Comments on the National Accounts of Well-Being

Well-designed measures of human, social, and natural capital captured in genuine progress indicators and properly put to work on the front lines of education, health care, social services, human and environmental resource management, etc. will harness the profit motive as a driver of growth in human potential, community trust, and environmental quality. But it is a tragic shame that so many well-meaning efforts ignore the decisive advantages of readily available measurement methods. For instance, consider the National Accounts of Well-Being (available at http://www.nationalaccountsofwellbeing.org/learn/download-report.html).

This report’s authors admirably say that “Advances in the measurement of well-being mean that now we can reclaim the true purpose of national accounts as initially conceived and shift towards more meaningful measures of progress and policy effectiveness which capture the real wealth of people’s lived experience” (p. 2).

Of course, as is evident in so many of my posts here and in the focus of my scientific publications, I couldn’t agree more!

But look at p. 61, where the authors say “we acknowledge that we need to be careful about interpreting the distribution of transformed scores. The curvilinear transformation results in scores at one end of the distribution being stretched more than those at the other end. This means that standard deviations, for example, of countries with higher scores, are likely to be distorted upwards. As the results section shows, however, this pattern was not in fact found in our data, so it appears that this distortion does not have too much effect. Furthermore, being overly concerned with the distortion would imply absolute faith that the original scales used in the questions are linear. Such faith would be ill-founded. For example, it is not necessarily the case that the difference between ‘all or almost all of the time’ (a response scored as ‘4’ for some questions) and ‘most of the time’ (scored as ‘3’), is the same as the difference between ‘most of the time’ (‘3’) and ‘some of the time’ (‘2’).”

This is just incredible, that the authors admit so baldly that their numbers don’t add up at the same time that they offer those very same numbers in voluminous masses to a global audience that largely takes them at face value. What exactly does it mean to most people “to be careful about interpreting the distribution of transformed scores”?

More to the point, what does it mean that faith in the linearity of the scales is ill-founded? They are doing arithmetic with those scores! There is no way a constant difference between each number on the scale cannot be assumed! Instead of offering cautions, the creators of anything as visible and important as National Accounts of Well Being ought to do the work needed to construct scales that measure in numbers that add up. Instead of saying they don’t know what the size of the unit of measurement is at different places on the ruler, why don’t they formulate a theory of the thing they want to measure, state testable hypotheses as to the constancy and invariance of the measuring unit, and conduct the experiments? It is not, after all, as though we do not have a mature measurement science that has been doing this kind of thing for more than 80 years.

By its very nature, the act of adding up ratings into a sum, and dividing by the number of ratings included in that sum to produce an average, demands the assumption of a common unit of measurement. But practical science does not function or advance on the basis of untested assumptions. Different numbers that add up to the same sum have to mean the same thing: 1+3+4=8=2+3+3, etc. So the capacity of the measurement system to support meaningful inferences as to the invariance of the unit has to be established experimentally.

There is no way to do arithmetic and compute statistics on ordinal rating data without assuming a constant, additive unit of measurement. Either unrealistic demands are being made on people’s cognitive abilities to stretch and shrink numeric units, or the value of the numbers as a basis for action is seriously and unnecessarily compromised.

A lot can be done to construct linear units of measurement that provide the meaningfulness desired by the developers of the National Accounts of Well-Being.

For explanations and illustrations of why scores and percentages are not measures, see https://livingcapitalmetrics.wordpress.com/2009/07/01/graphic-illustrations-of-why-scores-ratings-and-percentages-are-not-measures-part-one/.

The numerous advantages real measures have over raw ratings are listed at https://livingcapitalmetrics.wordpress.com/2009/07/06/table-comparing-scores-ratings-and-percentages-with-rasch-measures/.

To understand the contrast between dead and living capital as it applies to measures based in ordinal data from tests and rating scales, see http://www.rasch.org/rmt/rmt154j.htm.

For a peer-reviewed scientific paper on the theory and research supporting the viability of a metric system for human, social, and natural capital, see http://dx.doi.org/doi:10.1016/j.measurement.2009.03.014.

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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.
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