Numerical precision concerns the number of digits to which a measurement is made. If a scale has a range from 0 to 100, a measurement made to the nearest 1 is more precise than one rounded to the nearest 10. Precision is important because it indicates the potential ability of the scale to discriminate amongst the respondents.
Single-item global questions are frequently categorical in form, and these offer limited precision. For example, the SF-36 asks "In general, would you say your health is: . . .?" (response categories from 1 = excellent to 5 = poor), while the EORTC QLQ-C30 asks "How would you rate your overall quality of life during the past week?" (response categories from 1 = very poor to 7 = excellent). These questions have a precision that is delimited by the number of valid categories from which the respondent must choose, and the QLQ-C30, with seven categories, potentially offers more precision that the SF-36 with five. Although it might seem tempting to allow a larger number of response categories, this can lead to difficulties in distinguishing shades of meaning for adjacent ones. Offering a large number of categories also leads to unreliability in the sense that, in repeated testing, respondents will not consistently choose the same answer from the closely adjacent possibilities. Scales with a maximum of four or five response categories are often recommended, and it would seem of little value to go beyond seven to nine categories.
Multi-item tests, on the other hand, can have greater precision. For example, if four-point categorical questions are used, and five questions are summed into a summary score, the resultant score would have 20 possible categories of response.
Some single-item assessments attempt to overcome this by using visual analogue scales (VAS) in which a line, typically 10 cm long, is labelled at each end by extreme values. Respondents are invited to mark the line at a distance from the two ends according to their level of QoL. In principal such scales can provide fine discrimination, since the investigator may choose to measure the positions of the response very precisely. In practice, however, there must be doubt as to whether patients can really discriminate between fine differences of position along the line.
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