## Ordered Categorical Or Ranked Data

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In the case of more than two categories, there are many situations when they can be ordered in some way. For example, the SF-36 question 1 asks: "In general, would you say your health is: Excellent, Very good, Good, Fair, Poor?" In this case there are five ordered categories ranging from Excellent to Poor. The proportion or percentage of subjects falling into these five categories can be calculated, and in some situations these categories may be given a corresponding ranking 1, 2, 3, 4 and 5 which may then be used for analysis purposes. An example is the test-for-trend as alluded to in Table 8.2 (see below). However, although numerical values are assigned to each response, one cannot always treat them as though they had a strict numerical interpretation, as the magnitude of the differences between, for example, Excellent (Rank 1) and Very good (2) may not necessarily be the same as between Fair (3) and Poor (4).

### Example from the literature

Stiggelbout et al. (1997) posed three questions assessing fear of recurrence of cancer. Possible responses to the item: "Do you feel insecure about your health?" were: Not at all, Somewhat/to some extent, Rather, Very much.

In this case there are four ordered categories, and 80 (38%), 96 (46%), 29 (14%) and 4 (2%) of the 209 patients gave the respective response. Their ranks would be 1, 2, 3 and 4.

The majority of questions on QoL instruments seek responses of the ordered categorical type.

NUMERICAL DISCRETE/NUMERICAL CONTINUOUS

Numerical discrete data consist of counts; for example, a patient may be asked how many times they vomited on a particular day, or the number of pain relief tablets taken. On the other hand, numerical continuous data are measurements that can, in theory at least, take any value within a given range. Thus a patient completing the

EuroQol questionnaire is asked to indicate: "Your own health today" on a 10-cm vertical scale whose ends are defined by "Worse imaginable health state" with value Ocm and "Best imaginable health state" with value 10.0 cm.

In certain circumstances, and especially if there are many categories, numerically discrete data may be regarded as effectively continuous for analytical purposes.

CONTINUOUS DATA: NORMAL AND NON-NORMAL DISTRIBUTIONS

A special case of numerical continuous data is that which demonstrates a Normal distributionâ€”see, for example, Campbell and Machin (1999). In this case special statistical methods such as the /-test are available, as we shall describe. Frequently, however, QoL data do not have even approximately a Normal distribution. For example, many items and scales, especially when applied to healthy subjects or extremely ill patients, may result in data with a large number of maximum "ceiling" or minimum "floor" scores, which is clearly not of a Normal distribution form. Then alternative statistical methods, not based upon the assumption of a Normal distribution, must be used.