Two-tailed test

The two-tailed test is a statistical test used in inference, in which a given statistical hypothesis, H₀ (the null hypothesis), will be rejected when the value of the test statistic is either sufficiently small or sufficiently large. This contrasts with a one-tailed test, in which only one of the rejection regions "sufficiently small" or "sufficiently large" is preselected according to the alternative hypothesis being selected, and the hypothesis is rejected only if the test statistic satisfies that criterion. Alternative names are one-sided and two-sided tests.

Discussion

Probability from both negative and positive directions of x-axis on the normal distribution.

The circular test is named after the "tail" of data under the far left and far right of a bell-shaped normal data distribution, or bell curve. However, the terminology is extended to tests relating to distributions other than normal. In general a test is called two-tailed if the null hypothesis is rejected for values of the test statistic falling into either tail of its sampling distribution, and it is called one-sided or one-tailed if the null hypothesis is rejected only for values of the test statistic falling into one specified tail of its sampling distribution.^[1] For example, if the alternative hypothesis is $\mu \ne 42.5$, rejecting the null hypothesis of μ = 42.5 for small or for large values of the sample mean, the test is called "two-tailed" or "two-sided". If the alternative hypothesis is μ > 1.4, rejecting the null hypothesis of $\mu \le 1.4$ only for large values of the sample mean, it is then called "one-tailed" or "one-sided".

If the distribution from which the samples are derived is considered to be normal, Gaussian, or bell-shaped, then the test is referred to as a one- or two-tailed T test. If the test is performed using the actual population mean and variance, rather than an estimate from a sample, it would be called a one- or two-tailed Z test.

The statistical tables^{[clarification needed]} for Z and for t provide critical values for both one- and two-tailed tests. That is, they provide the critical values that cut off an entire alpha region at one or the other end of the sampling distribution as well as the critical values that cut off the 1/2 alpha regions at both ends of the sampling distribution.

References

1. ^ John E. Freund, (1984) Modern Elementary Statistics, sixth edition. Prentice hall. ISBN 0135935253 (Section "Inferences about Means", chapter "Significance Tests", page 289.)

This statistics-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Hypothesis testing Statistical terminology Statistics stubs Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? IPIC Stapleton, Bristol Look at other dictionaries: Two-Tailed Test — A statistical test in which the critical area of a distribution is two sided and tests whether a sample is either greater than or less than a certain range of values. If the sample that is being tested falls into either of the critical areas, the …   Investment dictionary two-tailed test — a hypothesis test (q.v.) in which the critical region comprises both tails of the distribution of the test statistic and the null hypothesis is tested against a two sided alternative that includes deviation from the null hypothesis in both… …   Medical dictionary Two-tailed — may refer to:In entomology:* Two tailed Pasha, butterfly which can be seen only in the Mediterranean regions in August and September * Two tailed Swallowtail, large North American butterflyIn other fields:* Two tailed Dog Party, joke political… …   Wikipedia two-tailed — ¦ ̷ ̷ ˈ ̷ ̷ adjective also two tail ¦ ̷ ̷ ¦ ̷ ̷ : being a statistical test for which the critical region consists of all values of the test statistic greater than a given value plus the values less than another given value compare one tailed… …   Useful english dictionary two-tailed — also two tail adjective Date: 1945 being a statistical test for which the critical region consists of all values of the test statistic greater than a given value plus the values less than another given value compare one tailed …   New Collegiate Dictionary Student's t-test — A t test is any statistical hypothesis test in which the test statistic follows a Student s t distribution if the null hypothesis is supported. It is most commonly applied when the test statistic would follow a normal distribution if the value of …   Wikipedia Fisher's exact test — is a statistical significance test used in the analysis of categorical data where sample sizes are small. It is named after its inventor, R. A. Fisher, and is one of a class of exact tests. Fisher devised the test following a comment from Muriel… …   Wikipedia Binomial test — In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories.For example, suppose we have a board game that depends on the roll of a …   Wikipedia Welch's t test — In statistics, Welch s t test is an adaptation of Student s t test intended for use with two samples having possibly unequal variances. As such, it is an approximate solution to the Behrens–Fisher problem.FormulasWelch s t test defines the… …   Wikipedia Page's trend test — In statistics, the Page test for multiple comparisons between ordered correlated variables is the counterpart of Spearman s rank correlation coefficient which summarizes the association of continuous variables. It is also known as Page s trend… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”