Download Calculation of Standard Deviation

Quality Control:
Analysis Of Data
Pawan Angra MS
Division of Laboratory Systems
Public Health Practice Program Office
Centers for Disease Control and
Prevention
How to carry out analysis of data?
• Need tools for data management and analysis
Basic statistics skills
 Manual methods
Graph paper
Calculator
 Computer helpful
Spreadsheet
• Important skills for laboratory personnel

2
Analysis of Control Materials
• Need data set of at least 20 points, obtained
over a 30 day period
• Calculate mean, standard deviation,
coefficient of variation; determine target
ranges
• Develop Levey-Jennings charts, plot results
3
Establishing Control Ranges
• Select appropriate controls
• Assay them repeatedly over time (at least 20
data points)
• Make sure any procedural variation is
represented: different operators, different
times of day
• Determine the degree of variability in the
data to establish acceptable range
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Measurement of Variability
• A certain amount of variability will naturally
occur when a control is tested repeatedly.
• Variability is affected by operator technique,
environmental conditions, and the
performance characteristics of the assay
method.
• The goal is to differentiate between
variability due to chance from that due to
error.
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Measures of Central Tendency
• Data distribution- central value or a
central location
• Central Tendency- set of data
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Measures of Central Tendency
• Median = the central value of a data set
arranged in order
• Mode = the value which occurs with most
frequency in a given data set
• Mean = the calculated average of all the
values in a given data set
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Calculation of Median
• Data set ( 30.0, 32.0, 31.5,45.5, 33.5, 32.0,
33.0, 29.0, 29.5, 31.0, 32.5, 34.5, 33.5, 31.5,
30.5, 30.0, 34.0, 32.0, 32.0, 35.0, 32.5.)
mg/dL
• Outlier: 45.5
• Arrange them in order ( 29.0, 29.5, 30.0,
30.0, 30.5, 31.0, 31.5, 31.5, 32.0, 32.0, 32.0,
32.0, 32.5, 32.5, 33.0, 33.5, 33.5, 34.0, 34.5,
35.0) mg/dL
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Calculation of Mode
• Data set (30.0, 32.0, 31.5, 33.5, 32.0, 33.0,
29.0, 29.5, 31.0, 32.5, 34.5, 33.5, 31.5, 30.5,
30.0, 34.0, 32.0, 32.0, 35.0, 32.5.) mg/ dL
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Calculation of Mean
• Data set (30.0, 32.0, 31.5, 33.5, 32.0, 33.0,
29.0,29.5, 31.0, 32.5, 34.5, 33.5, 31.5, 30.5,
30.0, 34.0,32.0, 32.0, 35.0, 32.5.) mg/ dL
• The sum of the values (X1 + X2 + X3 … X20)
divided by the number (n) of observations
• The mean of these 20 observations is (639.5
 20) = 32.0 mg/dL
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Normal Distribution
• All values are symmetrically distributed
around the mean
• Characteristic “bell-shaped” curve
• Assumed for all quality control statistics
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Normal Distribution
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Frequency
4
3
2
1
0
29 29.5 30 30.5 31 31.5 32 32.5 33 33.5 34 34.5 35
Value
Blood Urea mg/dL
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Accuracy and Precision
• “Precision” is the closeness of repeated
measurements to each other.
• Accuracy is the closeness of measurements
to the true value.
• Quality Control monitors both precision and
the accuracy of the assay in order to provide
reliable results.
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Precise and inaccurate
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Imprecise and inaccurate
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Precise and accurate
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Measures of Dispersion
or Variability
• There are several terms that describe the
dispersion or variability of the data around
the mean:
Range
Variance
Standard Deviation
Coefficient of Variation
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Range
• Range is the difference or spread between the
highest and lowest observations.
• It is the simplest measure of dispersion.
• It makes no assumption about the central
tendency of the data.
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Calculation of Variance
• Variance is the measure of variability about
the mean.
• It is calculated as the average squared
deviation from the mean.
 the sum of the deviations from the mean,
squared, divided by the number of
observations (corrected for degrees of
freedom)
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Calculation of Variance (S2)
S 
2
( X  X )
n 1
2
mg/dl
2
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Degrees of Freedom
• Represents the number of independent
comparisons that can be made among a
series of observations.
• The mean is calculated first, so the variance
calculation has lost one degree of freedom
(n-1)
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Calculation of Variance
(Urea level 1 control)
2

(X1 X )

2
2

Variance (S )
mg/dl
n 1
52.25/19
 2.75mg/dl2
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Calculation of Standard Deviation
• The standard deviation (SD) is the square
root of the variance
-SD is the square root of the average
squared deviation from the mean
-SD is commonly used due to the same
units as the mean and the original
observations
-SD is the principle calculation used to
measure dispersion of results around a
mean
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Calculation of Standard
Deviations
Urea level 1 control
s
 (X
X)
2
i
n 1
 variance
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Calculation of 1, 2 & 3 Standard
Deviations
1s  2.75  1.66 mg/dl
2s  1.66 x 2  3.32 mg/dl
3s = 1.66 x 3 = 4.98 mg/dl
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Standard Deviation and Probability
Frequency
X
68.2%
95.5%
99.7%
-3s
-2s
-1s
Mean
+1s
+2s
+3s
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Standard Deviation and
Probability
• For a data set of normal distribution, a value
will fall within a range of:
 +/- 1 SD 68.2% of the time
 +/- 2 SD 95.5% of the time
 +/- 3 SD 99.7% of the time
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Calculation of Range
Urea level 1 control
68.2% confidence limit: (1SD)
Mean + s = 32.0+1.66 mg/dl
Mean - s = 32.0-1.66 mg/dl
Range 33.66- 30.34 mg/dl
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Calculation of Range
Urea level 1 control
95. 5% confidence limit: (2SD)
Mean + 2s = 32.0+3.32 mg/dl
Mean - 2s = 32.0-3.32mg/dl
Range 28.68 – 35.32 mg/dl
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Calculation of Range
Urea level 1 control
99. 7 % confidence limit: (3SD)
Mean + 3s = 32.0+4.98
Mean - 3s = 32.0-4.98
Range 27.02 – 36.98 mg/dl
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Standard Deviation and Probability
• In general, laboratories use the +/- 2 SD
criteria for the limits of the acceptable range
for a test
• When the QC measurement falls within that
range, there is 95.5% confidence that the
measurement is correct
• Only 4.5% of the time will a value fall outside
of that range due to chance; more likely it will
be due to error
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Coefficient of Variation
• The Coefficient of Variation (CV) is the
standard Deviation (SD) expressed as a
percentage of the mean
-Also known as Relative Standard deviation
(RSD)
• CV % = (SD ÷ mean) x 100
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Summary
• Data set of at least 20 points,
obtained over a 30 day period
• Calculate mean, standard deviation,
coefficient of variation
• Determine target range
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