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Welcome to Chapter 2: Calculations. This module covers the most basic calculations used in
the laboratory.
QC statistics for each test performed in the laboratory are calculated from the QC database
collected by regular testing of control products. The data collected is specific for each level
of control. Consequently, the statistics and ranges calculated from this data are also
specific for each level of control and reflect the behavior of the test at specific concentrations.
The most fundamental statistics used by the laboratory are the mean and standard deviation.
The mean (or average) is the laboratory’s best estimate of the analyte’s true value
for a specific level of control.
To calculate a mean for a specific level of control, first, add all the values collected
for that control. Then divide the sum of these values by the total number of values.
For instance, to calculate the mean for the normal control (Level I), find the sum of
the data {4.0, 4.1, 4.0, 4.2, 4.1, 4.1, 4.2}. The sum is 28.7 mmol/L. The number of values
is 7 (n = 7). Therefore, the mean for the normal control is 4.1 mmol/L.
Now that you understand mean, we can move on to standard deviation. Standard deviation
is a statistic that quantifies how close numerical values (i.e., QC values) are in relation to
each other.
The term precision is often used interchangeably with standard deviation.
Another term, imprecision, is used to express how far apart numerical values are from each
other.
Standard deviation is calculated for control products from the same data used to calculate
the mean. It provides the laboratory an estimate of test consistency at specific concentrations.
The repeatability of a test may be consistent (low standard deviation, low imprecision)
or inconsistent (high standard deviation, high imprecision). Inconsistent repeatability
may be due to the chemistry involved or to a malfunction. If it is a malfunction, the
laboratory must correct the problem. It is desirable to get repeated measurements of
the same specimen as close as possible. Good precision is especially needed for tests that
are repeated regularly on the same patient to track treatment or disease progress.
For example, a diabetic patient in a critical care situation may have glucose levels run
every 2 to 4 hours. In this case, it is important for the glucose test to be precise because
lack of precision can cause loss of test reliability. If there is a lot of variability in the test
performance (high imprecision, high standard deviation), the glucose result at different
times may not be true.
Standard deviation may also be used to monitor on-going day-to-day performance. For instance,
if during the next week of testing, the standard deviation calculated in the example for the
normal potassium control increases from .08 to 0.16 mmol/L, this indicates a serious loss
of precision. This instability may be due to a malfunction of the analytical process.
Investigation of the test system is necessary and the following questions should be asked:
Has the reagent or reagent lot changed recently? Has maintenance been performed routinely and
on schedule? Does the potassium electrode require cleaning or replacement? Are the reagent
and sample pipettes operating correctly? Has the test operator changed recently?
So, how do you calculate a standard deviation? You’ll need to determine the mean or average
of the QC values. You’ll also need the sum of the squares of differences between individual
QC values and the mean. Finally, you’ll need the number of values in the data set.
Although most calculators and spreadsheet programs automatically calculate standard
deviation, it is important to understand the underlying mathematics. Therefore, let’s
look at an example using the same data set from before.
Begin by calculating the mean. First, add all the values collected for that control.
Then divide the sum of these values by the total number of values.
Now that the mean has been determined, let’s move on to the standard deviation. First,
enter the values into the formula. Let’s take a moment to understand the pattern. The
value to the left of the minus sign comes from the data set. The value to the right
of the minus sign is the mean that was just calculated. This pattern repeats for all of
the points in the data set. The divisor is the number of data points in the data set
minus one. The subtraction is done within the brackets. The values are squared… and
then added. Finally, the division occurs and the square root is taken. The standard deviation
for one week of testing of the normal potassium control level is 0.082 mmol/L. Now that the
amount of precision is known; some assumptions can be made about how well this test is performing.
We have reached the end of this module. Let’s review some basic points. QC statistics for
each test performed in the laboratory are calculated from the QC database collected
by regular testing of control products. The most fundamental statistics used by the laboratory
are the mean and standard deviation. The mean (or average) is the laboratory’s best estimate
of the analyte’s true value for a specific level of control. To calculate a mean for
a specific level of control, first, add all the values collected for that control. Then
divide the sum of these values by the total number of values. This is the formula for
calculating the mean.
Standard deviation is a statistic that quantifies how close numerical values (i.e., QC values)
are in relation to each other. This is the formula for calculating the standard deviation.The
term precision is often used interchangeably with standard deviation. Imprecision is used
to express how far apart numerical values are from each other.The repeatability of a
test may be consistent (low standard deviation, low imprecision) or inconsistent (high standard
deviation, high imprecision). It is desirable to get repeated measurements of the same specimen
as close as possible. Good precision is especially needed for tests that are repeated regularly
on the same patient to track treatment or disease progress.
For all your laboratory QC needs go to www.qcnet.com.