Motivating Example: It is of interest to the medical profession to identify whether a given change in a measured quantity is real or due to noise, for purposes of a diagnosis.
Precision from ISCD (Glossary on that website is helpful too)
In 1 the algorithm is:
- Measure the bone density of 30 patients, twice, or 15 patients, 3 times.
- Calculate standard deviation of each patient.
- Calculate the root mean square standard deviation of the entire group of patients. (I'm interpreting root mean square standard deviation as the standard deviation of the standard deviation)
- Multiply RMS SD by 2.77 to obtain a Reference Value at 95% confidence.
- Later, measure a patient's Bone Density on two separate consultations and compare to the Reference Value obtained in 4. If the change between these two values is greater than the Reference Value, then the change is "statistically significant".
Query: Shouldn't 2.77 be variable? Shouldn't it be a value looked up from a t-table, depending on the numbers of patients scanned, and so be either 1.761 or 1.708 depending on whether 15 or 30 patients were scanned?
Comment: The ISCD seem to be less than rigorous in their use of statistical terminology.
