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Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.
Zieffler et al. (2008) suggest three types of tasks that have been used in studies of students' informal inferential reasoning and its development. Estimate and draw a graph of a population based on a sample; Compare two or more samples of data to infer whether there is a real difference between the populations from which they were sampled
Archival research; Case study uses different research methods (e.g. interview, observation, self-report questionnaire) with a single case or small number of cases. Computer simulation (modeling) Ethnography; Event sampling methodology, also referred to as experience sampling methodology, diary study, or ecological momentary assessment
Inferential analysis can provide evidence that, with a certain percentage of confidence, there is a relationship between two variables. It is adopted that the sample will be different to the population, thus, we further accept a degree of uncertainty. [54] Example of sales forecasting, a form of predictive analysis
An example of Neyman–Pearson hypothesis testing (or null hypothesis statistical significance testing) can be made by a change to the radioactive suitcase example. If the "suitcase" is actually a shielded container for the transportation of radioactive material, then a test might be used to select among three hypotheses: no radioactive source ...
In the design-based approach, the model is taken to be known, and one of the goals is to ensure that the sample data are selected randomly enough for inference. Statistical assumptions can be put into two classes, depending upon which approach to inference is used. Model-based assumptions. These include the following three types:
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Causal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed.