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Additional tasks to unit “Mathematical statistics»
Task 1. Answer the questions:
- What definition can you give to the term “mathematical statistics”?
- What terms is mathematical statistics connected with?
- What areas of science does mathematical st»atistics border on?
- What methods does this science use?
- What is the main aim of mathematical statistics?
Task 2. Read the text below and check your answers.
Mathematical statistics is the study of
statistics from a mathematical standpoint, using
probability theory as well as other branches of
mathematics such as
linear algebra and
analysis. The term «mathematical statistics» is closely related to the term «
statistical theory» but also embraces modeling for
actuarial science and non-statistical
probability theory.
Statistics deals with gaining information from data. In practice,
data often contain some
randomness or
uncertainty. Statistics handles such data using methods of
probability theory.
Statistical science is concerned with the planning of studies, especially with the
design of randomized experiments and with the planning of
surveys using
random sampling. The initial analysis of the data from properly randomized studies often follows the study protocol.
Of course, the data from a randomized study can be analyzed to consider secondary hypotheses or to suggest new ideas. A secondary analysis of the data from a planned study uses tools from data analysis.
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 intervals).
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 it is subjective.
Mathematical statistics has been inspired by and has extended many procedures in
applied statistics.
Task 3. Give the title to each paragraph of the text above.
Task 4. Discuss the topic “Mathematical statistics” with your partner using the titles to the paragraphs from Task 3 as a plan
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