## Short Term Precision Studies

A separate precision study must be done for each skeletal site that might be used in following a patient. The precision for multiple regions within a skeletal site, such as the five regions of interest within the proximal femur, can be determined from a single proximal femur precision study.

The number of individuals and number of scans per individual needed for a precision study is determined by the degrees of freedom necessary to achieve the narrowest confidence limits for the precision estimate that are practical. Remember that one of the measurements on an individual will not contribute independently to the calculation of the mean for that individual. The number of measurements that do independently contribute are called the degrees of freedom (df) for the study. For statistical validity, it is recommended that a short-term precision study have 30 df (4). Thirty df are chosen to ensure that the upper limit for the 95% CI of the precision value is no more than 34% greater than the calculated precision value. If only one person is studied, 31 tests must be performed to obtain 30 df because one test will not contribute independently to the calculation of the mean. If 15 patients are studied, three tests per patient must be done because again, only two of the three tests per patient will be independent (15 x 2 = 30). The specific combinations of the number of patients and number of scans per patient that are recommended for a short-term precision study are shown in Table 11-2. A short-term precision study should be completed in 2-4 weeks. All the scans on any one patient can be completed on the same day if desired.

The following is the method for determining short-term precision as recommended by Gluer et al. (5). Using the combination of 15 patients and three scans each for the sake of example, the average value, SD, and CV should be found for each of the 15 sets of three measurements, just as was done for the set of three measurements on Mrs. B. Rather than reporting the arithmetic mean of the 15 SDs or 15 CVs (adding the 15 values and dividing by 15) as the precision value, the RMS-SD or the RMS-CV is calculated as shown in Equations 7 and 8. The RMS-SD and RMS-CV are preferred to the arithmetic mean SD and CV because the latter quantities tend to underestimate the Gaussian error.2

1 The Gaussian distribution is the symmetrical bell-shaped curve that is obtained from a plot of values of a variable in which the variation in the value is caused by several independent factors. It was named after Gauss, the individual who originally described it. If the variation in the value of a variable is primarily from only one factor, the distribution will not be a symmetrical bell-

shaped curve. Instead, it may be skewed in one direction or the other.

Table 11-3

The Measured and Mean PA Lumbar Spine Values for 15 Patients in a Short-Term Precision Study

Table 11-3

The Measured and Mean PA Lumbar Spine Values for 15 Patients in a Short-Term Precision Study

 Patient Scan 1 Scan 2 Scan 3 Mean 