item calibrations from the properties of the items, we want to obtain the same item calibrations across data sets, and we want to be able to predict measures on the basis of the observed responses (data) no matter which items or instrument was used to produce them.

Most importantly, we want a theory and practice of measurement that allows us to take missing data into account by providing us with the structural invariances we need as media for predicting the future from the past. As Ben Wright (1997, p. 34) said, any data analysis method that requires complete data to produce results disqualifies itself automatically as a viable basis for inference because we never have complete data—any practical system of measurement has to be positioned so as to be ready to receive, process, and incorporate all of the data we have yet to gather. This goal is accomplished to varying degrees in Rasch measurement (Rasch, 1960; Burdick, Stone, & Stenner, 2006; Dawson, 2004). Stenner and colleagues (Stenner, Burdick, Sanford, & Burdick, 2006) provide a trajectory of increasing degrees to which predictive theory is employed in contemporary measurement practice.

The explanatory and predictive power of theory is embodied in instruments that focus attention on recording observations of salient phenomena. These observations become data that inform the calibration of instruments, which then are used to gather further data that can be used in practical applications and in checks on the calibrations and the theory.

“Nothing is so practical as a good theory” (Lewin, 1951, p. 169). Good theory makes it possible to create symbolic representations of things that are easy to think with. To facilitate clear thinking, our words, numbers, and instruments must be transparent. We have to be able to look right through them at the thing itself, with no concern as to distortions introduced by the instrument, the sample, the observer, the time, the place, etc. This happens only when the structure of the instrument corresponds with invariant features of the world. And where words effect this transparency to an extent, it is realized most completely when we can measure in ways that repeatedly give the same results for the same amounts in the same conditions no matter which instrument, sample, operator, etc. is involved.

Where Might Full Mathematization Lead?

The attainment of mathematical transparency in measurement is remarkable for the way it focuses attention and constrains the imagination. It is essential to appreciate the context in which this focusing occurs, as popular opinion is at odds with historical research in this regard. Over the last 60 years, historians of science have come to vigorously challenge the widespread assumption that technology is a product of experimentation and/or theory (Kuhn, 1961/1977; Latour, 1987, 2005; Maas, 2001; Mendelsohn, 1992; Rabkin, 1992; Schaffer, 1992; Heilbron, 1993; Hankins & Silverman, 1999; Baird, 2002). Neither theory nor experiment typically advances until a key technology is widely available to end users in applied and/or research contexts. Rabkin (1992) documents multiple roles played by instruments in the professionalization of scientific fields. Thus, “it is not just a clever historical aphorism, but a general truth, that ‘thermodynamics owes much more to the steam engine than ever the steam engine owed to thermodynamics’” (Price, 1986, p. 240).

The prior existence of the relevant technology comes to bear on theory and experiment again in the common, but mistaken, assumption that measures are made and experimentally compared in order to discover scientific laws. History shows that measures are rarely made until the relevant law is effectively embodied in an instrument (Kuhn, 1961/1977, pp. 218-9): “…historically the arrow of causality is largely from the technology to the science” (Price, 1986, p. 240). Instruments do not provide just measures; rather they produce the phenomenon itself in a way that can be controlled, varied, played with, and learned from (Heilbron, 1993, p. 3; Hankins & Silverman, 1999; Rabkin, 1992). The term “technoscience” has emerged as an expression denoting recognition of this priority of the instrument (Baird, 1997; Ihde & Selinger, 2003; Latour, 1987).

Because technology often dictates what, if any, phenomena can be consistently produced, it constrains experimentation and theorizing by focusing attention selectively on reproducible, potentially interpretable effects, even when those effects are not well understood (Ackermann, 1985; Daston & Galison, 1992; Ihde, 1998; Hankins & Silverman, 1999; Maasen & Weingart, 2001). Criteria for theory choice in this context stem from competing explanatory frameworks’ experimental capacities to facilitate instrument improvements, prediction of experimental results, and gains in the efficiency with which a phenomenon is produced.

In this context, the relatively recent introduction of measurement models requiring additive, invariant parameterizations (Rasch, 1960) provokes speculation as to the effect on the human sciences that might be wrought by the widespread availability of consistently reproducible effects expressed in common quantitative languages. Paraphrasing Price’s comment on steam engines and thermodynamics, might it one day be said that as yet unforeseeable advances in reading theory will owe far more to the Lexile analyzer (Stenner, et al., 2006) than ever the Lexile analyzer owed reading theory?

Kuhn (1961/1977) speculated that the second scientific revolution of the early- to mid-nineteenth century followed in large part from the full mathematization of physics, i.e., the emergence of metrology as a professional discipline focused on providing universally accessible, theoretically predictable, and evidence-supported uniform units of measurement (Roche, 1998). Kuhn (1961/1977, p. 220) specifically suggests that a number of vitally important developments converged about 1840 (also see Hacking, 1983, p. 234). This was the year in which the metric system was formally instituted in France after 50 years of development (it had already been obligatory in other nations for 20 years at that point), and metrology emerged as a professional discipline (Alder, 2002, p. 328, 330; Heilbron, 1993, p. 274; Kula, 1986, p. 263). Daston (1992) independently suggests that the concept of objectivity came of age in the period from 1821 to 1856, and gives examples illustrating the way in which the emergence of strong theory, shared metric standards, and experimental data converged in a context of particular social mores to winnow out unsubstantiated and unsupportable ideas and contentions.

