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BIOSTATISTICS Statistical tests part I: t tests. 1.t test for 1 sample 2.t test for 2 independent samples 3.t test for 2 paired samples Applicability.

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Presentation on theme: "BIOSTATISTICS Statistical tests part I: t tests. 1.t test for 1 sample 2.t test for 2 independent samples 3.t test for 2 paired samples Applicability."— Presentation transcript:

1 BIOSTATISTICS Statistical tests part I: t tests

2 1.t test for 1 sample 2.t test for 2 independent samples 3.t test for 2 paired samples Applicability Definition Example Copyright ©2012, Joanna Szyda INTRODUCTION

3 SAMPLE STRUCTUREHYPOTHESES TEST Copyright ©2011, Joanna Szyda INTRODUCTION

4 T TEST - applicability 1.Comparison of means 2.Quantitative data 3.Normal distribution 4.Similar variances 5.Test variants: Single sampleH 0 :  A = Y Two independent samplesH 0 :  A =  B Two paired samplesH 0 :  A =  B Copyright ©2012, Joanna Szyda

5 T TEST – single sample DATA SET 1.Osteoporosis 2.Medical Research Council, Cambridge 3.Bone density [g/cm 2 ] 40 healthy adults BMDSEX 0.971 0.731 0.871 0.941 1.021 0.761 0.781 1.011 0.821 0.761 0.871 0.721 … 0.912 1.022 0.872

6 1.Formulate hypotheses H 0 and H 1 H 0 : average bone density is 1.0 g/cm 2 H 1 : average bone density is different from 1.0 g/cm 2 H 0 :  = 1.0 H 1 :  ≠ 1.0 2.Set the significance level  MAX = 0.05 3.Choose the statistical test and calculate test value Excel: example Copyright ©2014, Joanna Szyda T TEST – single sample

7 4.Determine distribution of the test Excel: example 5.Determine  t 6.Decision  t <  max H 0 H 1 average bone density is different from 1.0 g/cm 2 Copyright ©2012, Joanna Szyda T TEST – single sample

8 Copyright ©2012, Joanna Szyda T TEST - applicability 1.Comparison of means 2.Quantitative data 3.Normal distribution 4.Similar variances 5.Test variants: Single sampleH 0 :  A = Y Two independent samplesH 0 :  A =  B Two paired samplesH 0 :  A =  B

9 T TEST – two independent samples 1.Osteoporosis 2.Medical Research Council, Cambridge 3.Bone density [g/cm 2 ] 40 healthy adults 4.Values available for males and females DATA SET BMDSEX 0.971 0.731 0.871 0.941 1.021 0.761 0.781 1.011 0.821 0.761 0.871 0.721 … 0.912 1.022 0.872 Copyright ©2012, Joanna Szyda

10 1.Formulate hypotheses H 0 and H 1 H 0 : average bone density in males is the same as in females H 1 : average bone density in males is different than in females H 0 :  F =  M H 1 :  F ≠  M 2.Set the significance level  MAX = 0.05 3.Choose the statistical test and calculate test value Copyright ©2014, Joanna Szyda T TEST – two independent samples

11 3.Choose the statistical test and calculate test value Copyright ©2014, Joanna Szyda T TEST – two independent samples Excel: example

12 4.Determine distribution of the test 5.Determine  t 6.Decision  t <  max H 0 H 1 average bone density in males is different than in females Copyright ©2014, Joanna Szyda T TEST – two independent samples Excel: example

13 T TEST - applicability 1.Comparison of means 2.Quantitative data 3.Normal distribution 4.Similar variances 5.Test variants: Single sampleH 0 :  A = Y Two independent samplesH 0 :  A =  B Two paired samplesH 0 :  A =  B

14 T TEST – Two paired samples 1.Eyeball pressure 2.2 eyeballs of the same person 3.Based on cornea thickness: low CCT and high CCT DATA SET Low CCTHigh CCT 20.014.3 13.913.8 18.315.8 21.133.4 20.120.3 24.419.9 20.214.3 11.611.4 28.825.1 18.524.1 Copyright ©2012, Joanna Szyda

15 1.Formulate hypotheses H 0 and H 1 H 0 : eyeball pressure does not depend on cornea thickness H 1 : eyeball pressure depends on cornea thickness H 0 :  L =  H H 1 :  L ≠  H 2.Set the significance level  MAX = 0.05 3.Choose the statistical test and calculate test value Excel: example Copyright ©2012, Joanna Szyda T TEST – Two paired samples

16 3.Choose the statistical test and calculate test value Copyright ©2012 Joanna Szyda T TEST – Two paired samples

17 4.Determine distribution of the test 5.Determine  t 6.Decision  t >  max H 0 H 1 eyeball pressure does not depend on cornea thickness Excel: example Copyright ©2012, Joanna Szyda T TEST – Two paired samples

18 Copyright ©2012 Joanna Szyda T TEST 0.761 0.871 0.721 … 0.912 1.022 0.872

19 Copyright ©2012, Joanna Szyda Heiteger et al. (2004) Brain 127: 575-590 Analysed trait: speed of arm movement Data are normally distributed 2 groups: - 30 persons with head microinjury - 30 healthy persons persons in each group matched by age, years of education and sex QUIZ – WHICH T TEST TO USE ?

20 Copyright ©2010, Joanna Szyda QUIZ – WHICH T TEST TO USE ?

21 Copyright ©2012, Joanna Szyda 1.Single sample 2.Independent samples 3.Paired samples QUIZ – WHICH T TEST TO USE ?

22 Copyright ©2012, Joanna Szyda Mosimann et al. (2004) Brain 127: 431-438 Analysed time of clock reading by persons with Alzheimer disease After a person determined time on a clock, which was presented on a computer screen, he/she has to push a button For healthy persons average clock reading time is 2.31 sec. Data are normally distributed Sample: 24 persons with Alzheimer disease QUIZ – WHICH T TEST TO USE ?

23 Copyright ©2010, Joanna Szyda QUIZ – WHICH T TEST TO USE ?

24 Copyright ©2012, Joanna Szyda 1.Single sample 2.Independent samples 3.Paired samples QUIZ – WHICH T TEST TO USE ?

25 Copyright ©2012, Joanna Szyda Day (2007) Environmental Entomology 36: 1154-1158 Analysed parasitism rate by 2 species of Lygus Considered different developmental stages QUIZ – WHICH T TEST TO USE ?

26 Copyright ©2010, Joanna Szyda QUIZ – WHICH T TEST TO USE ?

27 Copyright ©2012, Joanna Szyda QUIZ – WHICH T TEST TO USE ? 1.Single sample 2.Independent samples 3.Paired samples

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