The Moral Implications of the Concept of Human Capital: More on How to Create Living Capital Markets

The moral reprehensibility of the concept of human capital hinges on its use in rationalizing impersonal business decisions in the name of profits. Even when the viability of the organization is at stake, the discarding of people (referred to in some human resource departments as “taking out the trash”) entails degrees of psychological and economic injury no one should have to suffer, or inflict.

There certainly is a justified need for a general concept naming the productive capacity of labor. But labor is far more than a capacity for work. No one’s working life should be reduced to a job description. Labor involves a wide range of different combinations of skills, abilities, motivations, health, and trustworthiness. Human capital has then come to be broken down into a wide variety of forms, such as literacy capital, health capital, social capital, etc.

The metaphoric use of the word “capital” in the phrase “human capital” referring to stocks of available human resources rings hollow. The traditional concept of labor as a form of capital is an unjustified reduction of diverse capacities in itself. But the problem goes deeper. Intangible resources like labor are not represented and managed in the forms that make markets for tangible resources efficient. Transferable representations, like titles and deeds, give property a legal status as owned and an economic status as financially fungible. And in those legal and economic terms, tangible forms of capital give capitalism its hallmark signification as the lifeblood of the cycle of investment, profits, and reinvestment.

Intangible forms of capital, in contrast, are managed without the benefit of any standardized way of proving what is owned, what quantity or quality of it exists, and what it costs. Human, social, and natural forms of capital are therefore managed directly, by acting in an unmediated way on whomever or whatever embodies them. Such management requires, even in capitalist economies, the use of what are inherently socialistic methods, as these are the only methods available for dealing with the concrete individual people, communities, and ecologies involved (Fisher, 2002, 2011; drawing from Hayek, 1948, 1988; De Soto, 2000).

The assumption that transferable representations of intangible assets are inconceivable or inherently reductionist is, however, completely mistaken. All economic capital is ultimately brought to life (conceived, gestated, midwifed, and nurtured to maturity) as scientific capital. Scientific measurability is what makes it possible to add up the value of shares of stock across holdings, to divide something owned into shares, and to represent something in a court or a bank in a portable form (Latour, 1987; Fisher, 2002, 2011).

Only when you appreciate this distinction between dead and living capital, between capital represented on transferable instruments and capital that is not, then you can see that the real tragedy is not in the treatment of labor as capital. No, the real tragedy is in the way everyone is denied the full exercise of their rights over the skills, abilities, health, motivations, trustworthiness, and environmental resources that are rightly their own personal, private property.

Being homogenized at the population level into an interchangeable statistic is tragic enough. But when we leave the matter here, we fail to see and to grasp the meaning of the opportunities that are lost in that myopic world view. As I have been at pains in this blog to show, statistics are not measures. Statistical models of interactions between several variables at the group level are not the same thing as measurement models of interactions within a single variable at the individual level. When statistical models are used in place of measurement models, the result is inevitably numbers without a soul. When measurement models of individual response processes are used to produce meaningful estimates of how much of something someone possesses, a whole different world of possibilities opens up.

In the same way that the Pythagorean Theorem applies to any triangle, so, too, do the coordinates from the international geodetic survey make it possible to know everything that needs to be known about the location and disposition of a piece of real estate. Advanced measurement models in the psychosocial sciences are making it possible to arrive at similarly convenient and objective ways of representing the quality and quantity of intangible assets. Instead of being just one number among many others, real measures tell a story that situates each of us relative to everyone else in a meaningful way.

The practical meaning of the maxim “you manage what you measure” stems from those instances in which measures embody the fullness of the very thing that is the object of management interest. An engine’s fuel efficiency, or the volume of commodities produced, for instance, are things that can be managed less or more efficiently because there are measures of them that directly represent just what we want to control. Lean thinking enables the removal of resources that do not contribute to the production of the desired end result.

Many metrics, however, tend to obscure and distract from what need to be managed. The objects of measurement may seem to be obviously related to what needs to be managed, but dealing with each of them piecemeal results in inefficient and ineffective management. In these instances, instead of the characteristic cycle of investment, profit, and reinvestment, there seems only a bottomless pit absorbing ever more investment and never producing a profit. Why?

The economic dysfunctionality of intangible asset markets is intimately tied up with the moral dysfunctionality of those markets. Drawing an analogy from a recent analysis of political freedom (Shirky, 2010), economic freedom has to be accompanied by a market society economically literate enough, economically empowered enough, and interconnected enough to trade on the capital stocks issued. Western society, and increasingly the entire global society, is arguably economically literate and sufficiently interconnected to exercise economic freedom.

Economic empowerment is another matter entirely. There is no economic power without fungible capital, without ways of representing resources of all kinds, tangible and intangible, that transparently show what is available, how much of it there is, and what quality it is. A form of currency expressing the value of that capital is essential, but money is wildly insufficient to the task of determining the quality and quantity of the available capital stocks.

