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The signed rank test can be used to make inferences about the median of an unknown distribution function F(x) under the assumption that the probability density (mass) function is symmetric. If the distribution is symmetric Georgios Papagiannis Jersey , then the median of the distribution is equal to the mean of the distribution, and they can both be denoted by μ = F −1 (0.5). The sign test can also be used to provide inferences about the median without the necessity of making any assumptions about the distribution function F(x). However, the motivation behind the use of the signed rank test is that it provides a more precise analysis in situations where the distribution function can reasonably be taken to be symmetric.

The assumption of symmetry may be justified by an experimenter through observation or through an understanding of the nature of the data. For example, a simple histogram of the data may be sufficient to indicate that the assumption of symmetry is not inappropriate. In other cases Gary Trent Jr. Jersey , the experimenter may expect that the randomness in the data is composed primarily of a measurement error that can reasonably be expected to be distributed symmetrically. The additional precision of the signed rank test over the sign test is achieved through the consideration of the magnitudes of the deviations of the observed data values xi from the hypothesized median valueμ0. The sign test is performed by looking at whether an observation xi is less than μ0 or is greater than μ0. The signed rank test not only takes into account this information but also considers

|xi − μ0|

Where, the magnitude of the distance is between xi and μ0. The magnitudes provide additional information about the location of the median when the distribution is assumed to be symmetric. The signed rank test provides a useful middle ground between the sign test and a fully parametric test such as the t-test under a normal distributional assumption. The sign test is a very general procedure that requires no distributional assumptions. The signed rank test utilizes the additional information provided by an assumption that the distribution is symmetric and allows more precise inferences to be made about the mean of the distribution in this case. This assumption of symmetry can often be justified by an experimenter and provides a middle ground that is less restrictive than the exact specification of a symmetric distribution such as the normal distribution.

The choice of which inference method to adopt should be made on the basis of which set of assumptions are reasonable, and histograms or other data plots may be useful to investigate the form of the distribution. The experimenter should make use of any reasonable assumptions, so that for example Evan Turner Jersey , the signed rank test should be used in preference to the sign test when the assumption of symmetry can be justified. Remember that the central limit theorem implies that the t-test (or equivalently the z-test) can be used for large enough sample sizes regardless of the actual distribution of the data observations, although the sign test and the signed rank test in practice often provide as precise an inference as the t-test and may still be preferred. 　　Tourists visit the Tiantan Park in Beijing, capital of China, Oct. 4 Ed Davis Jersey , 2017. China witnessed more than 710 million tourist trips during the eight-day National Day and Mid-Autumn holidays, ringing up to about 590 billion yuan (88.68 billion U.S. dollars) in tourism income