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MessagePosté le: Jeu 26/04/18 04:05    Sujet du message: rob-kelley Répondre en citant

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 , 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, 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, 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.
TIANJIN, China, Oct. 14 (Xinhua) -- Following are the medalists at the sixth East Asian Games here on Monday:



Gold: DPR Korea

Silver: South Korea

Bronze: Japan



Gold: Chinese Taipei

Silver: China

Bronze: South Korea


Gold: Japan

Silver: South Korea

Bronze: Chinese Taipei


Women's track 500m time trial

Gold: Zhong Tianshi, China

Silver: Lee Wai Sze, Hong Kong , China

Bronze: Kayono Maeda, Japan

Men's track 1km time trial

Gold: Yudai Nitta, Japan

Silver: Zhang Miao, China

Bronze: Hsiao Shihhsin, Chinese Taipei

Men's track individual pursuit

Gold: Kim Hongki, South Korea

Silver: Eiya Hashimoto, Japan

Bronze: Cheung King Lok , Hong Kong, China

Women's track individual pursuit

Gold: Huang Dongyan, China

Silver: Jiang Fan, China

Bronze: Huang Tingying, Chinese Taipei


Women's 45-48kg

Gold: Kim Sol Mi, DPR Korea

Silver: Cho Ara, South Korea

Bronze: Yamazaki Tamami , Japan

Bronze: Qiu Xiangting, Chinese Taipei

Women's 48-52kg

Gold: Takumi Miyakawa, Japan

Silver: Cha Ok Song, DPR KoreaP Bronze: Jung Eunjung, South Korea

Bronze: Baldinnyam baterdene, Mongolia

Women's 52-57kg

Gold: Kim Jandi, South Korea

Silver: Liu Yang , China

Bronze: Ri Un Ju, DPR Korea

Bronze: Hirai Nozomi, Japan

Men's 55-60kg

Gold: Kim Wonjin, South Korea

Silver: tang Xiaolong, China

Bronze: Ryo Kawabata, Japan

Bronze: Tsai Mingyen, Chinese Taipei

Men's 60-66kg

Gold: Morishita Jumpei , Japan

Silver: Hyon Song Chol, DPR Korea

Bronze: Hwang Bobae, South Korea

Bronze: Chien Chiahung, Chinese Taipei

Men's 66-73kg

Gold: Bang Guiman, South Korea

Silver: Takeshi Doi, Japan

Bronze: Hong Kuk Hyon, DPR Korea

Bronze: Khadbaatar Narankhuu , Mongolia


Women's 50m freestyle

Gold: Tang Yi, China

Silver: Siobhan Bernadette Haughey, Hong Kong, China

Bronze: Lee Jaeyoung, South Korea

Men's 50m freestyle

Gold: Ning Zetao, China

Silver: Yuki Kawachi, Japan

Bronze: Geoffrey Robin Cheah , Hong Kong, China

Men's 100m butterfly

Gold: Kohei Kawamoto, Japan

Silver: Shi Feng, China

Bronze: Masayuki Umemoto, Japan

Women's 200m breaststroke

Gold: Mio Motegi, Japan

Silver: Shi Jinglin, China

Bronze: Runa Imai , Japan

Women's 400m individual medley

Gold: Chen Xinyi, China

Silver: Sakiko Shimizu, Japan

Bronze: Kim Seoyeong, South Kore.
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