Today’s education, health care, human resource, and environmental quality markets are the diametric opposite of the markets in which investors, producers, and consumers are empowered. Only when dead human, social, and natural capital is brought to life in efficient markets (Fisher, 2011) will we empower ourselves with fuller degrees of creative control over our economic lives.

The crux of the economic empowerment issue is this: in the current context of inefficient intangibles markets, everyone is personally commodified. Everything that makes me valuable to an employer or investor or customer, my skills, motivations, health, and trustworthiness, is unjustifiably reduced to a homogenized unit of labor. And in the social and environmental quality markets, voting our shares is cumbersome, expensive, and often ineffective because of the immense amount of work that has to be done to defend each particular living manifestation of the value we want to protect.

Concentrated economic power is exercised in the mass markets of dead, socialized intangible assets in ways that we are taught to think of as impersonal and indifferent to each of us as individuals, but which is actually experienced by us as intensely personal.

So what is the difference between being treated personally as a commodity and being treated impersonally as a commodity? This is the same as asking what it would mean to be empowered economically with creative control over the stocks of human, social, and natural capital that are rightfully our private property. This difference is the difference between dead and living capital (Fisher, 2002, 2011).

Freedom of economic communication, realized in the trade of privately owned stocks of any form of capital, ought to be the highest priority in the way we think about the infrastructure of a sustainable and socially responsible economy. For maximum efficiency, that freedom requires a common meaningful and rigorous quantitative language enabling determinations of what exactly is for sale, and its quality, quantity, and unit price. As I have ad nauseum repeated in this blog, measurement based in scientifically calibrated instrumentation traceable to consensus standards is absolutely essential to meeting this need.

Coming in at a very close second to the highest priority is securing the ability to trade. A strong market society, where people can exercise the right to control their own private property—their personal stocks of human, social, and natural capital—in highly efficient markets, is more important than policies, regulations, and five-year plans dictating how masses of supposedly homogenous labor, social, and environmental commodities are priced and managed.

So instead of reacting to the downside of the business cycle with a socialistic safety net, how might a capitalistic one prove more humane, moral, and economically profitable? Instead of guaranteeing a limited amount of unemployment insurance funded through taxes, what we should have are requirements for minimum investments in social capital. Instead of employment in the usual sense of the term, with its implications of hiring and firing, we should have an open market for fungible human capital, in which everyone can track the price of their stock, attract and make new investments, take profits and income, upgrade the quality and/or quantity of their stock, etc.

In this context, instead of receiving unemployment compensation, workers not currently engaged in remunerated use of their skills would cash in some of their accumulated stock of social capital. The cost of social capital would go up in periods of high demand, as during the recent economic downturns caused by betrayals of trust and commitment (which are, in effect, involuntary expenditures of social capital). Conversely, the cost of human capital would also fluctuate with supply and demand, with the profits (currently referred to as wages) turned by individual workers rising and falling with the price of their stocks. These ups and downs, being absorbed by everyone in proportion to their investments, would reduce the distorted proportions we see today in the shares of the rewards and punishments allotted.

Though no one would have a guaranteed wage, everyone would have the opportunity to manage their capital to the fullest, by upgrading it, keeping it current, and selling it to the highest bidder. Ebbing and flowing tides would more truly lift and drop all boats together, with the drops backed up with the social capital markets’ tangible reassurance that we are all in this together. This kind of a social capitalism transforms the supposedly impersonal but actually highly personal indifference of flows in human capital into a more fully impersonal indifference in which individuals have the potential to maximize the realization of their personal goals.

What we need is to create a visible alternative to the bankrupt economic system in a kind of reverse shock doctrine. Eleanor Roosevelt often said that the thing we are most afraid of is the thing we most need to confront if we are to grow. The more we struggle against what we fear, the further we are carried away from what we want. Only when we relax into the binding constraints do we find them loosened. Only when we channel overwhelming force against itself or in a productive direction can we withstand attack. When we find the courage to go where the wild things are and look the monsters in the eye will we have the opportunity to see if their fearful aspect is transformed to playfulness. What is left is often a more mundane set of challenges, the residuals of a developmental transition to a new level of hierarchical complexity.

And this is the case with the moral implications of the concept of human capital. Treating individuals as fungible commodities is a way that some use to protect themselves from feeling like monsters and from being discarded as well. Those who find themselves removed from the satisfactions of working life can blame the shortsightedness of their former colleagues, or the ugliness of the unfeeling system. But neither defensive nor offensive rationalizations do anything to address the actual problem, and the problem has nothing to do with the morality or the immorality of the concept of human capital.

