(整理)實(shí)驗(yàn)七雙因素方差分析.

1、精品文檔實(shí)驗(yàn)七雙因素方差分析實(shí)驗(yàn)?zāi)康模赫莆諆梢蛩胤讲罘治龅幕纠碚?、統(tǒng)計(jì)意義與方法、掌握利用SAS進(jìn)行模型的建立與顯著性檢驗(yàn).實(shí)驗(yàn)要求：編寫程序，結(jié)果分析.實(shí)驗(yàn)內(nèi)容：1.寫出兩因素等重復(fù)實(shí)驗(yàn)下方差分析模型，檢驗(yàn)步驟；模型：Y一因素A和B,水平 A, A2,，Aa , BB2,，Bb ,組合水平（A，Bj）觀測(cè)值 yji, yj2,，yjcyijk 二t . ；ijk -. ： i . L . ij . ；ijk, i =1,2，a, j =1,2，b, k-1,2, ,c -2Sijk N(0,cr ), 且諸 卻相互獨(dú)立 abab、0,工匕=0, '、 ij =0, '、 i

2、j =0 i 1j 4i 4j 4SSt 二SSA SSb SSab SSe檢驗(yàn)步驟：(1)統(tǒng)計(jì)模型Y一因素A和B,水平A1,A2,，Aa,B”B2,，Bb,組合水平(Ai,Bj)觀測(cè)值yij 1, yij 2，yijcJiyjk=-ij +% =2+% +1+嘛,i =1,2，a, j =1,2，b, k = 1,2，c«qjk N(0,仃2), 且諸 時(shí)相互獨(dú)立ababE j = 0, g B j = 0, X - j = 0, Z 彳 j = 0、id：jdi 苴j4SS = SSa SSb SSab SSe(2)顯著檢驗(yàn)假設(shè)：Ha。：% =。2 ="" =

3、% =0修 H A1 ：至少有某個(gè)% #0H B0邛1 = £=Pb =01 H B1 :至少有某個(gè)Pj #0H Abo ： Zj =0, i =1,2,，a, j =1,2,，bi H abo :至少% ¥0.、，一MQ hao真MQ hb0真統(tǒng)計(jì)重FAa F(a -1, ab(c -1)Fbb F(b-1, ab(c-1)MSeMSeMS 2 HA° 真Fab =VSA1 F(a-1)(b-1), ab(c-1) MSe檢3P p值：如p <a ,拒絕相應(yīng)假設(shè)Pa =Pha°(Fa - fA) =P(F(a-1, ab(c-1) 一 £

4、;a)Pb =Pha°(Fb - fB) = P(F(b -1, ab(c-1) fB)Pab =Phab°(Fab -fAB)=P(F(a-1)(b-1)，ab(c-1) - fAB)(3)無(wú)交互效應(yīng)的各因素均值的估計(jì)與比較b ci1偏估計(jì)內(nèi)y/bcj 1 kW色.1 « 置信區(qū)間：(y .土t .ab(c1)，MSE/bc)一2林一九 置信區(qū)間：(yi«-yi2«±t -ab(c-1)j2MSE/bc), 1萬(wàn)m =a(a -1)/2個(gè) 代一匕2 的Bonferroni同時(shí)置信區(qū)間U1 靖一y2_a(ab(c -1)J2MSe /

5、bc)-2m(4)有交互效應(yīng)時(shí)因素各水平組合上的均值估計(jì)與比較(A,Bj)上均值均無(wú)偏估計(jì)：£ =yj. (i=1,2,|l,a, j=1,2川，b)匕的置信區(qū)間：(yj.+q .ab(c-1)jMSE /c), 一2由一匕上置信度不小于1 一口的Bonferroni同時(shí)置信區(qū)間(yi1j. yi2j. t ：.(ab(c -1) 2MSe/c)1 2m3.63.7 (選作)程序如下：(1)data examp3_6;input tielizi $ jldj $ jldjdz ;cards ;al bl 0.71al b1 1.66a1 b1 2.01a1 b1 2.16a1 b1

