Statistical Information and Courses from MediaLab, Inc.

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.

For each new lot of control materials, new control values must be calculated, and acceptable ranges established. The values necessary for calculating the acceptable ranges are the mean and standard deviation. At least 20 samples are necessary for good statistical data.The mean is calculated by adding all of the values, and dividing by the number of values. The formula is: For example, suppose you wanted to find the mean of the values 4, 6, 2, 8, and 5. The mean is: The standard deviation (abbreviated s or SD) is calculated according to the following formula:That is, calculate the deviation from the mean for each point, square those results, sum them, divide by the number of points minus one, and finally take the square root. For example, the deviations from the mean in the above example are -1, 1, -3, 3, and 0. The squared deviations are 1, 1, 9, 9, and 0. The standard deviation is therefore: The standard deviation will be larger if the data are spread out and smaller if the data are closely clustered about the mean.

Systematic error occurs when something alters the testing process, causing all results to be biased.For example, systematic error may occur when improper standards are used or a dirty lens is present in a measuring device. Both patient results and control measurements are affected by systematic error, making it more difficult to detect.Changes in the statistical mean are an indication of a systematic error and must be investigated.

A good QC program requires documenting control results and observing and assessing that documentation daily. This section is an overview of some of the ways to document and assess QC results. First, we'll cover some basic statistical terms:meanGaussian (or bell) curvestandard deviation

In the late 1950’s, Dr. William Youden (1900-1971) developed what has now become known as the Youden Plots. This statistical technique involves both normal and abnormal controls and graphically helps to differentiate between systematic and random errors. The inner square of the plot (yellow) represents one standard deviation (1SD). The next larger square (green) represents 2SD, and the outer square (blue) represents 3SD. A horizontal median line is drawn parallel to the X-axis and a second median line is drawn parallel to the Y-axis. The intersection of the two median lines is called the Manhattan Median. One or two 45-degree lines are drawn through the Manhattan Median. The results of at least two different levels of controls (e.g. Level 1/Level 2 or Normal/Abnormal) are then plotted on the chart as X-axis versus Y-axis.