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Significance testing Ioannis Karagiannis (based on previous EPIET material) 18 th EPIET/EUPHEM Introductory course

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The idea of statistical inference Sample Population Conclusions based on the sample Generalisation to the population Hypotheses 2

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Inferential statistics Uses patterns in the sample data to draw inferences about the population represented, accounting for randomness Two basic approaches: – Hypothesis testing – Estimation Common goal: conclude on the effect of an independent variable on a dependent variable 3

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The aim of a statistical test To reach a deterministic decision (yes or no) about observed data on a probabilistic basis. 4

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Why significance testing? Norovirus outbreak on a Greek island: The risk of illness was higher among people who ate raw seafood (RR=21.5). Is the association due to chance? 5

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The two hypotheses There is a difference between the two groups (=there is an effect) Alternative Hypothesis (H 1 ) (e.g.: RR=21.5) When you perform a test of statistical significance, you reject or do not reject the Null Hypothesis (H 0 ) There is NO difference between the two groups (=no effect) Null Hypothesis (H 0 ) (RR=1) 6

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Norovirus on a Greek island Null hypothesis (H 0 ): There is no association between consumption of raw seafood and illness. Alternative hypothesis (H 1 ): There is an association between consumption of raw seafood and illness. 7

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Hypothesis testing Tests of statistical significance Data not consistent with H 0 : – H 0 can be rejected in favour of some alternative hypothesis H 1 (the objective of our study). Data are consistent with the H 0 : – H 0 cannot be rejected You cannot say that the H 0 is true. You can only decide to reject it or not reject it. 8

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p value p value = probability that our result (e.g. a difference between proportions or a RR) or more extreme values could be observed under the null hypothesis H 0 rejected using reported p value 9

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p values – practicalities Low p values = low degree of compatibility between H 0 and the observed data: association unlikely to be by chance you reject H 0, the test is significant High p values = high degree of compatibility between H 0 and the observed data: association likely to be by chance you dont reject H 0, the test is not significant 10

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Levels of significance – practicalities We need of a cut-off ! 1% 5% 10% p value > 0.05 = H 0 not rejected (non significant) p value 0.05 = H 0 rejected (significant) BUT: Give always the exact p-value rather than significant vs. non-significant. 11

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The limit for statistical significance was set at p=0.05. There was a strong relationship (p<0.001). …, but it did not reach statistical significance (ns). The relationship was statistically significant (p=0.0361) Examples from the literature p=0.05 Agreed convention Not an absolute truth Surely, God loves the 0.06 nearly as much as the 0.05 (Rosnow and Rosenthal, 1991) 12

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p = 0.05 and its errors Level of significance, usually p = 0.05 p value used for decision making But still 2 possible errors: H 0 should not be rejected, but it was rejected : Type I or alpha error H 0 should be rejected, but it was not rejected : Type II or beta error 13

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H 0 is true but rejected: Type I or error H 0 is false but not rejected: Type II or error Types of errors Decision based on the p value Truth No diff Diff 14

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More on errors Probability of Type I error: – Value of α is determined in advance of the test – The significance level is the level of α error that we would accept (usually 0.05) Probability of Type II error: – Value of β depends on the size of effect (e.g. RR, OR) and sample size – 1- β : Statistical power of a study to detect an effect on a specified size (e.g. 0.80) – Fix β in advance: choose an appropriate sample size 15

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Quantifying the association Test of association of exposure and outcome E.g. chi 2 test or Fishers exact test Comparison of proportions Chi 2 value quantifies the association The larger the chi 2 value, the smaller the p value – the more the observed data deviate from the assumption of independence (no effect). 16

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Chi-square value 17

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Norovirus on a Greek island 2x2 table Raw seafood No raw seafood IllNon ill %81% Expected proportion of ill and not ill : x19% ill x 81% non-ill x 19% ill x 81% non-ill Expected number of ill and not ill for each cell :

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Chi-square calculation (29-6) 2 /6(9-31) 2 /31 (5-27) 2 /27 ( ) 2 / 114 Raw seafood No raw seafood IllNon ill χ 2 = 125 p < 0.001

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Norovirus on a Greek island The attack rate of illness among consumers of raw seafood was 21.5 times higher than among non consumers of these food items (p<0.001). The p value is smaller than the chosen significance level of α = 5%. The null hypothesis is rejected. There is a < probability (<1/1000) that the observed association could have occured by chance, if there were no true association between eating imported raw seafood and illness. 20

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C2012 vs facilitators The ultimate (eye) test. H 0 : the proportion of facilitators wearing glasses during the Tuesday morning sessions was equal to the proportion of fellows wearing glasses. H 1 : the above proportions were different. 21

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C2012 vs facilitators Fellow Facilitator GlassesNo glasses %67% Expected proportion of ill and not ill : x33% +ve x67% -ve x33% +ve x67% -ve Expected number of ill and not ill for each cell :

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Chi-square calculation (11-13) 2 /13(27-25) 2 /25 (6-4.6) 2 /4.6(8-9.4) 2 /9.4 Fellow Facilitator GlassesNo glasses 23 χ 2 = 1.11 p = 0.343

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t-test Used to compare means of a continuous variable in two different groups Assumes normal distribution 24

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t-test H 0 : fellows with glasses do not tend to sit further in the back of the room compared to fellows without glasses H 1 : fellows with glasses tend to sit further in the back of the room compared to fellows without glasses 25

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t-test 26

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Epidemiology and statistics 27

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Criticism on significance testing Epidemiological application need more than a decision as to whether chance alone could have produced association. (Rothman et al. 2008) Estimation of an effect measure (e.g. RR, OR) rather than significance testing. 28

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Suggested reading KJ Rothman, S Greenland, TL Lash, Modern Epidemiology, Lippincott Williams & Wilkins, Philadelphia, PA, 2008 SN Goodman, R Royall, Evidence and Scientific Research, AJPH 78, 1568, 1988 SN Goodman, Toward Evidence-Based Medical Statistics. 1: The P Value Fallacy, Ann Intern Med. 130, 995, 1999 C Poole, Low P-Values or Narrow Confidence Intervals: Which are more Durable? Epidemiology 12, 291,

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Previous lecturers Alain Moren Paolo DAncona Lisa King Ágnes Hajdu Preben Aavitsland Doris Radun Manuel Dehnert 30

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