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 Gaussian distribution parametric If this histogram is bell shape (Gaussian distribution) date analysed by standard (parametric) statistical tests (small departure don’t affect result). non parametric If the data deviate greatly from Gaussian distribution, it will be analyzed with distribution free (non 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:

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) = X test – C comp. (at least 40 specimen) Comparative method = reference method e.g. chromatography. Scatterplot of the individual measurements X Jaffe 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 conditions Criteria 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

Test performance characteristics:

Linear range: