概率论升级版Word文件下载.docx
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概率论升级版Word文件下载.docx
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Mu0=0
Test-Statistic------pValue------
SignM5.5Pr>
=|M|0.0010
SignedRankS33Pr>
=|S|0.0010
Quantiles(Definition5)
QuantileEstimate(分位数)
100%Max8
99%8
95%8
90%7
75%Q36
50%Median3
25%Q12
10%2
5%1
1%1
0%Min1
ExtremeObservations
----Lowest--------Highest---
ValueObsValueObs
1147
2358
2269
36710
35811
(二)需要输入频数的SAS程序(见课本138页)
inputxf@@;
5.547.5119.51711.523
13.51815.51417.51019.53
varx;
freqf;
(vardef=n是求样本的方差及标准差,如果去掉这个程序段,求出来的是修正后的标准差及修正方差,varx表示计算的是x的数字特征,freqf表示f为频数)
Variable:
Freq:
f
N100SumWeights100
Mean12.24SumObservations1224
StdDeviation3.43691722Variance11.8124
Skewness0.09092138Kurtosis-0.6788022
UncorrectedSS16163CorrectedSS1181.24
CoeffVariation28.0793891StdErrorMean.
BasicStatisticalMeasures
LocationVariability
Mean12.24000StdDeviation3.43692
Median11.50000Variance11.81240
Mode11.50000Range14.00000
InterquartileRange6.00000
SignM50Pr>
=|M|<
.0001
SignedRankS2525Pr>
=|S|<
QuantileEstimate
100%Max19.5
99%19.5
95%17.5
90%17.5
75%Q315.5
50%Median11.5
25%Q19.5
10%7.5
5%7.5
1%5.5
0%Min5.5
---------Lowest----------------Highest--------
ValueFreqObsValueFreqObs
5.54111.5234
7.511213.5185
9.517315.5146
11.523417.5107
13.518519.538
2:
求置信区间
(1)求一个正态总体均值的置信区间
SAS程序为
6.64.65.45.85.5
procmeansmeanstdclm;
procmeansmeanstdclmalpha=0.1;
运算结果AnalysisVariable:
Lower90%Upper90%
Mean(均值)StdDev(观测值的标准差)CLforMeanCLforMean
5.58000000.72249574.89117926.2688208
即在置信度为0.1的条件下此正太总体的均值的90%的置信区间为(4.8911792,6.2688208)
(2)求两个正态总体均值差的置信区间(此程序还可以用来方差分析)
SAS程序为:
doa=1to2;
inputn@@;
doi=1ton;
output;
end;
62.12.352.392.412.442.56
42.032.282.582.71
procanova;
classa;
modelx=a;
meansa/lsdcldiff;
run;
运算结果:
ClassLevelInformation
ClassLevelsValues
a212
DependentVariable:
SumofSourceDFSquaresMeanSquareFValuePr>
FModel10.001500000.001500000.030.8661Error80.395950000.04949375CorrectedTotal90.39745000
R-SquareCoeffVarRootMSExMean0.0037749.3279630.2224722.385000
SourceDFAnovaSSMeanSquareFValuePr>
Fa10.001500000.001500000.030.8661
tTests(LSD)forxNOTE:
ThistestcontrolstheTypeIcomparisonwiseerrorrate,nottheexperimentwiseerrorrate.
Alpha0.05
ErrorDegreesofFreedom8
ErrorMeanSquare0.049494
CriticalValueoft2.30600
Comparisonssignificantatthe0.05levelareindicatedby***.
