# Statistical Analysis Data

Fortunately, with a few simple convenient statistical tools most of the information needed in regular laboratory work can be obtained: the "t-test, the "F-test", and regression analysis.

Therefore, examples of these will be given in the ensuing pages. Simple inspection of data, without statistical treatment, by an experienced and dedicated analyst may be just as useful as statistical figures on the desk of the disinterested.

Error is the collective noun for any departure of the result from the "true" value*. Random or unpredictable deviations between replicates, quantified with the "standard deviation". Systematic or predictable regular deviation from the "true" value, quantified as "mean difference" (i.e. Particularly in soil science for several attributes there is no such thing as the true value as any value obtained is method-dependent (e.g. Obviously, this does not mean that no adequate analysis serving a purpose is possible.

the difference between the true value and the mean of replicate determinations). Constant, unrelated to the concentration of the substance analyzed (the analyte). It does, however, emphasize the need for the establishment of standard reference methods and the importance of external QC (see Chapter 9).

The relationship between these concepts can be expressed in the following equation: Figure The types of errors are illustrated in Fig. (When the distribution is skewed statistical treatment is more complicated). The figure shows that (approx.) 68% of the data fall in the range ¯ x± s, 95% in the range ¯x ± 2s, and 99.7% in the range ¯x ± 3s.

The primary parameters used are the mean (or average) and the standard deviation (see Fig. The average of a set of n data x This is the most commonly used measure of the spread or dispersion of data around the mean.Before embarking upon the actual analytical work, however, one more tool for the quality assurance of the work must be dealt with: the statistical operations necessary to control and verify the analytical procedures (Chapter 7) as well as the resulting data (Chapter 8).It was stated before that making mistakes in analytical work is unavoidable. CGIAR center researchers and staff, National Programs researchers, CIMMYT’s partners, postgraduate students, molecular marker specialists, bioinformaticians, biometrician/statisticians, and visitors who are interested in the analysis of phenotypic and genotypic information in Breeding Programs.Participants should be familiar with basic theories and methods in plant breeding, plant genetics and statistics. Primary lecturers: Lectures will be delivered by Juan Burgueño, José Crossa, Fernando Toledo, Paulino Pérez, Ángela Pacheco, and Gregorio Alvarado.There are several components contributing to bias: 1.Method bias The difference between the mean of replicate test results of a sample and the ("true") value of the target population from which the sample was taken. (Note that the qualifications apply to the mean of results: in c the mean is accurate but some individual results are inaccurate) In the discussions of Chapters 7 and 8 basic statistical treatment of data will be considered.We will discuss the analysis of f MRI data, from its acquisition to its use in locating brain activity, making inference about brain connectivity and predictions about psychological or disease states.A standard f MRI study gives rise to massive amounts of noisy data with a complicated spatio-temporal correlation structure.This can be done by critically looking at the performance of the analysis as a whole and also of the instruments and operators involved in the job.For the detection itself as well as for the quantification of the errors, statistical treatment of data is indispensable.