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Since standard deviation, mean, median, and mode are all absolute data on statistical samples, they do not permit a direct comparison of variation between samples with different means or different units of measurement.One way to obtain a measure of variation that has no units is to divide the standard deviation by the mean, and multiply by 100 to give a percent. This quantity is called the coefficient of variation, and can be used to compare methods that give different units.For example, the coefficient of variation for two different glucose methods would be calculated as shown below after the mean and standard deviation for each method has been established. The hexokinase method has = 99 mg/dL, and s = 8.0 mg/dL. The orthotoluidine method has = 105 mg/dL, and s = 12.5 mg/dL. From these CV's we would conclude that the hexokinase method is relatively more precise because it has a lower CV.

Coefficient of variation is commonly used as a means of measuring the variability of an instrument. The data are gathered by recording the values for the normal and abnormal controls for each test run. At the end of the month, the standard deviation, mean, and coefficient of variation are calculated. The testing data for a particular instrument might look like this: January February March Normal Control s CV 100.9 2.43 2.41 103.1 2.99 2.90 102.0 2.21 2.17 Abnormal Control s CV 209.5 4.41 2.11 211.6 4.00 1.89 206.8 3.95 1.91 The coefficient of variation stays fairly constant from month to month. If there is a sudden increase, there might be a problem with the method or the equipment.In the clinical laboratory, the use of CV as a measure of relative variability should not be confused with the use of the standard deviation as a measure of absolute variability. For example, support physicians agreed that for accurate patient treatment, the inherent variability in a glucose method should be less than 5 mg/dL. In this case, neither the hexokinase nor the orthotoluidine method is acceptable. It does not matter which is more precise if neither is precise enough to result in adequate patient care.

Another measure of the quality of fit is the correlation coefficient, r2. To calculate the correlation coefficient, square the total of the (x-)(y-) column, and divide by the total of the (x-)2 and the total of the (y-)2 column. The formula is: r2 equals 1 if the data all lie exactly along a straight line, and r2 equals 0 if the data are not correlated. Values between 1 and 0 indicate that the data have some linear relationship, but also have some scatter. Data with an r2 of above .8 are considered strongly correlated.

To illustrate the use of CUSUM in the laboratory, we'll use daily control values for glucose testing.First, we'll list daily control values under "daily results." Then, we'll calculate mean by using formula A. Next, we can find the difference from the mean for each result, and square that result for the two relevant columns. Using all of the squared differences from the mean, we can find the standard deviation using formula B. Using the mean from formula A and the standard deviation calculations from formulas B and C, we can plot our data points on the Levey-Jennings chart. Formula D helps us calculate the coefficient of variation (CV), which expresses SD as a percentage of mean value and is more reliable for comparing precision at different concentration levels. The lower the CV the greater the precision.