21/11/20181Hypothesis testing;Sign TestWeek 51Formal inference: hypothesis testing•Aim: to make objective inference from something that is just a sampleto awhole population•Method: take a random sample from a particular population, then usethis sample toinfer/deduceinformation about the whole population•We will use formal statistical tests such as the Sign Test, Z‐test, t‐test,chi‐squared test, ANOVA and linear regression – as well as confidenceintervals – for the rest of this course2FAQs•So 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 significant•We 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 ante‐natal class, 7 out of the 8 couples gavebirth to a boy•From a sample of 15 CEOs, 3 are female•We toss a coin 100 times and it lands on heads 76 times•The mean height of a random sample of 20 university students is 1.9m•There are proportionally far more people with a high level ofunderstanding of te reo in the younger age groups4Hypothesis testingA fundamental component of Statistical Analysis5New terms•HypothesisNull hypothesisAlternative hypothesis•Significance level•Test statistic•p‐value6

21/11/20183Hypothesis testing – the main idea7Hypothesis testing – the process•We start with a belief or suspicion about a population – this belief is ourhypothesis.For example•We collect information from a random sample, which is taken from thepopulation that the hypothesis is about•Use 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):"ܪ"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"ܪଵ"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 hypothesisܪଵ

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Term

Summer

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NoProfessor

Tags

physicist, younger age, Lecturer