The problem is the problem. That is, the way we approach and define the problem delimits the sphere of the creative options we have for solving it. As Henry Ford is supposed to have said, whether you think you can or you think you cannot, you’re probably right. It is up to us to decide whether we can create an economic system that justifies its reductions and actually lives up to its billing as impersonal and unbiased, or if we cannot. Either way, we’ll have to accept and live with the consequences.

References

DeSoto, H. (2000). The mystery of capital: Why capitalism triumphs in the West and fails everywhere else. New York: Basic Books.

Fisher, W. P., Jr. (2002, Spring). “The Mystery of Capital” and the human sciences. Rasch Measurement Transactions, 15(4), 854 [http://www.rasch.org/rmt/rmt154j.htm].

Fisher, W. P., Jr. (2011, Spring). Bringing human, social, and natural capital to life: Practical consequences and opportunities. Journal of Applied Measurement, 12(1), in press.

Hayek, F. A. (1948). Individualism and economic order. Chicago: University of Chicago Press.

Hayek, F. A. (1988). The fatal conceit: The errors of socialism (W. W. Bartley, III, Ed.) The Collected Works of F. A. Hayek. Chicago: University of Chicago Press.

Latour, B. (1987). Science in action: How to follow scientists and engineers through society. New York: Cambridge University Press.

Shirky, C. (2010, December 20). The political power of social media: Technology, the public sphere, and political change. Foreign Affairs, 90(1), http://www.foreignaffairs.com/articles/67038/clay-shirky/the-political-power-of-social-media.

LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Based on a work at livingcapitalmetrics.wordpress.com.
Permissions beyond the scope of this license may be available at http://www.livingcapitalmetrics.com.

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

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.

LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Based on a work at livingcapitalmetrics.wordpress.com.
Permissions beyond the scope of this license may be available at http://www.livingcapitalmetrics.com.

A Simple Example of How Better Measurement Creates New Market Efficiencies, Reduces Transaction Costs, and Enables the Pricing of Intangible Assets

One of the ironies of life is that we often overlook the obvious in favor of the obscure. And so one hears of huge resources poured into finding and capitalizing on opportunities that provide infinitesimally small returns, while other opportunities—with equally certain odds of success but far more profitable returns—are completely neglected.

The National Institute for Standards and Technology (NIST) reports returns on investment ranging from 32% to over 400% in 32 metrological improvements made in semiconductors, construction, automation, computers, materials, manufacturing, chemicals, photonics, communications and pharmaceuticals (NIST, 2009). Previous posts in this blog offer more information on the economic value of metrology. The point is that the returns obtained from improvements in the measurement of tangible assets will likely also be achieved in the measurement of intangible assets.

How? With a little bit of imagination, each stage in the development of increasingly meaningful, efficient, and useful measures described in this previous post can be seen as implying a significant return on investment. As those returns are sought, investors will coordinate and align different technologies and resources relative to a roadmap of how these stages are likely to unfold in the future, as described in this previous post. The basic concepts of how efficient and meaningful measurement reduces transaction costs and market frictions, and how it brings capital to life, are explained and documented in my publications (Fisher, 2002-2011), but what would a concrete example of the new value created look like?

The examples I have in mind hinge on the difference between counting and measuring. Counting is a natural and obvious thing to do when we need some indication of how much of something there is. But counting is not measuring (Cooper & Humphry, 2010; Wright, 1989, 1992, 1993, 1999). This is not some minor academic distinction of no practical use or consequence. It is rather the source of the vast majority of the problems we have in comparing outcome and performance measures.

Imagine how things would be if we couldn’t weigh fruit in a grocery store, and all we could do was count pieces. We can tell when eight small oranges possess less overall mass of fruit than four large ones by weighing them; the eight small oranges might weigh .75 kilograms (about 1.6 pounds) while the four large ones come in at 1.0 kilo (2.2 pounds). If oranges were sold by count instead of weight, perceptive traders would buy small oranges and make more money selling them than they could if they bought large ones.

But we can’t currently arrive so easily at the comparisons we need when we’re buying and selling intangible assets, like those produced as the outcomes of educational, health care, or other services. So I want to walk through a couple of very down-to-earth examples to bring the point home. Today we’ll focus on the simplest version of the story, and tomorrow we’ll take up a little more complicated version, dealing with the counts, percentages, and scores used in balanced scorecard and dashboard metrics of various kinds.

What if you score eight on one reading test and I score four on a different reading test? Who has more reading ability? In the same way that we might be able to tell just by looking that eight small oranges are likely to have less actual orange fruit than four big ones, we might also be able to tell just by looking that eight easy (short, common) words can likely be read correctly with less reading ability than four difficult (long, rare) words can be.

So let’s analyze the difference between buying oranges and buying reading ability. We’ll set up three scenarios for buying reading ability. In all three, we’ll imagine we’re comparing how we buy oranges with the way we would have to go about buying reading ability today if teachers were paid for the gains made on the tests they administer at the beginning and end of the school year.

