Editing Mathematical statistics (section)

==Introduction==
Statistical data collection is concerned with the planning of studies, especially with the [[design of experiments|design of randomized experiments]] and with the planning of [[statistical survey|surveys]] using [[random sampling]]. The initial analysis of the data often follows the study protocol specified prior to the study being conducted. The data from a study can also be analyzed to consider secondary hypotheses inspired by the initial results, or to suggest new studies. A secondary analysis of the data from a planned study uses tools from [[data analysis]], and the process of doing this is mathematical statistics.

Data analysis is divided into:

* [[descriptive statistics]] – the part of statistics that describes data, i.e. summarises the data and their typical properties.
* [[inferential statistics]] – the part of statistics that draws conclusions from data (using some model for the data): For example, inferential statistics involves selecting a model for the data, checking whether the data fulfill the conditions of a particular model, and with quantifying the involved uncertainty (e.g. using [[confidence interval]]s).

While the tools of data analysis work best on data from randomized studies, they are also applied to other kinds of data. For example, from [[natural experiments]] and [[observational studies]], in which case the inference is dependent on the model chosen by the statistician, and so subjective.<ref>[[David A. Freedman (statistician)|Freedman, D.A.]] (2005) ''Statistical Models: Theory and Practice'', Cambridge University Press. {{isbn|978-0-521-67105-7}}</ref><ref name=Freedman>{{cite book |last1=Freedman |first1=David A. |editor1-last=Collier |editor1-first=David |editor2-last=Sekhon |editor2-first=Jasjeet S. |editor3-last=Stark |editor3-first=Philp B. |title=Statistical Models and Causal Inference: A Dialogue with the Social Sciences |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-12390-7 |url=http://www.cambridge.org/9780521123907}}</ref>