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The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power .
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.
, X n) be an estimator based on a random sample X 1,X 2, . . . , X n, the estimator T is called an unbiased estimator for the parameter θ if E[T] = θ, irrespective of the value of θ. [1] For example, from the same random sample we have E(x̄) = μ (mean) and E(s 2) = σ 2 (variance), then x̄ and s 2 would be unbiased estimators for μ and ...
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.
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.
(The sample mean need not be a consistent estimator for any population mean, because no mean needs to exist for a heavy-tailed distribution.) A well-defined and robust statistic for the central tendency is the sample median, which is consistent and median-unbiased for the population median.
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 ...