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The GAISE document provides a two-dimensional framework, [11] specifying four components used in statistical problem solving (formulating questions, collecting data, analyzing data, and interpreting results) and three levels of conceptual understanding through which a student should progress (Levels A, B, and C). [12]
Students can learn from step-by-step approach of worked examples which later can be helpful to them in solving similar problems on their own. [3] Novices, however, often find it difficult to distinguish domain specific information and the information specific to solving that problem, which increases their cognitive load. [4]
Problem solving is the process of investigating the given information and finding all possible solutions through invention or discovery. Traditionally, it is argued that problem solving is a step towards decision making, so that the information gathered in that process may be used towards decision-making. [9] [page needed]
Statistics educators have cognitive and noncognitive goals for students. For example, former American Statistical Association (ASA) President Katherine Wallman defined statistical literacy as including the cognitive abilities of understanding and critically evaluating statistical results as well as appreciating the contributions statistical thinking can make.
The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, [1] "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by David Cox. [2]
This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory. However, there are intermediate methods that, for example, use theory to guide the method, an approach known as guided empiricism .
Statistical thinking is thought to help in different contexts, such as the courtroom, [5] biology labs, [6] and children growing up surrounded by data. [2] The American Statistical Association (ASA) has laid out what it means to be "statistically educated". [2] Here is a subset of concepts for students to know, that: data beat anecdotes
The typical problem begins with a system for which the Hamiltonian is known, it is at a given temperature and it follows the Boltzmann statistics. To obtain the mean value of some macroscopic variable, say A, the general approach is to compute, over all the phase space , PS for simplicity, the mean value of A using the Boltzmann distribution:
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