环境数据分析课件 (18).pdf

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1、Chapter 6 T testsWe are different or not?Significance level is the boss!4 Single sample t-test Dependent(Paired)samples t-testCONTENTS Independent samples t-test T-testSingle-sample t-testWith a small sample size,given hypothesis (normally theoretical,standard or empirical value),we compare them to

2、the t distribution.Fig.The difference of a mean of single sample and given value().xH:0meanSingle-sample t-testSingle-sample t-test statistic:mean of sampleStandard deviation of samplen:number of sample i=1,2,3,nwhere1-nsstxxxxnxnii1x1s21xnxxniiSingle-sample t-testpdft),(tpdft),(t2/Accepte H0Single-

3、sample t-testExample1-1 The value of COD discharged from wastewater treatment plant is 56.22 mg/L.The wastewater of effluent is measured by George as 55.29,57.33,54.95,56.81,58.95,56.62,55.84,59.94,56.10,60.42 mg/L(=0.05)Can we trust George?Only if his results are similarto 56.22 mg/L.Lets see!Singl

4、e-sample t-testExample22.56:,22.56:10HH66.1,61.0992.19110,10,22.56,92.1,23.5700 xxsxtsdfnsx05.013.)2,9,66.1()66.1(:226.2)9,05.0()9(66.1:1025.0TDISTtpTINVttGeorge Win!two-sided testSingle-sample t-testTips:,66.1,61.01092.1,16.310,92.1,23.570 xxsxtssxExcel equation:f(x)=average(x1,x2,x3.)f(x)=STDEV(x1,x2,x3.)f(x)=100.5f(x)=1.92/(100.5)f(x)=(57.23-56.22)/0.607Single-sample t-testQuestion?We can get if the sample data set similar or not to given,but how we know they are larger or smaller than?