Are bootstrapped samples independent?

Are bootstrapped samples independent?

Since the bootstrapping procedure is distribution-independent it provides an indirect method to assess the properties of the distribution underlying the sample and the parameters of interest that are derived from this distribution.

What does the t-test for independent samples assume?

Recall that the Independent Samples t Test requires the assumption of homogeneity of variance — i.e., both groups have the same variance. SPSS conveniently includes a test for the homogeneity of variance, called Levene’s Test, whenever you run an independent samples t test.

What is the difference between a t-test for independent samples and a t-test for dependent samples?

Dependent samples are paired measurements for one set of items. Independent samples are measurements made on two different sets of items. When you conduct a hypothesis test using two random samples, you must choose the type of test based on whether the samples are dependent or independent.

How are the bootstrap and the t-test similar?

Both the t-test and the bootstrap are based on sampling distributions, what the distribution of the test statistic is. The exact t-test is based on theory and the condition that the population/process generating the data is normal. The t-test happens to be fairly robust to the normality assumption (as far as the size of the test goes,

Can a bootstrap give you the sampling distribution?

The bootstrap does not give you normality, it gives you the sampling distribution (which sometimes looks normal, but still works when it is not) without needing the assumptions about the population. For t-tests where it is reasonable to assume that the population is normal (or at least normal enough) then the t-test will be best (of the 2).

When to use percentile bootstrap and percentile t test?

For inferences on the population mean, the standard ​T-test and the percentile bootstrap can give unsatisfactory results when sampling from skewed distributions, especially when sample size is small. To illustrate the problem with the t-test, imagine that we sample from populations of increasing skewness.

How are Bootstrap T values used in statistics?

5,000 bootstrap ​T​ values obtained by sampling with replacement from the mean centred data. In the asymmetric bootstrap-t technique, the quantiles (red vertical lines) of that distribution of ​T​ values are used to define the CI bounds. The insets contain the formulas for the lower (CI​lo)​ and upper bounds (CI​up)​ of the CI.