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Aktuelle News aus Politik, Sport, Unterhaltung, Wirtschaft & Finanzen | Ratgeber Leben, Gesundheit und Heim & Garten | E-Mail und Shopping bei poney-club-de-prunevaux.eu Telekom Social Wall. T-Systems MMS. Von Fax und E-Mail über den. Sie können die Domain poney-club-de-prunevaux.eu weiterhin nutzen und neue @poney-club-de-prunevaux.eu-​Adressen einfach hinzufügen. Zum Postfach. Sicher kommunizieren mit E-Mail made. T-Online (Eigenschreibweise: t-online) war der Markenname eines zunächst separaten Online-Dienstes der Deutschen Telekom AG. wurden die ersten​. Das Ţ (kleingeschrieben ţ) ist ein Buchstabe des lateinischen Schriftsystems, bestehend aus einem T mit Cedille. Er findet Anwendung im gagausischen. Visitenkarten im redaktionellen Umfeld. Mit monatlich über 27 Millionen Unique Usern ist poney-club-de-prunevaux.eu die. Bewerten Sie T Online wie schon Kunden vor Ihnen! Ihre Erfahrung kann anderen helfen, informierte Entscheidungen zu treffen.

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Your browser does not support the video tag. Advanced features for skilled torrenters. The sample standard deviations for the two samples are approximately 0.

For such small samples, a test of equality between the two population variances would not be very powerful.

Since the sample sizes are equal, the two forms of the two-sample t -test will perform similarly in this example.

The test statistic is approximately 1. The test statistic is approximately equal to 1. The t -test provides an exact test for the equality of the means of two i.

Welch's t -test is a nearly exact test for the case where the data are normal but the variances may differ. For moderately large samples and a one tailed test, the t -test is relatively robust to moderate violations of the normality assumption.

If the data are substantially non-normal and the sample size is small, the t -test can give misleading results. See Location test for Gaussian scale mixture distributions for some theory related to one particular family of non-normal distributions.

When the normality assumption does not hold, a non-parametric alternative to the t -test may have better statistical power. However, when data are non-normal with differing variances between groups, a t-test may have better type-1 error control than some non-parametric alternatives.

It will also have power in detecting an alternative by which group B has the same distribution as A but after some shift by a constant in which case there would indeed be a difference in the means of the two groups.

However, there could be cases where group A and B will have different distributions but with the same means such as two distributions, one with positive skewness and the other with a negative one, but shifted so to have the same means.

In such cases, MW could have more than alpha level power in rejecting the Null hypothesis but attributing the interpretation of difference in means to such a result would be incorrect.

In the presence of an outlier , the t-test is not robust. For example, for two independent samples when the data distributions are asymmetric that is, the distributions are skewed or the distributions have large tails, then the Wilcoxon rank-sum test also known as the Mann—Whitney U test can have three to four times higher power than the t -test.

For a discussion on choosing between the t -test and nonparametric alternatives, see Lumley, et al. One-way analysis of variance ANOVA generalizes the two-sample t -test when the data belong to more than two groups.

When both paired observations and independent observations are present in the two sample design, assuming data are missing completely at random MCAR , the paired observations or independent observations may be discarded in order to proceed with the standard tests above.

Alternatively making use of all of the available data, assuming normality and MCAR, the generalized partially overlapping samples t-test could be used.

A generalization of Student's t statistic, called Hotelling's t -squared statistic , allows for the testing of hypotheses on multiple often correlated measures within the same sample.

For instance, a researcher might submit a number of subjects to a personality test consisting of multiple personality scales e.

Because measures of this type are usually positively correlated, it is not advisable to conduct separate univariate t -tests to test hypotheses, as these would neglect the covariance among measures and inflate the chance of falsely rejecting at least one hypothesis Type I error.

In this case a single multivariate test is preferable for hypothesis testing. Fisher's Method for combining multiple tests with alpha reduced for positive correlation among tests is one.

Another is Hotelling's T 2 statistic follows a T 2 distribution. However, in practice the distribution is rarely used, since tabulated values for T 2 are hard to find.

Usually, T 2 is converted instead to an F statistic. The test statistic is Hotelling's t 2 :. The test statistic is Hotelling's two-sample t 2 :.

From Wikipedia, the free encyclopedia. Statistical method. Main article: Paired difference test. Main article: Welch's t-test.

This article may not properly summarize its corresponding main article. Please help improve it by rewriting it in an encyclopedic style.

Learn how and when to remove this template message. Main article: Hotelling's T-squared distribution.

Mathematics portal. October Zeitschrift für Anatomie und Entwicklungsgeschichte. Astronomische Nachrichten in German. Bibcode : AN A forerunner of the t-distribution".

MR Archive for History of Exact Sciences. Skew Variation in Homogeneous Material". Myers, H. New Delhi: Pearson.

Retrieved 24 July Silverman: Two "students" of science". The Concise Encyclopedia of Statistics. High-Yield Behavioral Science.

High-Yield Series. Annual Review of Public Health. The American Statistician. Statistical Methods in Medical Research. An Introduction to Medical Statistics.

Oxford University Press. Mathematical Statistics and Data Analysis 3rd ed. Duxbury Advanced. Clifford Psychological Bulletin.

January The Journal of Experimental Education. Clifford; Higgins, James J. Journal of Educational Statistics.

On assumptions for hypothesis tests and multiple interpretations of decision rules". Statistics Surveys.

The Quantitative Methods for Psychology. O'Mahony, Michael CRC Press. Press, William H. Cambridge University Press. Outline Index. Descriptive statistics.

Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments.

Index of dispersion. Grouped data Frequency distribution Contingency table. Data collection. Sampling stratified cluster Standard error Opinion poll Questionnaire.

Scientific control Randomized experiment Randomized controlled trial Random assignment Blocking Interaction Factorial experiment.

Adaptive clinical trial Up-and-Down Designs Stochastic approximation.

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When the scaling term is unknown and is replaced by an estimate based on the data , the test statistics under certain conditions follow a Student's t distribution.

The t -test can be used, for example, to determine if the means of two sets of data are significantly different from each other.

The term " t -statistic" is abbreviated from "hypothesis test statistic". Hence a second version of the etymology of the term Student is that Guinness did not want their competitors to know that they were using the t-test to determine the quality of raw material.

Although it was William Gosset after whom the term "Student" is penned, it was actually through the work of Ronald Fisher that the distribution became well known as "Student's distribution" [11] and "Student's t-test".

Gosset had been hired owing to Claude Guinness 's policy of recruiting the best graduates from Oxford and Cambridge to apply biochemistry and statistics to Guinness's industrial processes.

The t -test work was submitted to and accepted in the journal Biometrika and published in Guinness had a policy of allowing technical staff leave for study so-called "study leave" , which Gosset used during the first two terms of the — academic year in Professor Karl Pearson 's Biometric Laboratory at University College London.

Z may be sensitive to the alternative hypothesis i. In the t -test comparing the means of two independent samples, the following assumptions should be met:.

Most two-sample t -tests are robust to all but large deviations from the assumptions. Normality of the individual data values is not required if these conditions are met.

By the central limit theorem , sample means of moderately large samples are often well-approximated by a normal distribution even if the data are not normally distributed.

However, if the sample size is large, Slutsky's theorem implies that the distribution of the sample variance has little effect on the distribution of the test statistic.

Two-sample t -tests for a difference in mean involve independent samples unpaired samples or paired samples.

Paired t -tests are a form of blocking , and have greater power than unpaired tests when the paired units are similar with respect to "noise factors" that are independent of membership in the two groups being compared.

The independent samples t -test is used when two separate sets of independent and identically distributed samples are obtained, one from each of the two populations being compared.

In this case, we have two independent samples and would use the unpaired form of the t -test. Paired samples t -tests typically consist of a sample of matched pairs of similar units , or one group of units that has been tested twice a "repeated measures" t -test.

A typical example of the repeated measures t -test would be where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are tested again after treatment with a blood-pressure-lowering medication.

By comparing the same patient's numbers before and after treatment, we are effectively using each patient as their own control. That way the correct rejection of the null hypothesis here: of no difference made by the treatment can become much more likely, with statistical power increasing simply because the random interpatient variation has now been eliminated.

However, an increase of statistical power comes at a price: more tests are required, each subject having to be tested twice. Pairs become individual test units, and the sample has to be doubled to achieve the same number of degrees of freedom.

A paired samples t -test based on a "matched-pairs sample" results from an unpaired sample that is subsequently used to form a paired sample, by using additional variables that were measured along with the variable of interest.

This approach is sometimes used in observational studies to reduce or eliminate the effects of confounding factors.

Explicit expressions that can be used to carry out various t -tests are given below. In each case, the formula for a test statistic that either exactly follows or closely approximates a t -distribution under the null hypothesis is given.

Also, the appropriate degrees of freedom are given in each case. Each of these statistics can be used to carry out either a one-tailed or two-tailed test.