In the first scenario, the teachers make up their own tests. In the second, the teachers each use a different standardized test. In the third, each teacher uses a computer program that draws questions from the same online bank of precalibrated items to construct a unique test custom tailored to each student. Reading ability scenario one is likely the most commonly found in real life. Scenario three is the rarest, but nonetheless describes a situation that has been available to millions of students in the U.S., Australia, and elsewhere for several years. Scenarios one, two and three correspond with developmental levels one, three, and five described in a previous blog entry.

Buying Oranges

When you go into one grocery store and I go into another, we don’t have any oranges with us. When we leave, I have eight and you have four. I have twice as many oranges as you, but yours weigh a kilo, about a third more than mine (.75 kilos).

When we paid for the oranges, the transaction was finished in a few seconds. Neither one of us experienced any confusion, annoyance, or inconvenience in relation to the quality of information we had on the amount of orange fruits we were buying. I did not, however, pay twice as much as you did. In fact, you paid more for yours than I did for mine, in direct proportion to the difference in the measured amounts.

No negotiations were necessary to consummate the transactions, and there was no need for special inquiries about how much orange we were buying. We knew from experience in this and other stores that the prices we paid were comparable with those offered in other times and places. Our information was cheap, as it was printed on the bag of oranges or could be read off a scale, and it was very high quality, as the measures were directly comparable with measures from any other scale in any other store. So, in buying oranges, the impact of information quality on the overall cost of the transaction was so inexpensive as to be negligible.

Buying Reading Ability (Scenario 1)

So now you and I go through third grade as eight year olds. You’re in one school and I’m in another. We have different teachers. Each teacher makes up his or her own reading tests. When we started the school year, we each took a reading test (different ones), and we took another (again, different ones) as we ended the school year.

For each test, your teacher counted up your correct answers and divided by the total number of questions; so did mine. You got 72% correct on the first one, and 94% correct on the last one. I got 83% correct on the first one, and 86% correct on the last one. Your score went up 22%, much more than the 3% mine went up. But did you learn more? It is impossible to tell. What if both of your tests were easier—not just for you or for me but for everyone—than both of mine? What if my second test was a lot harder than my first one? On the other hand, what if your tests were harder than mine? Perhaps you did even better than your scores seem to indicate.

We’ll just exclude from consideration other factors that might come to bear, such as whether your tests were significantly longer or shorter than mine, or if one of us ran out of time and did not answer a lot of questions.

If our parents had to pay the reading teacher at the end of the school year for the gains that were made, how would they tell what they were getting for their money? What if your teacher gave a hard test at the start of the year and an easy one at the end of the year so that you’d have a big gain and your parents would have to pay more? What if my teacher gave an easy test at the start of the year and a hard one at the end, so that a really high price could be put on very small gains? If our parents were to compare their experiences in buying our improved reading ability, they would have a lot of questions about how much improvement was actually obtained. They would be confused and annoyed at how inconvenient the scores are, because they are difficult, if not impossible, to compare. A lot of time and effort might be invested in examining the words and sentences in each of the four reading tests to try to determine how easy or hard they are in relation to each other. Or, more likely, everyone would throw their hands up and pay as little as they possibly can for outcomes they don’t understand.

Buying Reading Ability (Scenario 2)

In this scenario, we are third graders again, in different schools with different reading teachers. Now, instead of our teachers making up their own tests, our reading abilities are measured at the beginning and the end of the school year using two different standardized tests sold by competing testing companies. You’re in a private suburban school that’s part of an independent schools association. I’m in a public school along with dozens of others in an urban school district.

For each test, our parents received a report in the mail showing our scores. As before, we know how many questions we each answered correctly, and, unlike before, we don’t know which particular questions we got right or wrong. Finally, we don’t know how easy or hard your tests were relative to mine, but we know that the two tests you took were equated, and so were the two I took. That means your tests will show how much reading ability you gained, and so will mine.

We have one new bit of information we didn’t have before, and that’s a percentile score. Now we know that at the beginning of the year, with a percentile ranking of 72, you performed better than 72% of the other private school third graders taking this test, and at the end of the year you performed better than 76% of them. In contrast, I had percentiles of 84 and 89.

The question we have to ask now is if our parents are going to pay for the percentile gain, or for the actual gain in reading ability. You and I each learned more than our peers did on average, since our percentile scores went up, but this would not work out as a satisfactory way to pay teachers. Averages being averages, if you and I learned more and faster, someone else learned less and slower, so that, in the end, it all balances out. Are we to have teachers paying parents when their children learn less, simply redistributing money in a zero sum game?

And so, additional individualized reports are sent to our parents by the testing companies. Your tests are equated with each other, and they measure in a comparable unit that ranges from 120 to 480. You had a starting score of 235 and finished the year with a score of 420, for a gain of 185.

