Continuous Scales: Increase of the Precision of Measurement
The category scale was for the first time used in 150 BC by Hipparchus to describe the brightness of stars classifying them in 6 categories. Of course in physics now much better measures than category scales have been developed for the brightness of stars, In the social science on the other hand these very imprecise measurement scales are still the most popular scales to measure opinions. The main reason is that researchers think that the respondents can not do better than providing ordinal judgements. However, in last century several studies have shown that much preciser measurement is possible.
Stevens 1956 and 1975, Gescheider 1975 and other researchers of psychophysics showed that people can provide very precise estimates of loudness of sounds and many other stimuli expressing their opinions using continuous scales like numbers, pressure of the hand, line production etc. The judgements and the stimuli correlated .99 using a power function.
Similar results were obtained by Rainwather 1971, Hamblin 1973 and Saris 1975 using as stimuli: incomes to measure social status, population size to measure power, number of drinks per week to measure the dislike of one self . Also in these cases the power function (eventually with a correction of the zero point) fitted equally well to the data. A typical example looks like the instruction presented below. This question has been presented to 500 workers in a steel factory. The result of the experiment is summarized in the figure at the right. This figure shows how strong the relationship is between the stimuli (years of experience) and the judgement of the capability of the person for his job after log transformation because as indicated above the relationships is in general a power function.
Stevens 1956 and 1975, Gescheider 1975 and other researchers of psychophysics showed that people can provide very precise estimates of loudness of sounds and many other stimuli expressing their opinions using continuous scales like numbers, pressure of the hand, line production etc. The judgements and the stimuli correlated .99 using a power function.
Similar results were obtained by Rainwather 1971, Hamblin 1973 and Saris 1975 using as stimuli: incomes to measure social status, population size to measure power, number of drinks per week to measure the dislike of one self . Also in these cases the power function (eventually with a correction of the zero point) fitted equally well to the data. A typical example looks like the instruction presented below. This question has been presented to 500 workers in a steel factory. The result of the experiment is summarized in the figure at the right. This figure shows how strong the relationship is between the stimuli (years of experience) and the judgement of the capability of the person for his job after log transformation because as indicated above the relationships is in general a power function.
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A new version of a continuous scale: VAS
This experiment and many others by authors mentioned above showed that people can provide very precise information about their opinions on continuous scales. For this reason continuous scales are also very popular in medical research, especially for the measurement of pain levels. In that field this approach is known under the name Visual Analogue Scale or VAS. In Wikipedia several more recent papers can be found. Many different forms have been developed where some omit the continuous character of the scale. In web surveys also experiments with different 101 points scales are made for example by Liu and Conrad (2015) |
Evaluation of non-numeric stimuli
One could do such experiments also with non-numeric stimuli such as asking to evaluate the status of different occupations or levels of pain. Respondents have no problem with these evaluations on a numeric scale or in loudness of sound or any other continuous scale (Neijens et al. 1981).
The problem is that one has no criterium to evaluate the quality of the judgements of non-numeric stimuli. This problem was solved by the work of Dawson and Brinker (1971) who suggested to ask respondents to evaluate the non-numeric stimuli twice, say once in numbers and once in lines. If these judgement had any relevance the correlations between these judgements should be very high. In psychophysics they expected a power function with a known value for the coefficient of the power function. In the social science experiments Saris (1986) suggested that the relationship should also be a power function and the correlation between the log-transformed data should be very high. The experiments done in this way by Lodge et al. (1981) and Saris et al. (1988) confirmed that the correlations were indeed again very high.
This research has shown that people can provide much more precise information about their opinions than they can express in category scales but in that case one has to provide them with the possibility to do so i.e.provide them with continuous scales such as number scales, line production scales or other visual analogue scales.
However there remained the problem that the results for different people may not be comparable because they use different response functions. Some people give extreme answers and others vary only minimally in their responses while they may express the same opinions but on a different scale
What we can do and what we can´t
One can use these procedures if one is interested in individual judgements of a single person about different objects; products for example
One can not use these procedures if one wants to compare which person likes a certain product more because that requires comparability of the response functions.
One could do such experiments also with non-numeric stimuli such as asking to evaluate the status of different occupations or levels of pain. Respondents have no problem with these evaluations on a numeric scale or in loudness of sound or any other continuous scale (Neijens et al. 1981).
