week 5.pdf - 21/11/2018 Hypothesis testing; Sign Test Week...

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21/11/20181Hypothesis testing;Sign TestWeek 51Formal inference: hypothesis testingAim: to make objective inference from something that is just a sampleto awhole populationMethod: take a random sample from a particular population, then usethis sample toinfer/deduceinformation about the whole populationWe will use formal statistical tests such as the Sign Test, Ztest, ttest,chisquared test, ANOVA and linear regression – as well as confidenceintervals – for the rest of this course2FAQsSo how can we use a sample to ‘prove’ what we suspect is true?Using a sample, wecannotprove beyond all doubt that a suspicion or beliefabout the population is true or false!Why do we need probability for Statistics?Probability theory deals with the analysis of random phenomena. We useprobability theory to find whether or not our result is a significant finding in astatistical sense (i.e. statistically significant) and if so, at whatlevelour resultis significantWe use Statistics (and probability in particular) to “quantify our uncertainty”about our findings[we could only do this if we sampledevery single member of the population,as in a census]3
21/11/20182What would surprise you? Would you draw any conclusions from these sample statistics?In a Statistics lecturer’s antenatal class, 7 out of the 8 couples gavebirth to a boyFrom a sample of 15 CEOs, 3 are femaleWe toss a coin 100 times and it lands on heads 76 timesThe mean height of a random sample of 20 university students is 1.9mThere are proportionally far more people with a high level ofunderstanding of te reo in the younger age groups4Hypothesis testingA fundamental component of Statistical Analysis5New termsHypothesisNull hypothesisAlternative hypothesisSignificance levelTest statisticpvalue6
21/11/20183Hypothesis testing – the main idea7Hypothesis testing – the processWe start with a belief or suspicion about a population – this belief is ourhypothesis.For exampleWe collect information from a random sample, which is taken from thepopulation that the hypothesis is aboutUse the sample results and statistical procedures to test whether thesuspicion we have is likely to be true for the whole population8Construct two opposing statements about your belief(these may be written in symbols):"Null hypothesis(sceptic’s point of view, there is no change/difference)e.g. there isno biasin the coin;there isno changein median cortex thickness;the median survival time doesnot differbetween drugs"Alternative hypothesis(the change you suspect, ‘research hypothesis’)e.g. the coinisbiased;thereisa change in cortex thickness;the average survival time islongerwith drug B than with drug A9
21/11/20184Null hypothesisܪan equality stated in terms of a population parametera statement of the value of the population parameter when there is no changee.g.ܪ: population median (or mean)a particular numberAlternative hypothesisܪ

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Term
Summer
Professor
NoProfessor
Tags
physicist, younger age, Lecturer

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