Inferential statistics — Estimate

Collecting and analyzing data are the two fundamental objectives of Statistics. To achieve this, several steps must be followed. First of all, we need to define the object under study, the statistical variables involved, the questionnaire to be drawn up, and then construct a representative sample according to a sampling plan. We won't go into detail on this last point, as it is beyond the scope of this article. We'll start by discussing the concept of sampling, to clarify the notions of population and sample.

Once the data have been collected and corrected (a laborious but essential task), they can be visualized in the form of tables or graphs, and summarized using parameters that reveal the essential characteristics of the phenomenon under study. These techniques are described in the article .

Next comes the modeling stage. Inferential statistics provides the elements needed to specify the probabilistic model that generated the data as accurately as possible, based on the observed sample: determining the model, estimating unknown parameters and validating the model. The aim is to make predictions and decisions based on observations.

The estimation part is described in paragraph 3 and presents the statistical methods used by engineers. These methods will generally be justified mathematically, to avoid a certain number of errors in interpreting the results, which are frequent in practice.

Statistical methods are used in many fields, including engineering (manufacturing quality control...), medicine (testing new treatments...), economics (quantitative market research...) and others.

Reading this article requires a prerequisite in Probability. All notions and notations used in the following can be found in the article of this treaty.

In the form , the use of statistical tables is explained using numerical examples.