6、2.42a1 b1 2.42a1 b1 2.56a1 b1 2.60a1 b1 3.31a1 b1 3.64a1 b1 3.74a1 b1 3.74a1 b1 4.39a1 b1 4.50a1 b1 5.07a1 b1 5.26a1 b1 8.15a1 b1 8.24a1 b2 2.20a1 b2 2.93a1 b2 3.08a1 b2 3.49a1 b2 4.11a1 b2 4.95a1 b2 5.16a1 b2 5.54a1 b2 5.68a1 b2 6.25a1 b2 7.25a1 b2 7.90a1 b2 8.85a1 b2 11.96a1 b2 15.54a1 b2 15.89a1

7、b2 18.30a1 b2 18.59a1 b3 2.25a1 b3 3.93a1 b3 5.08al b3 5.82al b3 5.84al b3 6.89al b3 8.50al b3 8.56al b3 9.44al b3 10.52al b3 13.46al b3 13.57al b3 14.76al b3 16.41a1 b3 16.96a1 b3 17.56a1 b3 22.82a1 b3 29.13a2 b1 2.20a2 b1 2.69a2 b1 3.54a2 b1 3.75a2 b1 3.83a2 b1 4.08a2 b1 4.27a2 b1 4.53a2 b1 5.32a2

8、 b1 6.18a2 b1 6.22a2 b1 6.33a2 b1 6.97a2 b1 6.97a2 b1 7.52a2 b1 8.36a2 b1 11.65a2 b1 12.45a2 b2 4.04a2 b2 4.16a2 b2 4.42a2 b2 4.93a2 b2 5.49a2 b2 5.77a2 b2 5.86a2 b2 6.28a2 b2 6.97a2 b2 7.06a2 b2 7.78a2 b2 9.23a2 b2 9.34a2 b2 9.91a2 b2 13.46a2 b2 18.40a2 b2 23.89a2 b2 26.39a2 b3 2.71a2 b3 5.43a2 b3

9、6.38a2 b3 6.38a2 b3 8.32a2 b3 9.04a2 b3 9.56a2 b3 10.01a2 b3 10.08a2 b3 10.62a2 b3 13.80a2 b3 15.99a2 b3 17.90a2 b3 18.25a2 b3 19.32a2 b3 19.87a2 b3 21.60a2 b3 22.25；run ;procanova data =examp3_6;classtielizi jldj;modeljldjdz=tielizi jldj tielizi*jldj ;meanstielizi jldj;run ;精品文檔樣本均值與標(biāo)準(zhǔn)值如下:me 者掰 sys

10、temThe ANOVA ProcedureLevel of t ielIzlal噓N5454j1dj dzMean7.884258268.40277770Std Dev6.143609546.03399690Levs 1 ofj i oj azJldjNMeanStd ttevbl364.817777B2,66785212b2368.91805566.05675435b33612.19472226.49327982The SAS SystemThe 直機(jī)ProcedureClass Levs I Informat ionClassLeveIsValuestielizi24 a2j Idj3b

11、l b2 b3Number of observations 108則 c=18n=abc=108 a=2,b=3注：SSr =SSa +SSb +SSab ,因素變量為自變量，個(gè)數(shù)為自由度p-1=ab-1=5f=i-、卜(心-1,岫9-1=先檢驗(yàn) H 0 ： ij =0,統(tǒng)計(jì)量F(5,102),_ '拎建=7 31J - 7$P = f H5r102 )> / )觀測(cè)值 山”，檢驗(yàn)p值電"ofSourceDFSquaresMeanSquareF VluePr > FMode 151054.1G7G52210.3335307.32<.0001Error1022

12、838.20881128,815918Carrected Total1078892.8712B3R-SquareCceffVarRootM8EjIdjdz Mean0.26404562,094095,3671146,643519SourceDFAnova SSMeanSquareF ValuePr > Ft is 1 2162.259259362.25325932.160.1446Jldj2963.817578649 L000788817.07<.0001t i 811 z i 1 dj28.29081304,14540650J40.8661The SAS System11:37