The tests I took are comparable and measure in the same unit, too, but not the same unit as your tests measure in. Scores on my tests range from 400 to 1200. I started the year with a score of 790, and finished at 1080, for a gain of 290.

Now the confusion in the first scenario is overcome, in part. Our parents can see that we each made real gains in reading ability. The difficulty levels of the two tests you took are the same, as are the difficulties of the two tests I took. But our parents still don’t know what to pay the teacher because they can’t tell if you or I learned more. You had lower percentiles and test scores than I did, but you are being compared with what is likely a higher scoring group of suburban and higher socioeconomic status students than the urban group of disadvantaged students I’m compared against. And your scores aren’t comparable with mine, so you might have started and finished with more reading ability than I did, or maybe I had more than you. There isn’t enough information here to tell.

So, again, the information that is provided is insufficient to the task of settling on a reasonable price for the outcomes obtained. Our parents will again be annoyed and confused by the low quality information that makes it impossible to know what to pay the teacher.

Buying Reading Ability (Scenario 3)

In the third scenario, we are still third graders in different schools with different reading teachers. This time our reading abilities are measured by tests that are completely unique. Every student has a test custom tailored to their particular ability. Unlike the tests in the first and second scenarios, however, now all of the tests have been constructed carefully on the basis of extensive data analysis and experimental tests. Different testing companies are providing the service, but they have gone to the trouble to work together to create consensus standards defining the unit of measurement for any and all reading test items.

For each test, our parents received a report in the mail showing our measures. As before, we know how many questions we each answered correctly. Now, though we don’t know which particular questions we got right or wrong, we can see typical items ordered by difficulty lined up in a way that shows us what kind of items we got wrong, and which kind we got right. And now we also know your tests were equated relative to mine, so we can compare how much reading ability you gained relative to how much I gained. Now our parents can confidently determine how much they should pay the teacher, at least in proportion to their children’s relative measures. If our measured gains are equal, the same payment can be made. If one of us obtained more value, then proportionately more should be paid.

In this third scenario, we have a situation directly analogous to buying oranges. You have a measured amount of increased reading ability that is expressed in the same unit as my gain in reading ability, just as the weights of the oranges are comparable. Further, your test items were not identical with mine, and so the difficulties of the items we took surely differed, just as the sizes of the oranges we bought did.

This third scenario could be made yet more efficient by removing the need for creating and maintaining a calibrated item bank, as described by Stenner and Stone (2003) and in the sixth developmental level in a prior blog post here. Also, additional efficiencies could be gained by unifying the interpretation of the reading ability measures, so that progress through high school can be tracked with respect to the reading demands of adult life (Williamson, 2008).

Comparison of the Purchasing Experiences

In contrast with the grocery store experience, paying for increased reading ability in the first scenario is fraught with low quality information that greatly increases the cost of the transactions. The information is of such low quality that, of course, hardly anyone bothers to go to the trouble to try to decipher it. Too much cost is associated with the effort to make it worthwhile. So, no one knows how much gain in reading ability is obtained, or what a unit gain might cost.

When a school district or educational researchers mount studies to try to find out what it costs to improve reading ability in third graders in some standardized unit, they find so much unexplained variation in the costs that they, too, raise more questions than answers.

In grocery stores and other markets, we don’t place the cost of making the value comparison on the consumer or the merchant. Instead, society as a whole picks up the cost by funding the creation and maintenance of consensus standard metrics. Until we take up the task of doing the same thing for intangible assets, we cannot expect human, social, and natural capital markets to obtain the efficiencies we take for granted in markets for tangible assets and property.

References

Cooper, G., & Humphry, S. M. (2010). The ontological distinction between units and entities. Synthese, pp. DOI 10.1007/s11229-010-9832-1.

Fisher, W. P., Jr. (2002, Spring). “The Mystery of Capital” and the human sciences. Rasch Measurement Transactions, 15(4), 854 [http://www.rasch.org/rmt/rmt154j.htm].

Fisher, W. P., Jr. (2003). Measurement and communities of inquiry. Rasch Measurement Transactions, 17(3), 936-8 [http://www.rasch.org/rmt/rmt173.pdf].

Fisher, W. P., Jr. (2004, October). Meaning and method in the social sciences. Human Studies: A Journal for Philosophy and the Social Sciences, 27(4), 429-54.

Fisher, W. P., Jr. (2005). Daredevil barnstorming to the tipping point: New aspirations for the human sciences. Journal of Applied Measurement, 6(3), 173-9 [http://www.livingcapitalmetrics.com/images/FisherJAM05.pdf].

Fisher, W. P., Jr. (2007, Summer). Living capital metrics. Rasch Measurement Transactions, 21(1), 1092-3 [http://www.rasch.org/rmt/rmt211.pdf].

