3. Descriptive statistics for groups of paired observations

COM (comparison of method) is common for laboratorians dealing with data for many patients per unit time. A COM examination entails evaluating the patient's specimens by a reference (existing) technique and a test (new) approach. The resultant data from such comparisons encompass two measurements accruing to each of the patient's specimen. Convention enables plotting of the values acquired via the reference approach on the x-axis, whereas the values yielded by the test approach dominate the y-axis. Nevertheless, linear regression is a statistical approach whose analysis offers objective measures accruing to the dispersion and location of the best fit line. A linear regression yields three aspects—the y-intercept, the correlation coefficient, and the slope. The sign of the correlation coefficient indicates the relationship between the two plotted variables, and a higher coefficient indicates the prevalence of a splendid agreement notably between the comparative methods and the test [3, 4].

The difference plot, also called the Bland–Altman plot, is an additional approach regarding visualization of paired data. This approach graphs the absolute bias or even the percent bias (difference) prevalent between the test method and the reference approach values divided by the range of the dataset. The difference plot further enables simple comparison regarding the differences in order to previously set up maximum limits [1]. Invariably, the main difference between reference and test method depicts the underlying error. COM experiments have a correlation with prevalence of two types of errors—systematic errors and random errors. The random errors are dominant in nearly all measurements besides being either negative or positive. Random error can emanate from environmental variations, an instrument used, reagent, and operator variations. Computation of the random error calls for calculation of the dataset's SD regarding the regression line. This error implies the average distance notably between the regression line and the data. A larger random error implies a wider scattered data values. Nevertheless, if the data points were perfectly in the same alignment as the regression line, the dataset's random error or rather the standard error would be zero. On the other hand, the systematic error affects observations in a consistent manner and also in one direction. The measures of y-intercept and slope yield an estimate regarding the systematic error. Invariably, systematic error can encounter categorization into proportional and constant errors. The constant systematic errors prevail once a continual difference exists between the test approach and the underlying comparative technique values, irrespective of the dataset's concentration. A proportional error prevails once the differences accruing to the test approach and the comparative approach values are fairly proportional to the underlying analyte concentration. Whenever the slope is not equal to one, a proportional error is present in that dataset.
