Statistical hypothesis testing. Testing one of the methods of statistical induction we verify validation of the hypothesis Testing methods: Parametric:

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Presentation transcript:

Statistical hypothesis testing

Testing one of the methods of statistical induction we verify validation of the hypothesis Testing methods: Parametric: require knowledge or estimation of population parameters (average, variance) Nonparametric: do not requiere knowledge, are based on ordering the values

General procedure of testing 1) formulation of Null hypothesis 2) choice of suitable test 3) test criterion computing 4) finding of table value 5) comparing of test criterion and table value 6) conclusion

Test conclusion H 0 : is not significant difference between values H 1 : is significant difference between values comparing of test criterion and table value  if test criterion>table value→H 0 is rejected and H 1 is valid

One-sample test for the average test criterion computing for data set with less than 30 units table value one-sidedtwo-sided

One-sample test for the average test criterion computing for data set with more than 30 units table value one-sidedtwo-sided

Scheme of two-sample test for the average 1.Step F – test (testing if σ 2 1=σ2 2 ) If H0 is not rejected (σ 2 1 =σ 2 2 ) 2. Step two-sample t- test If H0 is rejected (σ 2 1 >σ 2 2 ) 2. Step Welch test

Two-sample test for the average 1. step F – test of the variance test criterion σ 2 1 est >σ 2 2 est table value (one-sided α, two-sided α/2) H 0 is rejected >

Two-sample test for the average 2. step – see results of F – test o if H 0 is not rejected and is good (σ 2 1 =σ 2 2 ), is used Two-sample t-test Is used one variance for both samples H 0 is rejected >

Two-sample test for the average 2. step – see results of F – test o if H 0 is rejected and H 1 is good (σ 2 1 >σ 2 2 ), is used Welch test H 0 is rejected >

Paired t-test 2 measures, the same sample is analysed significance of difference between averages of two measures test criterion H 0 is rejected

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