Fisher, W. P., Jr. (2009a, November). Invariance and traceability for measures of human, social, and natural capital: Theory and application. Measurement, 42(9), 1278-1287.

Fisher, W. P.. Jr. (2009b). NIST Critical national need idea White Paper: Metrological infrastructure for human, social, and natural capital (Tech. Rep., http://www.livingcapitalmetrics.com/images/FisherNISTWhitePaper2.pdf). New Orleans: LivingCapitalMetrics.com.

Fisher, W. P., Jr. (2011). Bringing human, social, and natural capital to life: Practical consequences and opportunities. Journal of Applied Measurement, 12(1), in press.

NIST. (2009, 20 July). Outputs and outcomes of NIST laboratory research. Available: http://www.nist.gov/director/planning/studies.cfm (Accessed 1 March 2011).

Stenner, A. J., & Stone, M. (2003). Item specification vs. item banking. Rasch Measurement Transactions, 17(3), 929-30 [http://www.rasch.org/rmt/rmt173a.htm].

Williamson, G. L. (2008). A text readability continuum for postsecondary readiness. Journal of Advanced Academics, 19(4), 602-632.

Wright, B. D. (1989). Rasch model from counting right answers: Raw scores as sufficient statistics. Rasch Measurement Transactions, 3(2), 62 [http://www.rasch.org/rmt/rmt32e.htm].

Wright, B. D. (1992, Summer). Scores are not measures. Rasch Measurement Transactions, 6(1), 208 [http://www.rasch.org/rmt/rmt61n.htm].

Wright, B. D. (1993). Thinking with raw scores. Rasch Measurement Transactions, 7(2), 299-300 [http://www.rasch.org/rmt/rmt72r.htm].

Wright, B. D. (1999). Common sense for measurement. Rasch Measurement Transactions, 13(3), 704-5  [http://www.rasch.org/rmt/rmt133h.htm].

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One of the ironies of life is that we often overlook the obvious in favor of the obscure. And so one hears of huge resources poured into finding and capitalizing on opportunities that provide infinitesimally small returns, while other opportunities—with equally certain odds of success but far more profitable returns—are completely neglected.

The National Institute for Standards and Technology (NIST) reports returns on investment ranging from 32% to over 400% in 32 metrological improvements made in semiconductors, construction, automation, computers, materials, manufacturing, chemicals, photonics, communications and pharmaceuticals (NIST, 2009). Previous posts in this blog offer more information on the economic value of metrology. The point is that the returns obtained from improvements in the measurement of tangible assets will likely also be achieved in the measurement of intangible assets.

How? With a little bit of imagination, each stage in the development of increasingly meaningful, efficient, and useful measures described in this previous post can be seen as implying a significant return on investment. As those returns are sought, investors will coordinate and align different technologies and resources relative to a roadmap of how these stages are likely to unfold in the future, as described in this previous post. But what would a concrete example of the new value created look like?

The examples I have in mind hinge on the difference between counting and measuring. Counting is a natural and obvious thing to do when we need some indication of how much of something there is. But counting is not measuring (Cooper & Humphry, 2010; Wright, 1989, 1992, 1993, 1999). This is not some minor academic distinction of no practical use or consequence. It is rather the source of the vast majority of the problems we have in comparing outcome and performance measures.

Imagine how things would be if we couldn’t weigh fruit in a grocery store, and all we could do was count pieces. We can tell when eight small oranges possess less overall mass of fruit than four large ones by weighing them; the eight small oranges might weigh .75 kilograms (about 1.6 pounds) while the four large ones come in at 1.0 kilo (2.2 pounds). If oranges were sold by count instead of weight, perceptive traders would buy small oranges and make more money selling them than they could if they bought large ones.

But we can’t currently arrive so easily at the comparisons we need when we’re buying and selling intangible assets, like those produced as the outcomes of educational, health care, or other services. So I want to walk through a couple of very down-to-earth examples to bring the point home. Today we’ll focus on the simplest version of the story, and tomorrow we’ll take up a little more complicated version, dealing with the counts, percentages, and scores used in balanced scorecard and dashboard metrics of various kinds.

What if you score eight on one reading test and I score four on a different reading test? Who has more reading ability? In the same way that we might be able to tell just by looking that eight small oranges are likely to have less actual orange fruit than four big ones, we might also be able to tell just by looking that eight easy (short, common) words can likely be read correctly with less reading ability than four difficult (long, rare) words can be.

So let’s analyze the difference between buying oranges and buying reading ability. We’ll set up three scenarios for buying reading ability. In all three, we’ll imagine we’re comparing how we buy oranges with the way we would have to go about buying reading ability today if teachers were paid for the gains made on the tests they administer at the beginning and end of the school year.

