The paper by Feinstein provides clear and interesting discussion for interpreting indexes which describe disparity between two groups. The discussion is most helpful in explaining the logical relationships among alternative indexes, and in identifying their strengths and weaknesses. Feinstein quite
Indexes of contrast and quantitative significance for comparisons of two groups
β Scribed by Alvan R. Feinstein
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 197 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0277-6715
No coin nor oath required. For personal study only.
β¦ Synopsis
Although boundaries for &large' and &small' di!erences are needed to plan research and interpret results, the diverse indexes of descriptive contrast for the central indexes, A and B, of two groups, have not received intensive attention. For two means, the increment of " A!B " re#ects the slope of a line showing the &e!ect', but is altered by di!erent units of measurement. Division of " A!B " by the common standard deviation produces the standardized increment (SI), which is sometimes called the &e!ect size'. Despite many advantages, it does not contrast the relative magnitudes of A and B. For the latter contrast, the relative change or proportionate increment (" A!B "/B) is particularly easy to understand, and the relative translocation (" A!B "/[A#B]) produces a bounded range from !1 to #1. Nevertheless, all indexes of relative magnitude ablate the scales of measurement, thereby increasing di$culty in interpretation. Although seldom applied, proportionate reduction in overall system variance can be highly useful. Its square root leads to , the analogue of a correlation coe$cient, which corresponds to a standardized slope for the direct increment. The values of usually approximate (SI)/2. Although arbitrary levels have been proposed for &quantitative signi"cance' of the SI, the proportionate reduction in overall system variance is often regarded as ine!ectual unless *10 per cent. With this belief, minimum boundaries for quantitative signi"cance can often be set at *0)3 and SI*0)6. In indexes of relative magnitude for two proportions (or rates), p and p , confusion is produced if q and q are alternatively chosen for the denominators. The odds ratio, (p q /p q ), avoids these choices, but is often di$cult to interpret. For easy understanding and communication, the preferred index is NNE, the number needed to produce one excess e!ect, calculated as the inverse of the direct increment, that is, 1/" p !p ". The standardized increment, " p !p "/((PQ), (where P is the average of p and p and Q"1!P) could o!er a single index applicable to both dimensional and binary data, but when P becomes quite small, that is, (0)01, ((PQ) requires special calculations and also approaches the value of (P. Boundaries of &quantitative signi"cance' are particularly di$cult to establish for comparisons of two rates, because of additional consequences in populational extrapolations and clinical implications. Nevertheless, the principles of quantitative signi"cance can aid the ad hoc construction of boundaries that must be set for medical importance when sample sizes are calculated and when results are interpreted for studies of either e$cacy or equivalence.
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