# 6 Basic Statistical Tools

**Topics:**Normal distribution, Statistics, Standard deviation

**Pages:**22 (4827 words)

**Published:**August 20, 2013

6 BASIC STATISTICAL TOOLS

There are lies, damn lies, and statistics......

(Anon.)

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6.1 Introduction

6.2 Definitions

6.3 Basic Statistics

6.4 Statistical tests

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6.1 Introduction

In the preceding chapters basic elements for the proper execution of analytical work such as personnel, laboratory facilities, equipment, and reagents were discussed. 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. This is the reason why a complex system of precautions to prevent errors and traps to detect them has to be set up. An important aspect of the quality control is the detection of both random and systematic errors. 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.

A multitude of different statistical tools is available, some of them simple, some complicated, and often very specific for certain purposes. In analytical work, the most important common operation is the comparison of data, or sets of data, to quantify accuracy (bias) and precision. 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.

Clearly, statistics are a tool, not an aim. 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. The value of statistics lies with organizing and simplifying data, to permit some objective estimate showing that an analysis is under control or that a change has occurred. Equally important is that the results of these statistical procedures are recorded and can be retrieved.

6.2 Definitions

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6.2.1 Error

6.2.2 Accuracy

6.2.3 Precision

6.2.4 Bias

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Discussing Quality Control implies the use of several terms and concepts with a specific (and sometimes confusing) meaning. Therefore, some of the most important concepts will be defined first.

6.2.1 Error

Error is the collective noun for any departure of the result from the "true" value*. Analytical errors can be:

1. Random or unpredictable deviations between replicates, quantified with the "standard deviation". 2. Systematic or predictable regular deviation from the "true" value, quantified as "mean difference" (i.e. the difference between the true value and the mean of replicate determinations).

3. Constant, unrelated to the concentration of the substance analyzed (the analyte).

4. Proportional, i.e. related to the concentration of the analyte.

* The "true" value of an attribute is by nature indeterminate and often has only a very relative meaning. 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. cation exchange capacity). Obviously, this does not mean that no adequate analysis serving a purpose is possible. It does, however, emphasize the need for the establishment of standard reference methods and the...

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