In the first scenario, the teachers make up their own tests. In the second, the teachers each use a different standardized test. In the third, each teacher uses a computer program that draws questions from the same online bank of precalibrated items to construct a unique test custom tailored to each student. Reading ability scenario one is likely the most commonly found in real life. Scenario three is the rarest, but nonetheless describes a situation that has been available to millions of students in the U.S., Australia, and elsewhere for several years. Scenarios one, two and three correspond with developmental levels one, three, and five described in a previous blog entry.

Buying Oranges

When you go into one grocery store and I go into another, we don’t have any oranges with us. When we leave, I have eight and you have four. I have twice as many oranges as you, but yours weigh a kilo, about a third more than mine (.75 kilos).

When we paid for the oranges, the transaction was finished in a few seconds. Neither one of us experienced any confusion, annoyance, or inconvenience in relation to the quality of information we had on the amount of orange fruits we were buying. I did not, however, pay twice as much as you did. In fact, you paid more for yours than I did for mine, in direct proportion to the difference in the measured amounts.

No negotiations were necessary to consummate the transactions, and there was no need for special inquiries about how much orange we were buying. We knew from experience in this and other stores that the prices we paid were comparable with those offered in other times and places. Our information was cheap, as it was printed on the bag of oranges or could be read off a scale, and it was very high quality, as the measures were directly comparable with measures from any other scale in any other store. So, in buying oranges, the impact of information quality on the overall cost of the transaction was so inexpensive as to be negligible.

Buying Reading Ability (Scenario 1)

So now you and I go through third grade as eight year olds. You’re in one school and I’m in another. We have different teachers. Each teacher makes up his or her own reading tests. When we started the school year, we each took a reading test (different ones), and we took another (again, different ones) as we ended the school year.

For each test, your teacher counted up your correct answers and divided by the total number of questions; so did mine. You got 72% correct on the first one, and 94% correct on the last one. I got 83% correct on the first one, and 86% correct on the last one. Your score went up 22%, much more than the 3% mine went up. But did you learn more? It is impossible to tell. What if both of your tests were easier—not just for you or for me but for everyone—than both of mine? What if my second test was a lot harder than my first one? On the other hand, what if your tests were harder than mine? Perhaps you did even better than your scores seem to indicate.

We’ll just exclude from consideration other factors that might come to bear, such as whether your tests were significantly longer or shorter than mine, or if one of us ran out of time and did not answer a lot of questions.

If our parents had to pay the reading teacher at the end of the school year for the gains that were made, how would they tell what they were getting for their money? What if your teacher gave a hard test at the start of the year and an easy one at the end of the year so that you’d have a big gain and your parents would have to pay more? What if my teacher gave an easy test at the start of the year and a hard one at the end, so that a really high price could be put on very small gains? If our parents were to compare their experiences in buying our improved reading ability, they would have a lot of questions about how much improvement was actually obtained. They would be confused and annoyed at how inconvenient the scores are, because they are difficult, if not impossible, to compare. A lot of time and effort might be invested in examining the words and sentences in each of the four reading tests to try to determine how easy or hard they are in relation to each other. Or, more likely, everyone would throw their hands up and pay as little as they possibly can for outcomes they don’t understand.

Buying Reading Ability (Scenario 2)

In this scenario, we are third graders again, in different schools with different reading teachers. Now, instead of our teachers making up their own tests, our reading abilities are measured at the beginning and the end of the school year using two different standardized tests sold by competing testing companies. You’re in a private suburban school that’s part of an independent schools association. I’m in a public school along with dozens of others in an urban school district.

For each test, our parents received a report in the mail showing our scores. As before, we know how many questions we each answered correctly, and, as before, we don’t know which particular questions we got right or wrong. Finally, we don’t know how easy or hard your tests were relative to mine, but we know that the two tests you took were equated, and so were the two I took. That means your tests will show how much reading ability you gained, and so will mine.

But we have one new bit of information we didn’t have before, and that’s a percentile score. Now we know that at the beginning of the year, with a percentile ranking of 72, you performed better than 72% of the other private school third graders taking this test, and at the end of the year you performed better than 76% of them. In contrast, I had percentiles of 84 and 89.

The question we have to ask now is if our parents are going to pay for the percentile gain, or for the actual gain in reading ability. You and I each learned more than our peers did on average, since our percentile scores went up, but this would not work out as a satisfactory way to pay teachers. Averages being averages, if you and I learned more and faster, someone else learned less and slower, so that, in the end, it all balances out. Are we to have teachers paying parents when their children learn less, simply redistributing money in a zero sum game?

And so, additional individualized reports are sent to our parents by the testing companies. Your tests are equated with each other, so they measure in a comparable unit that ranges from 120 to 480. You had a starting score of 235 and finished the year with a score of 420, for a gain of 185.

The tests I took are comparable and measure in the same unit, too, but not the same unit as your tests measure in. Scores on my tests range from 400 to 1200. I started the year with a score of 790, and finished at 1080, for a gain of 290.

