STATISTICS IN CLINICAL LABORATORY,Central Tendency,, Symmetrical , Asymmetrical , Standard Deviation (SD), Coefficient of Variation (CV), Standard Error of the Mean (SEM)

STATISTICS IN CLINICAL LABORATORY

• Central Tendency

• Distribution

1. Symmetrical distribution, 

2. Asymmetrical distribution

• Standard Deviation (SD)

• Coefficient of Variation (CV)

• Standard Deviation of the Mean or Standard Error of the Mean (SEM)

 

STATISTICS IN CLINICAL LABORATORY

Statistics is the area of mathematics which deals with the collection, analysis, interpretation and presentation of data. The enormous data that is generated in a clinical laboratory can be more useful to the laboratory personnel and clinicians if it is analysed with the help of statistical tests. A single result obtained by a laboratory test is not enough to decide that a particular analysis is acceptable. Only by comparing the result of this test with those obtained by other methods, the test can be accepted for the analysis. By applying statistical evaluation, a laboratory scientist should select an accurate and precise method from several methods that may be available for performing a test.

The main application of statistics in a clinical laboratory is for the establishment of reference ranges and surveilance of quality control. Some basic and commonly used statistical terms and equations are described below.

Central Tendency

Central tendency of populations are the values about which these populations are centered and can

be described by three terms namely, mean, median and mode. 

Mean The arithmetic mean is the average of two or more values. It is designated as X, and is calculated by adding all the observations and dividing by the number of the observations. If the observations are x1, X2, X3, ..., X, then the mean x is calculated as:

Median If the numbers in a group are arranged from the smallest to the largest, the median is the middle number. For example, in the sample group of 5 numbers 10, 12, 15, 17 and 18, the median is 15. It divides the numbers into two groups, each containing equal numbers. The values in one group are smaller than the median, and those in the other are larger than the median. If the group has even number of observations, for example 6; the median is the average of two innermost numbers. That is, if the number 20 is added to the above group making it 10, 12, 15, 17, 18 and 20; the median will be average of 15 and 17 which is equal to 16.

Mode The mode is the value in the group that occurs most frequently. For example, in the group of numbers 25, 32, 36, 25, 28, 36 and 25; the mode is 25 because it occurs more frequently than any other number.

Distribution

Distribution of data is the way in which a group of numbers are distributed around a central point. Distribution can be of three types-symmetrical, asymmetrical and bimodal. 

Symmetrical distribution 

in a symmetrical distribution, mean, median and mode are equal to the same value. For example, a group of numbers 10, 12, 14, 16, 16, 18, 20 and 22 has a symmetrical distribution. Symmetrical distributions have mirror-image shapes from the mean to the lowest value, and from the mean to the highest value. A special case with a specific realtionship of the mean and standard deviation discussed later is known as a normal or Gaussian distribution (Fig. 4.3).

Asymmetrical distribution 

When there is a difference between the mean, median and mode of a population (group of numbers), the distribution of that population can be assumed to be asymmetrical. An asymmetrical distribution is tilted or skewed to one side and the arithmetic mean does not describe the centre of the distribution. 

Bimodal distribution A distribution of a population is bimodal when it has two distinct peaks in its distribution and can be separated into two distinct subpopulations.

Range

The range of a group of data or observations is the difference between the smallest and the largest value. It does not give any other information about the group.

Variance 

Variance is a difference in the value from the mean when multiple determinations are made on the same sample. For example, blood sugar estimation on a patient's blood sample was repeated 10 times and a range of values was obtained. The dispersion of each result from the mean is called variance. It can be calculated by adding the squares of the difference between each value and the mean, and dividing this sum by (n-1) where n is the number of observations. The variance of the observations .x₁, X₂ X₃..... X_n is

Variance 

Standard Deviation (SD)

The most commonly used statistical term in the clinical laboratory is the standard deviation which is represented by the symbol s or SD. The SD of the observartions X₁, X₂, X₃, ....,is 

In the equation, n - 1 is used instead of n because one degree of freedom (df) has been lost when the value of n has been used in the calculation of the mean. Degrees of freedom are the number of values that carry new information from one calculation to another.

Alternatively, SD can also be calculated by using the formula:

Alternatively, SD can also be calculated by using the formula:

In this equation, it is not necessary to calculate the mean before calculating SD.

As shown in Figure 4.3, for a data which has Gaussian distribution, approximately 68.2 per cent of the values will be between the limits of (X-SD) and (x + SD), 95.5 per cent will be between (X - 2SD) and (x + 2SD), and 99.7 per cent will appear between (x - 3SD) and (x + 3SD).

Coefficient of Variation (CV)

Standard deviation can also be expressed as coefficient of variation (CV) by dividing SD by th

mean value and multiplying by 100 to express it as a per cent:

Standard Deviation of the Mean or Standard Error of the Mean (SEM)

When data is collected for the estimation of a reference range, it is not possible to collect samples from the entire population. Therefore, a sample data is assumed to represent the population to a large extent. If a large sample size is used, the mean will be closer to the true mean of the population. If such data is collected from several subpopulations, the mean value of each subpopulation will vary or scatter around the actual mean of the whole population. The standard error of mean (SEM) is the measurement of this scatter and is calculated by dividing the standard deviation of the means of groups by the square root of the number of groups used to calculate the mean.

where n is the number of groups used. The SEM is decreased when the sample size increased, i.e., the mean of a large sample is likely to be closer to the true mean than that of a small sample.