Prof. of Clinical Chemistry, Mansoura University

Statistical procedures

Statistics defined as the science of:

• Gathering data• Analyzing data• Interpreting data • Presenting data

Discriptive statistics

Used to summarize the important feature of a group of data

Frequency histogram (diagram):

Repeated measurements The number of frequency of each result

on y – axis The value of the result on x-axis

If this histogram is bell shape (Gaussian Gaussian distributiondistribution) date analysed by standard

(parametricparametric) statistical tests (small departure don’t affect result).

If the data deviate greatly from Gaussian distribution, it will be analyzed with

distribution free (non parametricnon parametric) statistical test.

Skewness:

The most common deviation from Gaussian distribution

It is the presence of increased numbers of observation in one of the tails of the

distribution

It is used to calculate the statistical limit for the mean

It is the average error encountered if the sample mean was used to

estimate the population mean .SEM decreases as the sample size

increases The mean of large sample is likely to be closer to the true mean than the

mean of a small sample

The introduction of a new test illustrates the extensive use of

statistics in the laboratory.The test should be introduced only

ofter reviewing the data that document its usefulness in

diagnosis or monitoring a disease state.

If there are several methods to do this test chose the optimally acurate

and precise method accuracy and precision must be continualy

assessed to ensure reliable analyses

Descriptive statistics of groups of paired observations

This is the comparison – of – methods experiment in which the specirmens are measured by both

the new method and the old or comparative method.

Old method values are plotted on the x-axis .new method values are

plotted on the y-axis.

Linear regression analysis

Y = m x + y o The slop = m

Yo = y at x = O If there is perfect agreement

between the two methods , each value measused by the test method

will be equal to that measured by the comparative one

So y = x with m = 1 and yo = O

To distinguish between to variables:

Calibration involves measurment of the instrument response Y (absorbance) to

special samples called calibrators whose concentration X are known.

The calibration procedure is performed periodically to adjust for system drift.

Calibration:

Two kinds of errors are measured in comparison of method experiments (random and systemic error):

present in all measurements (if repeated)

due to chance can be positive or negative

The measure of dispersion sy/x estimate this error

Errors account for the difference between the test and comparative-method results.

Random error:Random error:

Systematic error (S.E): Systematic error (S.E):

Influences consistently in one direction

Should not be present in a method The slop and Y intercept can

measure systematic E May be constant regardless of the

concentration (constant S.E) Or proportional to analyte

concentration (proportional S.E)

Total analysis error (Xd) = XTotal analysis error (Xd) = Xtesttest – C – Ccompcomp..

(at least 40 specimen)(at least 40 specimen)Comparative method = reference method

e.g. chromatography.

Scatterplot of the individual measurements XJaffe against X HPLC, with least squares line (solid line) and line of identity (dotted line).

Inferential statistics

To compare the means and SDS of two groups of data.

T – test: used to determine if there is statistically significant difference between

means.

F – test :

• Between standard deviations.• Both have limited usefulness in

method evaluation Sig < 0.05 = the probabilty of the difference

between the two groups of data dlue to chance is less than 0.0

Factors necessary : Respect to age , sex and genetic

socioeconomic factors Physiologic and environmental

conditionsCriteria of excluding or including

individuals Specimen collection procedure

The analytical methods Normal value and normal range is that

corrospond to the health associated reference interval ( central 95%)

Reference entervals = Normal Range Reference entervals = Normal Range

Test performance characteristics:

Linear range: