Statistik. Statistik. Hvad er Statistik? Hvad er Statistik? Hvad er Statistik? 1. Hvad er statistik? 2. Mennesker som måleinstrumenter

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1 Statistik Statistik 1. statistik? Per Bruun Brockhoff Professor i Statistik DTU Informatik 27 august Mennesker som måleinstrumenter Egentlig ikke så meget: Danmarks Statistik: Præsident Zuma og statistik: ISI meeting 17/ Danske skolekarakterer: Men mere selve ANALYSEN og FORTOLKNINGEN: Statistik: Et af de 11 mest vigtige bidrag til medicin i 1000 år!!! Statistikere uundværlige for Google: New York Times 5/ Egentlig ikke så meget: Danmarks Statistik: Præsident Zuma og statistik: ISI meeting 17/ Danske skolekarakterer: Men mere selve ANALYSEN og FORTOLKNINGEN: Statistik: Et af de 11 mest vigtige bidrag til medicin i 1000 år!!! Statistikere uundværlige for Google: New York Times 5/ De 11 vigtigste bidrag til den medicinske forskning det seneste årtusind Elucidation of Human Anatomy and Physiology Discovery of Cells and Their Substructures Elucidation of the Chemistry of Life Application of Statistics to Medicine Development of Anesthesia Discovery of the Relation of Microbes to Disease Elucidation of Inheritance and Genetics Knowledge of the Immune System Development of Body Imaging Discovery of Antimicrobial Agents Development of Molecular Pharmacotherapy 1

2 Application of Statistics to Medicine 1747: James Lind behandlede 12 skørbugramte skibspassagerer med bla. citronsaft i verdens første kliniske forsøg 1854: John Snow opdagede sammenhæng mellem kolera og forurenet vand i London. ( Pumpen i Broad Street ) Egentlig ikke så meget: Danmarks Statistik: Præsident Zuma og statistik: ISI meeting 17/ Danske skolekarakterer: Men mere selve ANALYSEN og FORTOLKNINGEN: Statistik: Et af de 11 mest vigtige bidrag til medicin i 1000 år!!! Statistikere uundværlige for Google: New York Times 5/ Andre eksempler/ links NetStat: Vildfarne fortolkninger: Øresundsbroen har ikke fjernet ålene i Øresund. IMM nyheder: Øresundsbro frikendt for at genere fisk DR nyheder 24. mar : Forskning i Mobilstråling makværk! Ingeniøren 8. jan 2007: Mobiltelefoni og cancer. Abstract for dansk artikel i JNCI Journal of the National Cancer Institute: Flere misdannede børn i Danmark DR nyhederne, 14. sep Indland: Lotto fejl!! Lotto-fejl mindskede net-spilleres chance for den store gevinst: Bang & Olufsen Interfaces such as touch screens are becoming more and more common Switch investigation The relative importance of visual, auditory and haptic information for the user s experience of mechanical switches Ditte Hvas Mortensen, Department of Psychology, Aarhus University, Denmark and Bang & Olufsen a/s, Struer, Denmark Søren Bech, Bang & Olufsen a/s, Struer, Denmark Ranking of switches 2

3 Bang & Olufsen Bang & Olufsen This is the title The sensory panel: The sensory panel: The sensory panel: A subject is presented with 3 samples, two of which are equal: Question: Which is different? Binomial data: answer is correct or incorrect 3

4 Binomial models: X = Number of correct answers X follows a binomial distribution withsomeunknownp n=12 p=1/3 P( X n! k!( n k)! k n k k) p (1 p) Expected pattern when performing many triangle trials with n=12 and NO detectable difference. n=12 p=2/3 Discrimination test: Two situations in practice: 1. Analysis phase: 1. Observed x out of n correct responses: 2. Are the products similar or different? 2. Planning phase: 1. How many test should we carry out? Expected pattern when performing many triangle trials with n=12 and LARGE detectable difference. Analysis situation 1: P-value: Miss Anna Sens: 28 triangle tests, 14 correct responses Hypothesis: The products are similar Alternative: The products are different H 0 : p 1/ 3 H1 : p 1/ 3 Hypothesis test: 1. Find P-value and compare with the nominal level (alpha) 2. How odd does the data look? (IF the hypothesis is OK) n=28 p=1/3 Choose Type I risk: 0.05 P value P(Observing14 or larger "at random") P( X 14), X ~ bin(28,1/ 3) % (Table or Computer) Decision : Products are different Statistical significance 4

5 Type I risk Type I and II risks Probability of WRONGLY claiming a difference (=0.05) Probability of rejecting the null hypothesis even though it is true! Most commonly used levels: Products are similar Products are different Claiming Difference ( Rejection ) TYPE 1 ERROR (alpha) Correct decision Claiming Similarity ( Acceptance ) Correct decision TYPE 2 ERROR (beta) Type II risk Power Probability of WRONGLY accepting similarity Probability of accepting the null hypothesis even though it is false! Used primarily in the planning phase! Difficulty: A deviation from p=1/3 can be small or large (a continuum of possibilities) Power 1 Probability of rejecting when we should reject! The more power the better A property of the test procedure NOT depending on the actual data! In practice: Trade-off between type I and type II risks! Risk of not finding large difference: Risk of not finding medium difference: Beta risk=10% (Power=90%) Beta risk=37% (Power=63%) 5

6 Risk of not finding small difference: Consequences of errors: Beta risk>50% (Power<50%) Example: New and better recipe for an existing product is saught! Type I error: A perfect recipe is rejected (Production department is unhappy!) Type II error: A wrong product is accepted and sent on the market (Marketing department is VERY unhappy) Confidence intervals Intervals are used instead of single numbers Good tool to summarize information Example: δ p 1.96 p(1 p) n 3-AFC test: Which is most sweet? The paradox is resolved! δ 6

7 Statistics DTU Profile Bachelor i Matematik og Teknologi: Examples: Characteristics: Climatology Working with the use and development Energy(Wind) of statistics in several areas Pharmaceutics KORT vej fra kursusviden til Finance forskning og/eller business Food science Environmental research Marine biology Microbiology 7