环境数据分析课件 (17).pdf

Chapter 6 T testsWe are different or not?Significance level is the boss!t-testF-testANOVA4 Single sample t-test Dependent(Paired)samples t-testCONTENTS Independent samples t-test T-testNeeded to be answered What is the standard error of the difference between means?When we do F-test before t-test?4 Single sample t-test Dependent(Paired)samples t-testCONTENTS Independent samples t-test T-testt-test W W.S.Gosset.S.Gosset pseudonym pseudonym asas “Student.Student.”t-testn30 t-testz-testl Single samplel Independent samplesl Dependent samplesFF1F2F1F1F2F2Dependent samples t-testT-testdf(degrees of freedom)Refers to the maximum number of logically independent values,which are values that have the freedom to vary,in the data sample.e.g.6,7,3,10 and 4 Mon.to Sat.ONLY ONE choice in Sat.average mean=6the fifth number must be 10normally df=N-1 6,7,3,and 4 T-testT distributionWhen the population variance is unknown(the usual case)and sample size is small(n 30),we use z-test.Fig.The t distribution is a short,fat relative of the normal.The shape of t depends on its df.As N becomes infinitely large,t becomes normal.T-testt distribution,null hpothesis .Normal or t distributionK-S test,histogram,p-p plot,Q-Q plot or skewness,kurtosisLarge sample normal distribution,1,0ndf