- 作者: 葉樹藩
- 作者服務機構: 國立臺灣大學農學院
- 中文摘要: 本研究應用泰勒氏級數導出穩定變方時變值變換之基本式,並在變方與變值有直線關係下,獲得卜瓦松分布變值變換式為,,/x+c,其穩定變方近似V(V x平必)c-/i14(a+c)。當變換值之機率仍為卜瓦松機率時,其變方為V(州夾平下)。=z p(二)(x十c) 一佻卜)jx+中。作者令c等於0,0.5及3/8,製成u自0.5至15.0之各種變方表,發現c一0,變方之穩定性最差,c一0.5者其次,c二3/8者最佳,但因V(州面荊巧)〈V(;'x+3/8),故卜氏資料宜用ji變換。同時由多種實際責料變換分析證明:變換值之理論變方不能代替變換值機差均方作試項效應差異顯著性測驗,僅可作機差分析研究之基準。 成數資料,成數在0 .1至0.9之間,用逆正弦變換分析效果晨佳,獲得責訊最多,成數在0.1以F& 0.9以上,遇信0及1時,最好用巴氏經驗矯正變換。 試項平均與均方有二次曲線關係之趨勢時“變值用對數變換分析,容易顯示試項效應,可提高試驗之精密度。 同一個試驗資料可能適用許多種變換分析,決定最佳變換之法,最好用巴氏州側驗各種變換之試項均方純度,凡′、“不顯著而最小者為最佳之變換怯“為簡化計,亦可用各種變換值試項之最大變域與最小變域之比決定之,凡此1,69最小者,即為可用之變換法。 本研究所用實際試驗資料分析結果,請閱本報告主文。
- 英文摘要: The basic formula of transformation of a random variable x is dedu-ced by using Taylor's polynomials of f (x) at x一E(x),and the trans-formed variates are approximately normally distributed with stablizedvariance·Under the condition of the linear relationship between variates,and their variances,the transformed formulaJx+c in which the x's arePoisson series is obtained.The stablized variance of -}- -X-+C■is appoxi-mately equal to V(,/蒲平必)。二〞∕‘(〞+c),and the true variance of t/ x+Cis equal to V(‘′X+C )·兀日。Pc·)(X+C)一想P(·):∕X+C ) 2·Both the stablizedvariances and the-true-variances of,′X,一L一xxrt-0:5 and、′x+3,8 with thetrue means ranged from 0.5 to 15.0 of x's are calculated and presented inthis paper.It is found that the variation of V(、′‘x+0.5- )Is is larger thanthat of V(、/x+3.8)Is,and the variation of V(、)()fs is the largest. Be-cause of that V(、、不而J)<V(′′x+3%8),the.x-~0.5 transformation issuggested for xfs of Poisson series.By the results of analyzing experimen-tal data,it is proved that the stablized (or true) variance can not besubstituted the error mean square for testing the null hypothesis of treat-ment effects,and can be only used to discriminate the sources of errors· In making use of the arcsine transformation to the data of binomialevents expressed in fractions or percentages,the most of information willbe acquired provided the fractions among the range of 0.1<p<0.9.Ifmost fractions are below 0.1 and including 0,or most fractions are above0.9 and including 1 from experiments,the empirical transformation ofBartlett's adjustment should be used· The logarithmic transformation will be appropriate for the data ifthere exists a quadratic relationship between the means and mean squaresof treatments·This transformation is always to increase the precision,and treatment effects will be easily distinguished· There are many transformations which can be applied to the samedata.To determine the best one,the x2 test of the homogeneity of va-riances of treatments in transformed variates should be carried out。If the‘忽is nonsignificant and is the smallest among the others,the transforma-tion is proved to be good for statistical analysis·For simplification,theadmissible transformation also may be determined by the ratio of the lar-gest to the smallest range of transformed variates of treatments。Thetransformation producing the smallest ratio can be selected as the appro-priate one· As to the practical results of the experimental data used in the study,the readers are requested to refer to the text of this report·
- 中文關鍵字: --
- 英文關鍵字: --