Digit Preference and Sample Size
- PDF / 173,874 Bytes
- 3 Pages / 504 x 719.759 pts Page_size
- 98 Downloads / 240 Views
D r ~ gInformation Journal. Vol. 31. pp. 923-925,1997 Rintcd in the USA. All rights reserved.
DIGIT PREFERENCE AND SAMPLE SIZE ALAINSPRIET,MD, PHD, AND THBR&SE DUPIN-SPRIET, PHARMD Alain Spriet Conseil, Paris,France
Digit preference in clinical measurements results in loss ofpower: A methodfor quantifying this loss of power and aajusting sample sizes accordingly is described. Emphasis is placed on prevention, insisting on measuring variables with precision in clinical research.
Key Wordr:Digit preference; Clinical research; Statistical power; Sample size
INTRODUCTION MEASUREMENT OF continuous variables in clinical trials is often in practice transformed into discrete data, “rounding off to the next multiple of five or 10. Examples are: blood pressure (1,2), body weight, heart rate, duration of illness, temperature, and so forth. The effect of such loss of precision is to increase the variance and, therefore, the sample size necessary to obtain the desired power for a statistical test. Although this loss of power is often considered “negligible,” it usually is not quantified. This paper seeks to determine the loss of power for various degrees of digit preference.
METHOD
gral of width 6 centered on each of these values, by a constant large number, that is, c = 1,o0o,o0o: b
n, = int[ c[ @( x, +
x, -
;)I]
with C = 1,0oO,OOOin order to obtain a large sample size. f,I, is the density of probability of a normal variate with p = o and O = 1 @,I, is the cumulative function of this variate, and is calculated using an approximation given in (3). The variance can then be calculated from the resulting discrete distribution:
The effect of a digit preference on variance can be calculated in the following way. Assuming a normal distribution, discontinuous values are defined within a broad range from XMlN = -5 o to XMAX = 5 O. Let h be the interval between adjacent values, and 6 = h/o the standardized interval. The number of possible values is K = (XMM- X M I N ) / ~ . A large sample distribution can be created by multiplying the probability function inte-
Reprint address: Paris,France.
4) - +(
N=
C n,. RESULTS
The above method was used to calculate values in tables of variance for increasing values of standardized digit preference 6. Table 1 gives the calculated variance for increasing values of 6 from 0.1 to 2.0 (beyond this last Alain Spriet, 21 rue de Cotte. F75012, value, the discontinuity interval is larger than two standard deviations, and it seems unrea923 Downloaded from dij.sagepub.com at The University of Auckland Library on May 14, 2015
Alain Sprier and ThCrkse Dupin-Sprier
924
TABLE 1 Digit Preference (Interval 6, Median interval Centered) and Effect on Variance (v’)of a Normal Varlate (Mean = 0, Q = 1 Before Digit Preference), and Power (p:, p:, pj) of a t Test (A = a) with Sample Size Calculated for Power p, = .05, 82 = .lo, p3= .20 6
V’
1 -p*,
1 -P.2
1 -P.3
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
1.001 1.003 1.007 1.013 1.021 1.030 1.041 1.053 1.067 1
Data Loading...
