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The term "Z-test" is often used to refer specifically to the one-sample location test comparing the mean of a set of measurements to a given constant when the sample variance is known. For example, if the observed data X 1 , ..., X n are (i) independent, (ii) have a common mean μ, and (iii) have a common variance σ 2 , then the sample average ...
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-tailed or two-tailed Z-test. The statistical tables for t and for Z provide critical values for both one- and two-tailed tests. That is, they provide the critical values that cut off an entire region at one or ...
Test name Scaling Assumptions Data Samples Exact Special case of Application conditions One sample t-test: interval: normal: univariate: 1: No [8]: Location test: Unpaired t-test: interval
The one-sample location test compares the location parameter of one sample to a given constant. An example of a one-sample location test would be a comparison of the location parameter for the blood pressure distribution of a population to a given reference value.
As improvements are made to experimental design (e.g. increased precision of measurement and sample size), the test becomes more lenient. Unless one accepts the absurd assumption that all sources of noise in the data cancel out completely, the chance of finding statistical significance in either direction approaches 100%. [71]
Suppose we are using a Z-test to analyze the data, where the variances of the pre-treatment and post-treatment data σ 1 2 and σ 2 2 are known (the situation with a t-test is similar). The unpaired Z-test statistic is ¯ ¯ / + /, The power of the unpaired, one-sided test carried out at level α = 0.05 can be calculated as follows:
I edited the top parts of this page to make it more parallel to the t-test page, which defines a t-test as being any test for which the test statistic follows a t-distribution (rather than just covering the one-sample and two-sample t-tests). Nevertheless, I agree that the one-sample/two-sample tests need to be covered in detail.
The Wilcoxon signed-rank test is a non-parametric rank test for statistical hypothesis testing used either to test the location of a population based on a sample of data, or to compare the locations of two populations using two matched samples. [1] The one-sample version serves a purpose similar to that of the one-sample Student's t-test. [2]