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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.
In statistical hypothesis testing, a two-sample test is a test performed on the data of two random samples, each independently obtained from a different given population. The purpose of the test is to determine whether the difference between these two populations is statistically significant .
Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position ( null hypothesis ) is incorrect.
A permutation test involves two or more samples. The null hypothesis is that all samples come from the same distribution H 0 : F = G {\displaystyle H_{0}:F=G} . Under the null hypothesis , the distribution of the test statistic is obtained by calculating all possible values of the test statistic under possible rearrangements of the observed data.
Equivalence tests are a variety of hypothesis tests used to draw statistical inferences from observed data. In these tests, the null hypothesis is defined as an effect large enough to be deemed interesting, specified by an equivalence bound. The alternative hypothesis is any effect that is less extreme than said equivalence bound.
Bayesian statistics are based on a different philosophical approach for proof of inference.The mathematical formula for Bayes's theorem is: [|] = [|] [] []The formula is read as the probability of the parameter (or hypothesis =h, as used in the notation on axioms) “given” the data (or empirical observation), where the horizontal bar refers to "given".
Whereas descriptive statistics describe a sample, inferential statistics infer predictions about a larger population that the sample represents. The outcome of statistical inference may be an answer to the question "what should be done next?", where this might be a decision about making further experiments or surveys, or about drawing a ...
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: