Search results
Results From The WOW.Com Content Network
The significance level is 5% and the number of cases is 60. Power of unpaired and paired two-sample t-tests as a function of the correlation. The simulated random numbers originate from a bivariate normal distribution with a variance of 1 and a deviation of the expected value of 0.4. The significance level is 5% and the number of cases is 60.
In a two-tailed test, the rejection region for a significance level of α = 0.05 is partitioned to both ends of the sampling distribution and makes up 5% of the area under the curve (white areas). Statistical significance plays a pivotal role in statistical hypothesis testing.
Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...
In any situation where this statistic is a linear function of the data, divided by the usual estimate of the standard deviation, the resulting quantity can be rescaled and centered to follow Student's t distribution. Statistical analyses involving means, weighted means, and regression coefficients all lead to statistics having this form. Quite ...
Select a significance level (α), the maximum acceptable false positive rate. Common values are 5% and 1%. Compute from the observations the observed value t obs of the test statistic T. Decide to either reject the null hypothesis in favor of the alternative or not reject it.
T(y) is the value of the test statistic for an outcome y, with larger values of T representing cases which notionally represent greater departures from the null hypothesis, and where the sum ranges over all outcomes y (including the observed one) that have the same value of the test statistic obtained for the observed sample x, or a larger one.
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.