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It deduces the continuous variable Z probability density function p(z)=e^\u003c-x^2/2\u003e/√\u003c2π\u003e(-∞\u003cz\u003c∞) according to N(0,1^2), the standard normal distribution. I deduce the variable X probability density function f(x)=e\u003c-(x-m)^2/2σ^2/√\u003c2π\u003eσ(-∞\u003cx\u003c∞), (σ\u003eo) according to N(m, σ^2), the normal distribution from the relation between the continuous variable Z probability density function and the discrete variable X probability density function pn(x)=_nC_xp^x(1-p)^\u003cn-x\u003e (x=0,l,2,…,n), (0\u0026gnE;p\u0026gnE;1) according to the binominal distribution. Using these functions, I analyze the Z-score : z=(x-x^^-)/s which is used as the standardized raw score in the fields of pedagogy and psychology nowadays and the T-score: t=50+10(x-x^^-)/s which is ofen used at lessons as the practical application on the basis of the central limit theorem lim__\u003cn→∞\u003eP(α\u0026lnE;√\u003cn\u003e(x^^--μ)/δ\u0026lnE;β)=\u0026lmoust;^β_ap(z)dz (μ:population mean, δ:population variance and x^^-:sample mean) consisting in the connection betwoon the population and the sample. 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中心極限定理を巡って : Tスコアーの教育的有効性
https://nagoya-wu.repo.nii.ac.jp/records/1732
https://nagoya-wu.repo.nii.ac.jp/records/17328bc818e9-9ef1-440d-af1b-b37d65df6880
名前 / ファイル | ライセンス | アクション |
---|---|---|
KJ00000178910.pdf (298.8 kB)
|
BY-NC-ND
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Item type | 紀要論文(ELS) / Departmental Bulletin Paper(1) | |||||
---|---|---|---|---|---|---|
公開日 | 1989-03-10 | |||||
タイトル | ||||||
タイトル | 中心極限定理を巡って : Tスコアーの教育的有効性 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Centering around the Central Limit Theorem : The Educational Efficiency of T-Score | |||||
言語 | ||||||
言語 | jpn | |||||
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 | |||||
ページ属性 | ||||||
内容記述タイプ | Other | |||||
内容記述 | P(論文) | |||||
論文名よみ | ||||||
その他のタイトル | 〓 | |||||
著者名(日) |
林, 真護
× 林, 真護 |
|||||
著者名よみ |
ハヤシ, シンゴ
× ハヤシ, シンゴ |
|||||
著者名(英) |
HAYASHI, Shingo
× HAYASHI, Shingo |
|||||
著者所属(日) | ||||||
名古屋女子大学 | ||||||
著者所属(英) | ||||||
en | ||||||
NAGOYA WOMEN'S UNIVERSITY | ||||||
抄録(英) | ||||||
内容記述タイプ | Other | |||||
内容記述 | "The function f:x→e^<-x2>(-∞<x<∞) representing a symmetrical hanging graph about the straight line x=0 is ⎰^∞_<-∞e^<-x2>dx=√<π>. It deduces the continuous variable Z probability density function p(z)=e^<-x^2/2>/√<2π>(-∞<z<∞) according to N(0,1^2), the standard normal distribution. I deduce the variable X probability density function f(x)=e<-(x-m)^2/2σ^2/√<2π>σ(-∞<x<∞), (σ>o) according to N(m, σ^2), the normal distribution from the relation between the continuous variable Z probability density function and the discrete variable X probability density function pn(x)=_nC_xp^x(1-p)^<n-x> (x=0,l,2,…,n), (0≩p≩1) according to the binominal distribution. Using these functions, I analyze the Z-score : z=(x-x^^-)/s which is used as the standardized raw score in the fields of pedagogy and psychology nowadays and the T-score: t=50+10(x-x^^-)/s which is ofen used at lessons as the practical application on the basis of the central limit theorem lim__<n→∞>P(α≨√<n>(x^^--μ)/δ≨β)=⎰^β_ap(z)dz (μ:population mean, δ:population variance and x^^-:sample mean) consisting in the connection betwoon the population and the sample. I conclude by considering the mathematical significance and educational efficiency for the practical application." | |||||
雑誌書誌ID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN1008856X | |||||
書誌情報 |
名古屋女子大学紀要. 人文・社会編 en : Journal of Nagoya Women's University. Humanities・social science 巻 35, p. 11-16, 発行日 1989-03-10 |