Now the confusion in the first scenario is overcome, in part. Our parents can see that we each made real gains in reading ability. The difficulty levels of the two tests you took are the same, as are the difficulties of the two tests I took. But our parents still don’t know what to pay the teacher because they can’t tell if you or I learned more. You had lower percentiles and test scores than I did, but you are being compared with what is likely a higher scoring group of suburban and higher socioeconomic status students than the urban group of disadvantaged students I’m compared against. And your scores aren’t comparable with mine, so you might have started and finished with more reading ability than I did, or maybe I had more than you. There isn’t enough information here to tell.

So, again, the information that is provided is insufficient to the task of settling on a reasonable price for the outcomes obtained. Our parents will again be annoyed and confused by the low quality information that makes it impossible to know what to pay the teacher.

Buying Reading Ability (Scenario 3)

In the third scenario, we are still third graders in different schools with different reading teachers. This time our reading abilities are measured by tests that are completely unique. Every student has a test custom tailored to their particular ability. Unlike the tests in the first and second scenarios, however, now all of the tests have been constructed carefully on the basis of extensive data analysis and experimental tests. Different testing companies are providing the service, but they have gone to the trouble to work together to create consensus standards defining the unit of measurement for any and all reading test items.

For each test, our parents received a report in the mail showing our measures. As before, we know how many questions we each answered correctly. Now, though we don’t know which particular questions we got right or wrong, we can see typical items ordered by difficulty lined up in a way that shows us what kind of items we got wrong, and which kind we got right. And now we also know your tests were equated relative to mine, so we can compare how much reading ability you gained relative to how much I gained. Now our parents can confidently determine how much they should pay the teacher, at least in proportion to their children’s relative measures. If our measured gains are equal, the same payment can be made. If one of us obtained more value, then proportionately more should be paid.

In this third scenario, we have a situation directly analogous to buying oranges. You have a measured amount of increased reading ability that is expressed in the same unit as my gain in reading ability, just as the weights of the oranges are comparable. Further, your test items were not identical with mine, and so the difficulties of the items we took surely differed, just as the sizes of the oranges we bought did.

This third scenario could be made yet more efficient by removing the need for creating and maintaining a calibrated item bank, as described by Stenner and Stone (2003) and in the sixth developmental level in a prior blog post here. Also, additional efficiencies could be gained by unifying the interpretation of the reading ability measures, so that progress through high school can be tracked with respect to the reading demands of adult life (Williamson, 2008).

Comparison of the Purchasing Experiences

In contrast with the grocery store experience, paying for increased reading ability in the first scenario is fraught with low quality information that greatly increases the cost of the transactions. The information is of such low quality that, of course, hardly anyone bothers to go to the trouble to try to decipher it. Too much cost is associated with the effort to make it worthwhile. So, no one knows how much gain in reading ability is obtained, or what a unit gain might cost.

When a school district or educational researchers mount studies to try to find out what it costs to improve reading ability in third graders in some standardized unit, they find so much unexplained variation in the costs that they, too, raise more questions than answers.

But we don’t place the cost of making the value comparison on the consumer or the merchant in the grocery store. Instead, society as a whole picks up the cost by funding the creation and maintenance of consensus standard metrics. Until we take up the task of doing the same thing for intangible assets, we cannot expect human, social, and natural capital markets to obtain the efficiencies we take for granted in markets for tangible assets and property.

References

Cooper, G., & Humphry, S. M. (2010). The ontological distinction between units and entities. Synthese, pp. DOI 10.1007/s11229-010-9832-1.

NIST. (2009, 20 July). Outputs and outcomes of NIST laboratory research. Available: http://www.nist.gov/director/planning/studies.cfm (Accessed 1 March 2011).

Stenner, A. J., & Stone, M. (2003). Item specification vs. item banking. Rasch Measurement Transactions, 17(3), 929-30 [http://www.rasch.org/rmt/rmt173a.htm].

Williamson, G. L. (2008). A text readability continuum for postsecondary readiness. Journal of Advanced Academics, 19(4), 602-632.

Wright, B. D. (1989). Rasch model from counting right answers: Raw scores as sufficient statistics. Rasch Measurement Transactions, 3(2), 62 [http://www.rasch.org/rmt/rmt32e.htm].

Wright, B. D. (1992, Summer). Scores are not measures. Rasch Measurement Transactions, 6(1), 208 [http://www.rasch.org/rmt/rmt61n.htm].

Wright, B. D. (1993). Thinking with raw scores. Rasch Measurement Transactions, 7(2), 299-300 [http://www.rasch.org/rmt/rmt72r.htm].

Wright, B. D. (1999). Common sense for measurement. Rasch Measurement Transactions, 13(3), 704-5  [http://www.rasch.org/rmt/rmt133h.htm].