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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.
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.
Rather than comparing two sets, members are paired between samples so the difference between the members becomes the sample. Typically the mean of the differences is then compared to zero. The common example scenario for when a paired difference test is appropriate is when a single set of test subjects has something applied to them and the test ...
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.
Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that the assumption allows us to calculate the probability of any event. As an example, consider a pair of ordinary six-sided dice. We will study two different statistical assumptions about the dice.
Differentiating between two-sided and one-sided intervals on a standard normal distribution curve. Two-sided intervals estimate a parameter of interest, Θ, with a level of confidence, γ, using a lower and upper bound (). Examples may include estimating the average height of males in a geographic region or lengths of a particular desk made by ...