Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

## The Data

The basis of all statistical analyses is the data. The data set to be analyzed should describe one or more than one characteristic of the observed object. When analyzing data, we should always be aware of the data source, keeping the following points in mind:

• Details of the data acquisition: the type of data acquisition (manual, automatic, frequency and intensity resolution, sampling plan, etc.) may influence the results considerably, and may require different methods of interpretation.
• Is the measured data a population or a sample? Different formulas and the precision of results follow from this.
• What is the precision of the measurements. This knowledge is necessary to avoid an excessive number of decimal places. It may be misleading, for example, if the results of an exit poll during elections are presented as "23.71% for party xy" if the uncertainty is approximately 2 %. A correct specification would be 23 +/- 2 %.
• Is the observed variable really significant for the problem to be solved? In some cases, the selection of the significant variables is not obvious a priori.
• What exactly is the problem to be solved? It can be shown, that using a set of statistical methods by trial and error (especially test statistics) increases the probability of drawing certain conclusions.