CLINICAL LAB SCIENEC

CHAPTER 10: QUALITY ASSURANCE 237
Standard Deviation and Normal
Frequency Distribution
When the methods and tools presented in this section are used, it
is easier to determine factors contributing to poor QC. When QC
is out of range, results necessary for following a patient’s diagnosis
or care are delayed.
Random Error
Random error is just what the term implies: an error that occurs
for no known reason and may be based on any number of factors.
Quite often a random error is not even detected unless it occurs
with controls and not with a patient sample. The reason for the
error is often not determined. Statistically, random errors occur as a fraction of
a percent for all tests performed. Random errors are often discovered when a
particular result does not match the clinical picture or does not correlate well
with tests for other analytes (constituents of body fluids tested for) for a specific
patient.
Random errors are difficult to detect and analyze. They may result from
various environmental factors, differences between operator functions, fatigue
of certain components that affect high or low levels, transient interference, and
almost any other factor that could be included in operation of high technology
equipment.
Degree of precision is best expressed in terms of standard deviation, which
is also the distribution of random error. This denotes the dispersion or variability
in a distribution of results. Normal distribution frequency refers to a curve
or bell-shaped curve, which may also be called the Gaussian random variable
distribution.
Critical Reminder
Statistical Terms Used in Quality
Control Calculations
Mean—average of all values (total of
all values divided by the number of
analyses) frequently used in calculations
Median—middle value within the range
Mode—most frequently occurring value
NOTE: In a good QC program, the mean,
median, and mode should be virtually
the same.
Standard Deviation (SD)
Basically, the standard deviation is used as a measure of the variation in a distribution
of values around the mean value for a group of the same tests. From
the mean value, the standard deviations are calculated by taking the sum of the
squared differences for each individual test from the mean value and dividing it
by n – 1, where n is the number of tests performed. The square root of the figure
derived from this process is equal to 1 SD and is doubled to determine 2 SD
ranges. The mean, median, and mode are all common statistical terms that will
be further discussed along with the detailed procedure for determining standard
deviations.
To determine standard deviation, start by determining the mean of a
group of tests (such as those for glucose) by adding all of the test values
together and dividing by the number of tests performed. For each determination
you do after this, subtract your test results from the mean. This number
may be positive or negative. Square the differences and then use a calculator
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