粗大误差判别

粗大误差判别：假设以下数据不含有系统误差，试用3d、肖维勒、t检验、格拉布斯、狄克松准则来判别该数据中是否含有粗大误差。Q=0.01)序号数值序号186698775510数值序号93115412461314数值序号186698775510数值序号931154124613143915序号xVV2v'V‘2118-39.531562.62-43.51892.252668.4771.744.520.2539840.471637.8236.51332.2547719.47379.0815.5240.25555-2.536.40-6.542.2569335.471258.1231.5992.25754-3.5312.46-7.556.25846-11.53132.94-15.5240.2592-55.533083.58-59.5—1039-18.53343.36-22.5506.2511679.4789.685.530.251256-1.532.34-5.530.25137517.47305.2013.5182.25149133.471120.2429.5870.251526-31.47990.36-35.51260.25计算结果x=57.53X'二61.5工V2=10995.94工v'2=7695.5数值6756912675解：1)d二解：1)d二28.033d二3x28.03二84.09Q|v|<3d,i二1,2,L,15i•••根据3d准则，该数据不含粗大误差。2)工V2i-i=12)工V2i-i=1——n一1.'10995.941T~=28.03，k二2.13xqxk二28.03x2.13二59.7xQV|<Qxk,qxk二28.03x2.13二59.7xQV|<Qxk,i二1,2,L,15i x・•・根据肖维勒准则，该数据不含粗大误差。(3)根据t检验，认为x可疑，剔除x，计算亍,L得99q=24.33，K(15,0.01)二3.12LxK(15,0.05)=24.33x3.12二75.9Q|x-〒|<q'xK(15,0.01),i二1,2,L,15・•・根据t检验准则，该数据不含粗大误差。(4)将x,x,…,x按从小到大的顺序排列为:1 2 15x(1)=2,x(2)=18,x(3)=26…'x(13)=91,x(14)=93,x(15)=98x-xg二(15)q98-57.5328.03二1.44(1)x-x (1)二q57.53-228.03二1.98g(15,0.01)二2.700g<g(15,0.01),g()<g(15,0.01)TOC\o"1-5"\h\z(1) 0 (15) 0・•・根据格拉布斯准则，该数据不含粗大误差。(5)将x,x,…,x按从小到大的顺序排列为：1 2 15x=2,x=18,x=26,…,x =91,x=93,x=98(1) (2) (3) (13) (14) (15)•n=15，d (15)=0.6160.01x-x98-91 x-x 26-20.27d=+g= - =0.1,・•・d=7 4= ——0.270(15) x-x98-26 0(1) x-x91-2(15) (3) (13) (1)•d<d(15),d <d (15)0(1) 0.01 0(15) 0.01.根据狄克松准则，该数据不含粗大误差。

试验设计与数据处理用表

肖维勒准则常用的k值

xn567891011k=6/gx1.651.731.791.801.921.962.00n12131415161718k=6/gx2.042.072.12.132.162.182.20n19202122232425k=6/gx2.222.242.262.282.32.312.33n26272829303540k=6/gx2.342.352.372.382.392.452.50n5060708090100150k=6/gx2.582.642.692.732.782.812.92n185200250500100020005000k=6/gx3.003.023.113.293.483.663.89

t检验系数K(n)表n显著性水平n显著性水平K (n)0.05K (n)0.01K (n)0.05K (n)0.0144.9711.46182.183.0153.566.53192.173.0063.045.04202.162.9572.784.36212.152.9382.623.96222.142.9192.513.71232.132.90102.433.54242.122.88112.373.41252.112.86122.333.31262.102.85132.293.23272.102.84142.263.17282.092.83152.243.12292.092.82162.223.08302.082.81172.203.04

格拉布斯检验系数表g(n,a)0nana0.050.010.05 0.01go(n，a)g(n,a)031.151.16172.482.7841.461.49182.502.8251.671.75192.532.8561.821.94202.562.8871.942.10212.582.9182.032.22222.602.9492.112.32232.622.96102.182.41242.642.99112.232.48252.663.01122.282.55302.743.10132.332.61352.813.18142.372.66402.873.24152.412.70502.963.34162.442.751003.173.59

Dixon检验系数及d的计算公式0nd(n)ad的计算公式0显著性水平ax可疑⑴x(n)可疑0.010.0530.9880.94140.8890.765x一x(2)(1)x-(n)x(n)-x——(n-1)一x(1)50.7800.642x-x(n) (1)60.6980.56070.6370.50780.6830.554x一x(2)(1)x--x90.6350.512V山丿 '丄丿x一x(n-1) (1)x(n)w丄丿一x(2)100.5970.477110.6790.576x一x(3) (1)x-—(n—x(n)-x——(n-2)一x(2)120.6420.546x一x(n-1) (1)130.6150.521140.6410.546150.6160.525160.5950.507170.5770