13、FirThe ANOVA Procedurejz由結(jié)果可知，產(chǎn)泅=0 8661 > °-05 ,接受h Abo ,認(rèn)為鐵離子與劑量等級(jí)的交互不顯著，即 兩種形式的鐵離子在不同劑量下在動(dòng)物體內(nèi)的存留量認(rèn)為相同.而檢驗(yàn)HA0和HB0,檢驗(yàn)p值分另I為pA=0.1446和Pb =0.001 ,接受Hao,拒絕Hbo.說(shuō)明因素A寸劑量等級(jí)的值 的影響不顯著。由輸出結(jié)果可看出，高劑量水平的標(biāo)準(zhǔn)差與其他兩個(gè)的標(biāo)準(zhǔn)差是有顯著性差 異的，中劑量和低劑量水平的標(biāo)準(zhǔn)差無(wú)明顯差異，所以可以認(rèn)為各組和水平上的標(biāo)準(zhǔn)差有顯著相差異，而認(rèn)為誤差的等方差性不合理。(2)程序如下：data change3_6;

14、set examp3_6;aaa = log (jldjdz);run ;proc anova data = change3_6;class jldj;model aaa = jldj;means jldj;run ;20:44 ThursdiThe SAS SystemThe ANOVA ProcedurediI 12 3 J b b baaaMeanStd Dev1.420526281.995634722.341685040.583637570.616140060.60676504由以上輸出結(jié)果可以看出，各組合水平上的標(biāo)準(zhǔn)差趨于一致(3)程序如下：proc anova data = cha

15、nge3_6;class tielizi jldj;model aaa = tielizi jldj tielizi*jldj;means tielizi jldj tielizi*jldj;means tielizi jldj/bon cldiff alpha =0.05 ;run ;flnova SSMean SquareF ValuePrF2.0738394 I2.07383941S, 990.01EI15-588407977>79420398£2.52J MOI0.810269470.405134731.1?0.3143SourceDFSun of SquaresMea

16、n SquareF ValuePr > FMode)S18.472516843.6945033710.68< .«00tError10235.2958G0180.34603784Corrected Total10?53.76837702R-SquareCoeff UarRoot MSEaaa Mean0.34355730 M4 9470.5802501.9192Q2存留量的方差分析表、.、.廣. 力左來(lái)源自由度離子12.07382.07385.990.0161劑量215.58847.794222.520.0001交互 效應(yīng)20.81030.40511.170.314310

17、235.29590.3460總和10753.7648由此結(jié)果可看出離子與劑量之間的交互效應(yīng)是不顯著的，也就是說(shuō)離子的不同對(duì)劑量差異無(wú)影響；同樣，劑量之間的差異與鐵離子的差異無(wú)關(guān)。兩種離子在小白鼠體內(nèi)存留量百分比是有顯著差異的，不同劑量在小白鼠體內(nèi)存留量百分比也是有顯著差異的。(4)程序如下：means tielizi jldj/bon cldiff alpha=0.05;run;The SHS System14:54 ThursdayThe ANOVA ProcedureLeve 1of 一- Witie】i z iNMeanStd Deval541.780709950.77926M3日254

18、2.057054080.60672273Levs i TL口口口JldJNMeanStd Devbl361.420526280.58363757b?361.995634720.61614006b3362.341605040.60076504TheANOVA ProcedureBonferron i(Dunn) t Tests foraaa>ntrols the Type I exper imentw ise error rate, but i t generally has i error rate than Tukey's for al 1 pairwise compar i

19、sons -AlphaQ.0SError Degrees of Freedom102Error (lean Square0.346038Cr i t ical Value oft1.98350M in imun Signif icant D jfference0,2245Compar isons signi f icant at the 0,05 1 eve 1 are ind icated by *.t i e 1 i z i Comparison-al al - a2D i fferenceBetween Means0.2771-0.2771Simultaneous95M Conf ide

20、nceLimits0,0526 0.5017 *-0.5017 -0.0526 *%. =20578 7=0一055對(duì)于專業(yè)因素A,由上述結(jié)果求得其，,=1-7807,個(gè)差匕Z，故m=1,皿7)= &41吟=°O5 ,憶匕,的置信度).因此認(rèn)為 .父也.，即三價(jià)鐵離子對(duì)小白鼠為95%勺置信區(qū)間為(-0.5017 -0.0526的影響顯著差于二價(jià)鐵離子的影響。Bonferron i (Dunn) t Tests for aaa：the Type I exper imen ise error rate, but i t genera 1 Iy has error rate than Tulkey 1 s