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Measurement

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In the natural sciences, attributes of the physical world, such as space, time, temperature, velocity and acceleration, are all measured quantitatively. Psychologists, concerned with behaviour and experience, are unable to measure many of the most interesting psychological attributes in the same objective manner and have struggled to justify the discipline as a science.

Psychology’s early years as an infant science were spent developing psychophysics and ability testing. Despite some apparent successes in these two areas, the measurement problem in psychology had not been satisfactorily resolved. In the 1950s the influential Handbook of Experimental Psychology was published by a professor at Harvard, Stanley Smith Stevens (1951). Stevens proposed a solution, or so he hoped, to the measurement problem by invoking the principle of operationism. Since that time, psychologists have assumed that measurement is simply what Stevens said it was: the assignment of numbers to attributes according to rules. Unfortunately, Stevens’ solution is purely illusory.

It is apparent that numbers can be readily allocated to attributes using a non-random rule (the operational definition of measurement) that would generate ‘measurements’ that are not quantitatively meaningful. For example, numerals can be allocated to colours: red = 1, blue = 2, green = 3, etc. The rule used to allocate the numbers is clearly not random, and the allocation therefore counts as measurement, according to Stevens. However, it would be patent nonsense to assert that ‘green is 3 × red’ or that ‘blue is 2 × red’, or that ‘green – blue = red’. Intervals and ratios cannot be inferred from a simple ordering of scores along a scale. Yet this is how psychological measurement is usually carried out. Despite its obvious flaws, Stevens’ approach circumvented the requirement for quantitative measurement that only quantitative attributes can be measured (Michell, 1999). This is because psychological constructs, such as the quality of life, are nothing at all like physical variables that are quantitative in nature. However, psychologists have routinely treated psychological constructs as if they are quantitative in nature and as amenable to measurement as physical characteristics. For more than 60 years, psychology has been living in a make-believe world where making rules for applying numbers to attributes has been treated as if it were proper measurement. This fundamental issue cuts off at its very roots the claim that psychology is a quantitative science on a par with the natural sciences.

However, this would be a very short textbook if we were to give up at this point! We must soldier on as if we have solid ground to walk upon rather than boggy sand.

Measurement can be defined as the estimation of the magnitude of a quantitative attribute relative to a unit (Michell, 2003). Before quantification can happen, it is first necessary to obtain evidence that the relevant attribute is quantitative in structure. This has rarely, if ever, been carried out in psychology. Unfortunately, it is arguably the case that the definition of measurement within psychology since Stevens’ (1951) operationism is incorrect and psychologists’ claims about being able to measure psychological attributes can be questioned (Michell, 1999, 2002). Contrary to common beliefs within the discipline, psychological attributes may not actually be quantitative at all, and hence not amenable to coherent numerical measurement and statistical analyses that make unwarranted assumptions about the numbers collected as data.

The situation is akin to the ‘Emperor has no clothes’ story. Psychometricians are forced to pretend/make the inference that the ordering of scores is a reflection of an underlying quantity and therefore that psychological attributes are measurable on interval scales. Otherwise there would be no basis for quantitative measurement in psychology. Michell (2012: 255) argued that: ‘the most plausible hypothesis is that the kinds of attributes psychometricians aspire to measure are merely ordinal attributes with impure differences of degree, a feature logically incompatible with quantitative structure. If so, psychometrics is built upon a myth.’ This view is supported by Sijtsma (2012), who argued that the real measurement problem in psychology is the absence of well-developed theories about psychological attributes and a lack of any evidence to support the assumption that psychological attributes are continuous and quantitative in nature. This fundamental measurement problem exists as much within health psychology as it does within psychology as a whole.

BOX 1.5 Measuring a psychological attribute – what the majority of textbooks don’t tell you and about which you are not supposed to ask

A typical study requires participants to complete a set of ratings on questionnaire scales that are designed to measure a psychological attribute. The essential issue is whether the total score obtained from the numbers (ratings) provided by an individual is in any way a measure of an attribute along a quantitative scale, like the readings from a tape measure, which reflect the quantity of distance. Distance has an absolute zero and different objects can be placed at equal distances from each other or in fixed ratios. Now let’s consider the example of Diener’s Satisfaction with Life Scale (SWLS) (Table 1.2). The total scores on the SWLS are obtained by summing the seven-point ratings of each of five items. Thus, a maximum score is 35 and the minimum score is 5. The scoring scheme is given here:

 31–35 Extremely satisfied

 26–30 Satisfied

 21–25 Slightly satisfied

 20 Neutral

 15–19 Slightly dissatisfied

 10–14 Dissatisfied

 5–9 Extremely dissatisfied

Is there any basis for assuming the total scores on the SWLS are measures of a quantitative attribute ‘Life Satisfaction’ such that there is an absolute zero (as there would be in any ratio scale) and a person with a score of 20 has exactly double the life satisfaction of a person who has a score of 10 and/or that two people with scores of 30 and 25 have a life satisfaction that is the same ‘distance’ apart (5 points) as in the case of two people with scores of 20 and 15? If the 5-point differences were shown to be the same, then the SWLS would be an interval scale. However, neither of the hypotheses is plausible. We can only infer a person’s life satisfaction from their answers to items on the SWLS. This is because we have no independent definition of life satisfaction, and no evidence that life satisfaction is a quantitative attribute, apart from the SWLS scores themselves.

The total scores on the SWLS really only allow respondents to be placed along an ordinal scale, yet it is common practice to treat the scores as if they were interval scale data that can be added together, subtracted, averaged and compared between groups using standard deviations and variance scores in statistical analyses.

This measurement problem cuts through the entire discipline of psychology. We infer or, in truth, are forced to act on the unproven assumption (i.e., prejudice) that a person’s score on a questionnaire is a measure on a continuous quantitative interval scale. That assumption has never been tested and psychometrics, therefore, has been challenged as a form of ‘pathological science’ (Michell, 2008).

[Nobody promised you a rose garden! We said at the outset that we would adopt a critical stance, and the measurement problem we have described here, which, for obvious reasons, is not normally talked about, is a good start. The situation is not completely hopeless, however, so please do read on.]

Fortunately, for a practical domain like health psychology, it is possible to ‘get by’ without any proper solution to the measurement problem. Yes, it’s a fudge, but a necessary fudge, because otherwise psychological science would be no more advanced today than it was in 1900. One of the main goals of health psychologists is to design interventions that are effective solutions to health problems. Normally we can find ways to objectively compare different interventions to see what works and what doesn’t work. The associations between interventions and outcomes can be observed and measured in quantitative terms. Additionally, a patient seeking treatment for an unpleasant condition can express their thoughts, feelings and motives using plain words by answering questions or items on a questionnaire. In the vast majority of cases, either psychological measures are assumed, for the sake of convenience, to lie along an interval scale or the data are purely categorical.

Health psychologists are concerned with patient–practitioner interactions, public health promotion, or working in communities where actions are carried out, all with observable inputs and outputs. Outcomes in these various scenarios are all objectively observable and measurable, even if the measurements themselves are not shown to have an underlying quantitative attribute. In addition, it is the experiences of the actors that are important, and these are amenable to qualitative methods where the presumption of quantitative attributes and the associated measurement problem do not apply.

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