Letters to the Editor
Dichotomization and Manipulation of Numbers
Dear Editor:
With reference to Dr Streiner’s article (1), I agree that numerical data should not usually be dichotomized, but researchers should actively choose numbers that reflect clinical or scientific reality (2), and there may be good reasons for dichotomizing or otherwise manipulating data. (To maintain validity of the hypothesis testing, a decision to manipulate the numbers must be taken before seeing them!)
I offer some examples of situations wherein manipulation of numbers is appropriate:
1. Caseness. Dr Streiner considers the possibility that there is a qualitative difference between people suffering and those not suffering from depression and that this “caseness” is what chiefly interests us. He proposes that a reasonable cut-point on the Beck Depression Inventory (BDI) is 15/16. If we take the (unusual) view that caseness, not BDI score, is affected by independent variables and may in turn affect other variables (that is, effects are direct and not via BDI score), we should dichotomize.
2. Floor and ceiling. Streiner offers the following example: “Within the range of low income (up to, say, $10 000 a year), the actual dollar amount is unimportant, insofar as it buffers against stress, while above a certain amount ($60 000, for example), more money doesn’t provide more protection. Within the middle range, however, we may suspect that there is a linear relation” (1). I suggest that the appropriate treatment of this variable is to recode amounts below $10 000 to $10 000 and amounts above $60 000 to $60 000.
3. Pathology at both extremes. Sometimes there is a healthy range, and both higher and lower values are undesirable. Then, we may choose to analyze severity or degree of pathology. If the healthy range of x is from 40 to 60, we may recode values below 40 to 40 – x, values between 40 and 60 to 0, and values above 60 to x – 60.
With regard to this discussion, I should like to note several points. First, after manipulation, numbers will often not satisfy the mathematical assumptions required for some statistical tests. However, randomization (permutation) tests are widely accepted and are readily available in such software as StatXact (3). Assumptions of normality and equality of variances are then unnecessary. We calculate the statistic of interest for our data (for example, the difference between the means). Then, by assigning the observations randomly to the groups, we get a computer to repeatedly generate artificial datasets and calculate the statistic of interest, thereby obtaining a null distribution of this statistic. Some of the well-known nonparametric or rank tests are based on this philosophy, but with critical values determined theoretically rather than by computer simulation.
The second point of note is this: in contrast to the caseness example above, it may be that independent variables which change the BDI in 2 people from (say) 30 to 25, or from 15 to 10, are also likely to change the caseness of other people, moving them from “depressed” to “not depressed.” For example, the factors may act on the mean of the continuous variable, with caseness being a consequence. Dichotomization would then foolishly discard information. Thus, with such variables, researchers need to decide whether caseness or the score is the reality, because it affects whether dichotomization is appropriate.
The third point to note is that, if a psychological or medical test results in a number, we may be tempted to perform mathematical operations such as subtraction and averaging. However, we are then implying that a change from 30 to 25 (say) equates to a change from 15 to 10. Do we really know this? Further, do we know whether 3 patients having 5%, 50%, and 95% stenosis is equally as desirable as their having 50%, 50%, and 50% stenosis? (If we average, we lose the distinction between these situations.) I doubt that such questions have been answered, even about such widely used measures as the BDI and percentage stenosis. A recent example of the issue (4) is that the relation between pain intensity and its interference with function may be nonlinear: a reduction of pain intensity from 7 to 4 might be considered more beneficial and more clinically relevant than a reduction from 4 to 1.
In summary, researchers should worry about whether their dependent variable truly represents what is of interest. However, if using a randomization test, they do not need to worry about mathematical assumptions.
References
1. Streiner DL. Breaking up is hard to do: the heartbreak of dichotomizing continuous data. Can J Psychiatry 2002;47:262–6.
2. Hutchinson TP, Cairns D, Chekaluk E. The construction of data to reflect the research objective, and how randomisation tests make such data usable. Statistical Papers 2002;43:349–59.
3. Mehta C, Patel N. StatXact 3 for Windows. Cambridge (MA): Cytel Software; 1995.
4. Jensen MP, Smith DG, Ehde DM, Robinsin LR. Pain site and the effects of amputation pain: further clarification of the meaning of mild, moderate, and severe pain. Pain 2001;91:317–22.
T Paul Hutchinson, PhD
Sydney, Australia
|
