STATISTICS â UNDERSTANDING HYPOTHESIS TESTS

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Statistics – Understanding Hypothesis Tests:Proportions2014 If you take 1000 samples, based on the same sampling protocol, thenyou can expect approximately 950 of these samples will contain the truevalue (e.g. true mean, true difference between means) of the population.Sample1st2nd3rd4th5th6th7th8th9th100th..........500th24.8310th90.0%.......... ..........501st502nd..........991st992nd993rd994th995th996th997th998th999th1000thTrue meanoCoverageto date100%100%100%100%100%100%100%100%88.9%94.0%..........96.0%96.0%96.0%..........95.2%95.2%95.2%95.2%95.2%95.2%95.2%95.2%95.2%95.2%24.8224.8324.84Figure 8.1.2True meanSamples of size 10 from a Normal(µ=24.83, s=.005)distribution and their 95% confidence intervals for µ..From Chance Encounters by C.J. Wild and G.A.F. Seber, © John Wiley & Sons, 1999.© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 18 of 44The University of Auckland
Statistics – Understanding Hypothesis Tests:Proportions2014Interpreting the CI limits Step 9 for story type 4:CIs for the difference between two proportions: If the CI contains 0 (i.e. one negative and one positive number),there may be no difference between the two proportions. If CI is positive, then p 1 is higher/larger than p 2 . If CI is negative, then p 1 is lower/smaller than p 2 .Examples:(-.15, .09)(.09, .15)(-.15, -.09)Practical significance versus Statistical significanceStatistical significance Relates to having evidence of the existence of an effect or difference. Determined by examining the P-value of your significance test.To be statistically significant at the 5% level, the P-value must begreater than / less than 0.05 (5%).Practical significance Depends on the size of the effect or difference. Determined by examining the confidence interval in relation to theresearch in question.The link between the p-value and the confidence intervalLet’s say we’re interested in statistical significance at the 5% level. Then the“magic number” for the p-value is 0.05 and any p-value less than 0.05 issignificant at the 5% level. Then we also know, before calculating the95% confidence interval that the hypothesised value will beinside/outside it. If our p-value is more than 0.05, it is not significant atthe 5% level. Then we also know, before calculating the 95% CI that thehypothesised value will be inside/outside it.Let’s say we’re interested in statistical significance at the 1% level. Then the“magic number” for the p-value is 0.01 and any p-value less than 0.01 issignificant at the 1% level. Then we also know, before calculating the99% confidence interval that the hypothesised value will beinside/outside it. If our p-value is more than 0.01, it is not significant atthe 1% level. Then we also know, before calculating the 99% CI that thehypothesised value will be inside/outside it.© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 19 of 44The University of Auckland
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STATISTICS â UNDERSTANDING HYPOTHESIS TESTS