DifferenceaBetween95%ConfidenceComparisonMeans(样本均值差)Limits(两个样本均值差的95%置信区间)
2-1(x2-x1)0.02500-0.306150.35615
1-2(x1-x2)-0.02500-0.356150.30615
3:
应用SAS作总体分布参数的假设检验
(1)一个正态总体均值作假设检验的SAS程序(课本186页)
dataex;
y=x-14;
cards;
10.41213.213.714.615.115.515.9
;
procmeansmeanstdtprt;
vary;
程序运行的结果为:
MeanStdDev(观测值的标准差)tValuePr>
|t|
-0.20000001.8822479-0.300.7725
T的观测值为-0.30,而根据查表可知当自由度为8,t值为1.860,也就是落在了拒绝域,因此拒绝原假设,接受对立假设。
(2)两个正态总体均值作假设检验的SAS程序(课本179页,例题1.5,公式六,F分布)
dataxzh;
doi=1to8;
8.68.75.69.38.49.37.57.9
87.95.89.17.78.27.46.6
;
procttest;
LowerCLUpperCLLowerCLUpperCLVariableaNMeanMean(均值)MeanStdDevStdDevStdDevStdErrx187.15348.16259.17160.79811.2072.45670.4268x286.74267.58758.43240.66821.01062.05680.3573xDiff(1-2)-0.6190.5751.76870.8151.11321.75560.5566
T-Tests
VariableMethodVariances(方差)DFtValuePr>
|t|(只要大于显著水平0.05便可)
xPooledEqual(方差相等时)141.030.3191
xSatterthwaiteUnequal(方差不相等时)13.61.030.3196
EqualityofVariances
VariableMethodNumDFDenDFFValuePr>
F(只要大于置信度,即0.05便接受原假设)
xFoldedF771.430.6509
首先进行F检验,检验其方差是否相等,因为T检验中提供了两种均值的检测方法,一种是方差相等一种是方差不等,然后再通过T检验看均值是否相等。
在此题中F的观测值是1.43,而在95%的置信度中F的值为3.79,即落在接受域中,接受方差相等,再看T检验,T值为1.03,而查表知T的0.05置信度的值为1.761,因此接受原假设,认为均值相等。
4.应用SAS作正态性检验(详见课本193页)
10.41213.113.813.814.615.115.515.9
procunivariatenormal;
4.独立性检验的SAS程序
doa=1to3;
dob=1to3;
inputf@@;
323858454428141823
procfreq;
weightf;
tablesa*b/chisp;
运行结果:
ab
Frequency‚
Percent‚
RowPct‚
ColPct‚1‚2‚3‚Total
1‚32‚38‚58‚128
‚10.67‚12.67‚19.33‚42.67
‚25.00‚29.69‚45.31‚
‚35.16‚38.00‚53.21‚
2‚45‚44‚28‚117
‚15.00‚14.67‚9.33‚39.00
‚38.46‚37.61‚23.93‚
‚49.45‚44.00‚25.69‚
3‚14‚18‚23‚55
‚4.67‚6.00‚7.67‚18.33
‚25.45‚32.73‚41.82‚
‚15.38‚18.00‚21.10‚
Total91100109300
30.3333.3336.33100.00
StatisticsforTableofabyb
StatisticDFValueProb
Chi-Square(卡方检验值)413.58620.0087(概率小于显著水平0.05因此拒绝原假设)LikelihoodRatioChi-Square413.93660.0075
Mantel-HaenszelChi-Square11.44880.2287
PhiCoefficient0.2128
ContingencyCoefficient0.2081
Cramer'
sV0.1505
SampleSize=300
5:
应用SAS作单因素试验方差分析
(1)不等重复的情形:
(课本200页例题1.1)
Output;
8
2129242225302726
10
20252523293124262021
6
242228252126
(如果要作多重比较并求均值差的置信区间,则增加
)
a3123
Numberofobservations24
TheANOVAProcedure
Sumof
SourceDF(自由度)Squares(平方和)MeanSquare(均方和)FValuePr>
F
Model(因素A)26.76666673.38333330.320.7314
Error(误差)21223.733333310.6539683
CorrectedTotal(总和)23230.5000000
R-SquareCoeffVarRootMSExMean
0.02935613.188053.26404224.75000
a26.766666673.383333330.320.7314
tTests(LSD)forx
NOTE:
ErrorDegreesofFreedom21
ErrorMeanSquare10.65397
CriticalValueoft2.07961
Comparisonssignificantatthe0.05levelareindicatedby***.
Difference
aBetween95%Confidence
ComparisonMeansLimits
1-21.100-2.1204.320
1-31.167-2.4994.833
2-1-1.100-4.3202.120
2-30.067-3.4393.572
3-1-1.167-4.8332.499
3-2-0.067-3.5723.439
(2)等重复的情形:
(课本201页,例题1.2)
doa=1to4;
doi=1to4;
1923211321242720
2018191522252722
a41234
Numberofobservations16
SourceDF(自由度)Squares(平方和)MeanSquareFValuePr>
Model(因素A)3104.000000034.66666673.530.0487
Error(误差)12118.00000009.8333333
CorrectedTotal(总和)15222.0000000
0.46846814.932453.13581521.00000
a3104.000000034.66666673.530.0487
TheANOVAProcedure
ErrorDegreesofFreedom12
ErrorMeanSquare9.833333
CriticalValueoft2.17881
LeastSignificantDifference4.8312
4-21.000-3.8315.831
4-15.0000.1699.831***
4-36.0001.16910.831***
2-4-1.000-5.8313.831
2-14.000-0.8318.831
2-35.0000.1699.831***
1-4-5.000-9.831-0.169***
1-2-4.000-8.8310.831
1-31.000-3.8315.831
3-4-6.000-10.831-1.169***
3-2-5.000-9.831-0.169***
3-1-1.000-5.8313.831
此处的Pr>
F值小于显著性水平0.05,所以落在拒绝域,因此拒绝原假设,接受对立假设,认为苗高之间有显著差异。
6.双因素试验方差分析(不考虑交互作用)(课本212页例题2.1)
dataanova01;
dob=1to5;
output;
end;
53564552494750474753
57635457584552424148
classab;
modelx=ab;
meansab/lsdduncancldiff;
b512345
Numberofobservations20
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