The problem is that one has no criterium to evaluate the quality of the judgements of non-numeric stimuli. This problem was solved by the work of Dawson and Brinker (1971) who suggested to ask respondents to evaluate the non-numeric stimuli twice, say once in numbers and once in lines. If these judgement had any relevance the correlations between these judgements should be very high. In psychophysics they expected a power function with a known value for the coefficient of the power function. In the social science experiments Saris (1986) suggested that the relationship should also be a power function and the correlation between the log-transformed data should be very high. The experiments done in this way by Lodge et al. (1981) and Saris et al. (1988) confirmed that the correlations were indeed again very high.
This research has shown that people can provide much more precise information about their opinions than they can express in category scales but in that case one has to provide them with the possibility to do so i.e.provide them with continuous scales such as number scales, line production scales or other visual analogue scales.
However there remained the problem that the results for different people may not be comparable because they use different response functions. Some people give extreme answers and others vary only minimally in their responses while they may express the same opinions but on a different scale
What we can do and what we can´t
One can use these procedures if one is interested in individual judgements of a single person about different objects; products for example
One can not use these procedures if one wants to compare which person likes a certain product more because that requires comparability of the response functions.
References:
Stevens S.S. (1957) On the psycophysics law . PsychologicaL Review,64, 530-541
Rainwather L. (1971) What money buys: Inequality and social meaning of income. New York, Basic books.
Hamblin R.L. (1974) Social attitudes: magnitude estimation and Theory. In H.M.Blalock (ed) Measurement in the social sciences, Chicago, Aldine, 61-120
Gescheider G. (1975) Psychophysics; method and theory. New York , Wiley
Saris W.E. Bruinsma C. Schoots W and Vermeulen C (1977) The use of maginitude estimation in large scale survey research. Mens en Maatschappij,52, 369-395
Dawson W.F. and Brinker R.P. (1971) Validation of ratio scales of opinion by multi-modality matching. Perception and Psychophysics, 9, 413-417
Neijens P., L. van Doorn, W.E. Saris (1981) De meting van beroepsprestige met behulp van psychophysische schaaltechnieken. Mens en Maatschappij.
Saris W.E.(1987) Individual response functions and correlations between judgements, In W.E.Saris and I.N. Gallhofer (eds) Sociometric Research, 1. Data collection and scaling. London , MacMillan.
Saris W.E, (1998) Words are sometimes not enough to express the existing information. In M.Fennema, C.van der Eijk and H. Schijf (Eds) In search of structure: Essays in social science and methodology.Amsterdam. Het Spinhuis (63-73)
Lodge M. (1981) Magnitude scaling: Quantitative measurement of opinions. Sage University Papers Series on quantitative application in the social sciences. Beverly Hills. Sage
Liu M. and Conrad F.G. (2015) An experiment testing six formats of 101- point rating scales . Computers in Human Behavior 364-371.
Stevens S.S. (1957) On the psycophysics law . PsychologicaL Review,64, 530-541
Rainwather L. (1971) What money buys: Inequality and social meaning of income. New York, Basic books.
Hamblin R.L. (1974) Social attitudes: magnitude estimation and Theory. In H.M.Blalock (ed) Measurement in the social sciences, Chicago, Aldine, 61-120
Gescheider G. (1975) Psychophysics; method and theory. New York , Wiley
Saris W.E. Bruinsma C. Schoots W and Vermeulen C (1977) The use of maginitude estimation in large scale survey research. Mens en Maatschappij,52, 369-395
Dawson W.F. and Brinker R.P. (1971) Validation of ratio scales of opinion by multi-modality matching. Perception and Psychophysics, 9, 413-417
Neijens P., L. van Doorn, W.E. Saris (1981) De meting van beroepsprestige met behulp van psychophysische schaaltechnieken. Mens en Maatschappij.
Saris W.E.(1987) Individual response functions and correlations between judgements, In W.E.Saris and I.N. Gallhofer (eds) Sociometric Research, 1. Data collection and scaling. London , MacMillan.
Saris W.E, (1998) Words are sometimes not enough to express the existing information. In M.Fennema, C.van der Eijk and H. Schijf (Eds) In search of structure: Essays in social science and methodology.Amsterdam. Het Spinhuis (63-73)
Lodge M. (1981) Magnitude scaling: Quantitative measurement of opinions. Sage University Papers Series on quantitative application in the social sciences. Beverly Hills. Sage
Liu M. and Conrad F.G. (2015) An experiment testing six formats of 101- point rating scales . Computers in Human Behavior 364-371.
