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In order to explain the type of statistical bias, let us consider a racing with m participants. We denote by {a, b, c}(1 ≦ a \u003c b \u003c c ≦ m) a set of numbers of the first, second and third racehorses to reach the goal. The number of each participant is determined by lot, which leads us to the following null hypothesis: H0: A set {a,b,c} is nothing but a result of random sampling from the set {1,2,…,m}. Studying the probability distributions of various random variables arising in the random sampling of H0 , we are in a position to examine, by means of the chisquare test, how frequency distributions observed in the data mentioned above deviate from the expected ones under the null hypothesis H0 . Our method of contracting the original data consists of studying two random variables, R = c  a (the range) and D = min {b  a, c  b} (the adjacent interval of three numbers), as well as the following pair of partitions of the total event: A0 = {2b = a + c}, A1 = {2b \u003c a + c} and A2={2b \u003e a + c} ; B0 = {a + b = c}, B1 = {a + b \u003c c} and B2 = {a + b \u003e c}. In this paper (1), we take up three racetracks, Chukyo, Hanshin and Kyoto, to examine all racings of m = 16 (and also m =14) carried out on these racetracks. Indeed, we sum up the original data into two kinds of contingency tables, the one corresponding to the joint probability distribution of (R,D) and the other to the 3×3 probability table of the product events Ai ∩ Bj (i, j = 0, 1,2). Performing the chisquare tests for these contingency tables, we are able to detect some types of statistical bias for each racetrack. 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競馬データにみられる統計的偏りについて （1）
http://hdl.handle.net/10271/13
http://hdl.handle.net/10271/1346d1e815e7664a588b79839f02042962
名前 / ファイル  ライセンス  アクション 

kiyo18_1.pdf (656.4 kB)


Item type  紀要論文 / Departmental Bulletin Paper(1)  

公開日  20130827  
タイトル  
タイトル  競馬データにみられる統計的偏りについて （1）  
言語  
言語  jpn  
キーワード  
主題Scheme  Other  
主題  contingency table  
キーワード  
主題Scheme  Other  
主題  chisquare test  
キーワード  
主題Scheme  Other  
主題  sampling as the null hypothesis  
キーワード  
主題Scheme  Other  
主題  adjacent interval  
資源タイプ  
資源タイプ識別子  http://purl.org/coar/resource_type/c_6501  
資源タイプ  departmental bulletin paper  
著者 
野田, 明男
× 野田, 明男 

書誌情報 
浜松医科大学紀要. 一般教育 巻 18, p. 111, 発行日 20040329 

出版者  
出版者  浜松医科大学  
抄録  
内容記述タイプ  Abstract  
内容記述  The purpose of the present paper is to report what type of statistical bias the author has found in the horse racing data (based on [3]). In order to explain the type of statistical bias, let us consider a racing with m participants. We denote by {a, b, c}(1 ≦ a < b < c ≦ m) a set of numbers of the first, second and third racehorses to reach the goal. The number of each participant is determined by lot, which leads us to the following null hypothesis: H0: A set {a,b,c} is nothing but a result of random sampling from the set {1,2,…,m}. Studying the probability distributions of various random variables arising in the random sampling of H0 , we are in a position to examine, by means of the chisquare test, how frequency distributions observed in the data mentioned above deviate from the expected ones under the null hypothesis H0 . Our method of contracting the original data consists of studying two random variables, R = c  a (the range) and D = min {b  a, c  b} (the adjacent interval of three numbers), as well as the following pair of partitions of the total event: A0 = {2b = a + c}, A1 = {2b < a + c} and A2={2b > a + c} ; B0 = {a + b = c}, B1 = {a + b < c} and B2 = {a + b > c}. In this paper (1), we take up three racetracks, Chukyo, Hanshin and Kyoto, to examine all racings of m = 16 (and also m =14) carried out on these racetracks. Indeed, we sum up the original data into two kinds of contingency tables, the one corresponding to the joint probability distribution of (R,D) and the other to the 3×3 probability table of the product events Ai ∩ Bj (i, j = 0, 1,2). Performing the chisquare tests for these contingency tables, we are able to detect some types of statistical bias for each racetrack. Furthermore, these results tell us interesting dependency of the type of detected bias upon the racetrack, which suggests that the individual character of racetrack can be extracted from the longterm racing files [3].  
ISSN  
収録物識別子タイプ  ISSN  
収録物識別子  09140174  
NII書誌ID  
収録物識別子タイプ  NCID  
収録物識別子  AN10032827  
フォーマット  
内容記述タイプ  Other  
内容記述  application/pdf  
著者版フラグ  
出版タイプ  VoR  
出版タイプResource  http://purl.org/coar/version/c_970fb48d4fbd8a85 