Once the t value and degrees of freedom are determined, a p -value can be found using a table of values from Student's t -distribution.

If the calculated p -value is below the threshold chosen for statistical significance usually the 0. The standard error of the slope coefficient :.

The t score, intercept can be determined from the t score, slope :. The t statistic to test whether the means are different can be calculated as follows:.

The denominator of t is the standard error of the difference between two means. This test is used only when it can be assumed that the two distributions have the same variance.

When this assumption is violated, see below. This test, also known as Welch's t -test, is used only when the two population variances are not assumed to be equal the two sample sizes may or may not be equal and hence must be estimated separately.

The t statistic to test whether the population means are different is calculated as:. For use in significance testing, the distribution of the test statistic is approximated as an ordinary Student's t -distribution with the degrees of freedom calculated using.

This is known as the Welch—Satterthwaite equation. The true distribution of the test statistic actually depends slightly on the two unknown population variances see Behrens—Fisher problem.

This test is used when the samples are dependent; that is, when there is only one sample that has been tested twice repeated measures or when there are two samples that have been matched or "paired".

This is an example of a paired difference test. The t statistic is calculated as. The pairs are e. Let A 1 denote a set obtained by drawing a random sample of six measurements:.

We will carry out tests of the null hypothesis that the means of the populations from which the two samples were taken are equal.

The difference between the two sample means, each denoted by X i , which appears in the numerator for all the two-sample testing approaches discussed above, is.

The sample standard deviations for the two samples are approximately 0. For such small samples, a test of equality between the two population variances would not be very powerful.

Since the sample sizes are equal, the two forms of the two-sample t -test will perform similarly in this example.

The test statistic is approximately 1. The test statistic is approximately equal to 1. The t -test provides an exact test for the equality of the means of two i.

Welch's t -test is a nearly exact test for the case where the data are normal but the variances may differ. For moderately large samples and a one tailed test, the t -test is relatively robust to moderate violations of the normality assumption.

If the data are substantially non-normal and the sample size is small, the t -test can give misleading results.

See Location test for Gaussian scale mixture distributions for some theory related to one particular family of non-normal distributions.

When the normality assumption does not hold, a non-parametric alternative to the t -test may have better statistical power.

However, when data are non-normal with differing variances between groups, a t-test may have better type-1 error control than some non-parametric alternatives.

It will also have power in detecting an alternative by which group B has the same distribution as A but after some shift by a constant in which case there would indeed be a difference in the means of the two groups.

However, there could be cases where group A and B will have different distributions but with the same means such as two distributions, one with positive skewness and the other with a negative one, but shifted so to have the same means.

In such cases, MW could have more than alpha level power in rejecting the Null hypothesis but attributing the interpretation of difference in means to such a result would be incorrect.

In the presence of an outlier , the t-test is not robust. For example, for two independent samples when the data distributions are asymmetric that is, the distributions are skewed or the distributions have large tails, then the Wilcoxon rank-sum test also known as the Mann—Whitney U test can have three to four times higher power than the t -test.

For a discussion on choosing between the t -test and nonparametric alternatives, see Lumley, et al. One-way analysis of variance ANOVA generalizes the two-sample t -test when the data belong to more than two groups.

When both paired observations and independent observations are present in the two sample design, assuming data are missing completely at random MCAR , the paired observations or independent observations may be discarded in order to proceed with the standard tests above.

Alternatively making use of all of the available data, assuming normality and MCAR, the generalized partially overlapping samples t-test could be used.

A generalization of Student's t statistic, called Hotelling's t -squared statistic , allows for the testing of hypotheses on multiple often correlated measures within the same sample.

For instance, a researcher might submit a number of subjects to a personality test consisting of multiple personality scales e.

Because measures of this type are usually positively correlated, it is not advisable to conduct separate univariate t -tests to test hypotheses, as these would neglect the covariance among measures and inflate the chance of falsely rejecting at least one hypothesis Type I error.

In this case a single multivariate test is preferable for hypothesis testing. Fisher's Method for combining multiple tests with alpha reduced for positive correlation among tests is one.

Another is Hotelling's T 2 statistic follows a T 2 distribution. However, in practice the distribution is rarely used, since tabulated values for T 2 are hard to find.

Usually, T 2 is converted instead to an F statistic. The test statistic is Hotelling's t 2 :. The test statistic is Hotelling's two-sample t 2 :.

From Wikipedia, the free encyclopedia. Statistical method. Main article: Paired difference test. Main article: Welch's t-test.

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