![]() ![]() As discussed in an earlier lesson, laboratorians often use the SD to impose "gates" on the expected normal distribution of control values. Using the SD, it is possible to predict the range of control values that should be observed if the method remains stable. In many applications, however, the SD is often preferred because it is expressed in the same concentration units as the data. One common application of the variance is its use in the F-test to compare the variance of two methods and determine whether there is a statistically significant difference in the imprecision between the methods. By squaring the SD, the problem of signs is eliminated. The SD may be either positive or negative in value because it is calculated as a square root, which can be either positive or negative. VarianceĪnother statistical term that is related to the distribution is the variance, which is the standard deviation squared (variance = SD² ). In the SD formula, the degrees of freedom are n minus 1 because the mean of the data has already been calculated (which imposes one condition or restriction on the data set). Therefore, the degrees of freedom have been limited by 1 and only n-1 degrees of freedom remain. The number 10 must be selected to make the sum come out to 92. For the last number there is no freedom of choice. For example, if the first three numbers chosen at random are 28, 18, and 36, these numbers add up to 82, which is 10 short of the goal. However, if the sum of the four numbers is stipulated to be 92, the choice of the first 3 numbers is fairly free (as long as they are low numbers), but the last choice is restricted by the condition that the sum must equal 92. For example, if you were to sum four numbers to get a total, you have the freedom to select any numbers you like. ![]() Loosely interpreted, the term "degrees of freedom" indicates how much freedom or independence there is within a group of numbers. ![]() The "n-1" term in the above expression represents the degrees of freedom (df). Finally, the predictable dispersion or standard deviation (SD or s) can be calculated as follows:.Next the squared difference scores are summed.The third manipulation is to square the difference score to make all the terms positive, as shown in Column C.As can be seen here, individual difference scores can be positive or negative and the sum of the difference scores is always zero. This term, shown as X value - Xbar, is called the difference score. The second manipulation is to subtract the mean value from each control value, as shown in column B.The first mathematical manipulation is to sum ( ) the individual points and calculate the mean or average, which is 877 divided by 10, or 87.7 in this example.The dispersion of values about the mean is predictable and can be characterized mathematically through a series of manipulations, as illustrated below, where the individual x-values are shown in column A. The values observed will show a dispersion or distribution about the mean, and this distribution needs to be characterized to set a range of acceptable control values. When assaying control materials, it is obvious that technologists will not achieve the mean value each and every time a control is analyzed. Although the mean is the value most likely to be observed, many of the actual values are different than the mean. The mean value characterizes the "central tendency" or "location" of the data. For example, given the following ten analyses of a control material - 90, 91, 89, 84, 88, 93, 80, 90, 85, 87 - the mean or Xbar is 877/10 or 87.7. Years ago, when laboratories were beginning to assay controls, it was easy to calculate a mean and use that value as the "target" to be achieved. The simplest statistic is the mean or average. The lesson sets up a pattern to be followed in future lessons. The importance of this current lesson, however, resides in the process. It is highly recommended that you study these lessons online or in hard copy. Many of the terms covered in this lesson are also found in the lessons on Basic QC Practices, which appear on this website. EdD Assistant ProfessorĬlinical Laboratory Science Program University of Louisville Do you know what they mean when they talk about mean? These are the bread and butter statistical calculations. ![]() Don't be caught in your skivvies when you talk about CV's, or confuse STD's with SD's. ![]()
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