# Presentation: 305855

## 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

## 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

## 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

## 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.

## Measures of Central Tendency

- Data distribution- central value or a central location
- Central Tendency- set of data

## 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

## 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

## 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

## 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

## Normal Distribution

- All values are symmetrically distributed around the mean
- Characteristic “bell-shaped” curve
- Assumed for all quality control statistics

## Normal Distribution

## 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.

## Precise and inaccurate

**Precise and inaccurate**

## Imprecise and  inaccurate

**Imprecise and  inaccurate**

## Precise and accurate

**Precise and accurate**

## 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

## 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.

## 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)

## Calculation of Variance (S2)

**Calculation of Variance (S****2****)**

## 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)

## Calculation of Variance (Urea level 1 control)

## 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

## Calculation of Standard Deviations Urea level 1 control

** **

**Calculation of Standard Deviations ****Urea level 1 control**

## Calculation of 1, 2 & 3 Standard Deviations

**3s = 1.66 x 3 =  4.98 mg/dl**

**mg/dl**

** **

**3.32**

** **

**2**

** **

**x**

** **

**1.66**

**2s**

**mg/dl**

** **

**1.66**

**2.75**

**1s**

- 

- 

- 

****

## Standard Deviation and Probability

## 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

## 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

## 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

- Mean + 2s  = 32.0+3.32 mg/dl
- Mean - 2s  = 32.0-3.32mg/dl
- Range 28.68 – 35.32 mg/dl

**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

- Mean + 3s = 32.0+4.98
- Mean - 3s = 32.0-4.98
- Range 27.02 – 36.98 mg/dl

**Calculation of Range**** Urea level 1 control**

## 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

## 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

## Summary

- Data set of at least 20 points,
- 	obtained over a 30 day period
- Calculate mean, standard deviation,
- 	coefficient of variation
- Determine target range