Might a similar revolution and new advances in the human sciences follow from the introduction of evidence-based, theoretically predictive, instrumentally mediated, and mathematical uniform measures? We won’t know until we try.

Figure. The Dialectical Interactions and Mutual Mediations of Theory, Data, and Instruments

Figure. The Dialectical Interactions and Mutual Mediations of Theory, Data, and Instruments

Acknowledgment. These ideas have been drawn in part from long consideration of many works in the history and philosophy of science, primarily Ackermann (1985), Ihde (1991), and various works of Martin Heidegger, as well as key works in measurement theory and practice. A few obvious points of departure are listed in the references.

References

Ackermann, J. R. (1985). Data, instruments, and theory: A dialectical approach to understanding science. Princeton, New Jersey: Princeton University Press.

Alder, K. (2002). The measure of all things: The seven-year odyssey and hidden error that transformed the world. New York: The Free Press.

Aldrich, J. (1989). Autonomy. Oxford Economic Papers, 41, 15-34.

Andrich, D. (2004, January). Controversy and the Rasch model: A characteristic of incompatible paradigms? Medical Care, 42(1), I-7–I-16.

Baird, D. (1997, Spring-Summer). Scientific instrument making, epistemology, and the conflict between gift and commodity economics. Techné: Journal of the Society for Philosophy and Technology, 3-4, 25-46. Retrieved 08/28/2009, from http://scholar.lib.vt.edu/ejournals/SPT/v2n3n4/baird.html.

Baird, D. (2002, Winter). Thing knowledge – function and truth. Techné: Journal of the Society for Philosophy and Technology, 6(2). Retrieved 19/08/2003, from http://scholar.lib.vt.edu/ejournals/SPT/v6n2/baird.html.

Burdick, D. S., Stone, M. H., & Stenner, A. J. (2006). The Combined Gas Law and a Rasch Reading Law. Rasch Measurement Transactions, 20(2), 1059-60 [http://www.rasch.org/rmt/rmt202.pdf].

Carroll-Burke, P. (2001). Tools, instruments and engines: Getting a handle on the specificity of engine science. Social Studies of Science, 31(4), 593-625.

Daston, L. (1992). Baconian facts, academic civility, and the prehistory of objectivity. Annals of Scholarship, 8, 337-363. (Rpt. in L. Daston, (Ed.). (1994). Rethinking objectivity (pp. 37-64). Durham, North Carolina: Duke University Press.)

Daston, L., & Galison, P. (1992, Fall). The image of objectivity. Representations, 40, 81-128.

Dawson, T. L. (2004, April). Assessing intellectual development: Three approaches, one sequence. Journal of Adult Development, 11(2), 71-85.

Galison, P. (1999). Trading zone: Coordinating action and belief. In M. Biagioli (Ed.), The science studies reader (pp. 137-160). New York, New York: Routledge.

Hacking, I. (1983). Representing and intervening: Introductory topics in the philosophy of natural science. Cambridge: Cambridge University Press.

Hankins, T. L., & Silverman, R. J. (1999). Instruments and the imagination. Princeton, New Jersey: Princeton University Press.

Heelan, P. A. (1983, June). Natural science as a hermeneutic of instrumentation. Philosophy of Science, 50, 181-204.

Heelan, P. A. (1998, June). The scope of hermeneutics in natural science. Studies in History and Philosophy of Science Part A, 29(2), 273-98.

Heidegger, M. (1977). Modern science, metaphysics, and mathematics. In D. F. Krell (Ed.), Basic writings [reprinted from M. Heidegger, What is a thing? South Bend, Regnery, 1967, pp. 66-108] (pp. 243-282). New York: Harper & Row.

Heidegger, M. (1977). The question concerning technology. In D. F. Krell (Ed.), Basic writings (pp. 283-317). New York: Harper & Row.

Heilbron, J. L. (1993). Weighing imponderables and other quantitative science around 1800. Historical studies in the physical and biological sciences), 24(Supplement), Part I, pp. 1-337.

Hessenbruch, A. (2000). Calibration and work in the X-ray economy, 1896-1928. Social Studies of Science, 30(3), 397-420.

Ihde, D. (1983). The historical and ontological priority of technology over science. In D. Ihde, Existential technics (pp. 25-46). Albany, New York: State University of New York Press.

Ihde, D. (1991). Instrumental realism: The interface between philosophy of science and philosophy of technology. (The Indiana Series in the Philosophy of Technology). Bloomington, Indiana: Indiana University Press.

Ihde, D. (1998). Expanding hermeneutics: Visualism in science. Northwestern University Studies in Phenomenology and Existential Philosophy). Evanston, Illinois: Northwestern University Press.

Ihde, D., & Selinger, E. (Eds.). (2003). Chasing technoscience: Matrix for materiality. (Indiana Series in Philosophy of Technology). Bloomington, Indiana: Indiana University Press.

Kuhn, T. S. (1961/1977). The function of measurement in modern physical science. Isis, 52(168), 161-193. (Rpt. In T. S. Kuhn, The essential tension: Selected studies in scientific tradition and change (pp. 178-224). Chicago: University of Chicago Press, 1977).

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