Quality Control:Analysis Of Data

Pawan Angra MSDivision of Laboratory Systems

Public Health Practice Program OfficeCenters for Disease Control and

Prevention

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How to carry out analysis of data?• Need tools for data management and analysis

Basic statistics skills Manual methods

Graph paperCalculator

Computer helpfulSpreadsheet

• Important skills for laboratory personnel

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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

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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

Blood Urea mg/dL

0

1

2

3

4

5

29 29.5 30 30.5 31 31.5 32 32.5 33 33.5 34 34.5 35

Value

Freq

uenc

y

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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:

RangeVarianceStandard DeviationCoefficient 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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2

1)(

mg/dln

XX S

Calculation of Variance (S2)

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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

22

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2.75mg/dl

52.25/19

mg/dl1n

)X(X)(S Variance

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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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variance

1

2

n

)X(Xs i

Calculation of Standard Deviations

Urea level 1 control

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Calculation of 1, 2 & 3 Standard Deviations

3s = 1.66 x 3 = 4.98 mg/dlmg/dl 3.32 2 x 1.662s

mg/dl 1.662.751s

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Standard Deviation and Probability

68.2%

95.5%99.7%

Freq

uenc

y

-3s -2s -1s Mean +1s +2s +3s

X

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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/dlMean - s = 32.0-1.66 mg/dlRange 33.66- 30.34 mg/dl

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95. 5% confidence limit: (2SD)Mean + 2s = 32.0+3.32 mg/dl Mean - 2s = 32.0-3.32mg/dlRange 28.68 – 35.32 mg/dl

Calculation of Range Urea level 1 control

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99. 7 % confidence limit: (3SD)Mean + 3s = 32.0+4.98Mean - 3s = 32.0-4.98Range 27.02 – 36.98 mg/dl

Calculation of Range Urea level 1 control

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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