Session 5 - What does 'not significant' really mean.docx

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University of Toronto St. George
Cell and Systems Biology
William Navarre

HMB325H © Lisa| Page 113 S E S S I O N 5 : W H AT D O E S ' N O T S I G N I F I C A N T ' R E A L LY M E A N ? ( C H A P T E R 6 ) LEARNING OBJECTIVES 1. recognize the relevant study question 2. recognize & describe the characteristics of the data (i.e. types of variables & levels of measurement) associated w the study 3. describe the descriptive statistics to be used 4. identify & carry out the appropriate statistical test & determine the associated probability (P) 5. discuss the factors influencing study power & sample size & how they interact 6. describe how the width of a confidence interval are influenced by a study’s power 7. calculate study power for t-tests & difference of proportion analyses THE ROLE OF CHANCE • studies are done to advance & inform biomedicine/healthcare • relevant data needs to be collected in these studies • statistical tools enable 2 study tasks:  summarize the data (descriptive statistics)  measure the role of chance (statistical testing) • the role of chance?  is an observed study result real?  does it indicate a real effect or real difference  this can’t be determined directly, so we examine other possible explanations like chance to see what role they might play  what is the probability of observing study results as extreme as those by chance?  is random variation/chance a reasonable explanation for the observed results?  need to identify & use the applicable statistical test, which returns the probability (P) of study results as extreme as these arising by chance WHICH STATISTICAL TEST? 1. level of measurement of outcome variable: continuous, dichotomous, discrete, nominal, ordinal 2. type of comparison/study design: 2 groups OR 2+ (independent) groups compared,… Type of Comparis Test data on ANOVA quantitative 2+ groups * quantitative t test * 2 groups z test dichotomou 2 groups s χ test nominal ≠ 2+ groups Fisher’s exact dichotomou # 2 groups test s ≠discrete or continuous, & normally distributed includes dichotomous #if expected value of any cell is <5 • all statistical tests answer the question: what is the probability of results as extreme as these occurring simply by chance? • all tests answer this question by examining the ratio of the observed results to those that would be expected simply by chance: observedresults ratio= expectedresults HMB325H © Lisa Z| Page 2 • this ‘ratio’ is called the test statistic • the larger it is, the less probable that the study’s results might have arisen by chance • to determine the applicable probability (P) value, find the ratio value in the applicable statistical table • this probability never goes to 0  every result has some probability of arising by chance • how probably do study results need to be for us to conclude they are due to chance? • how improbably do study results need to be for us to conclude that chance is not a probably explanation? HOW IMPROBABLE? • how low (improbable) should the probability (P) be for use to conclude that the study results are indicative of a ‘real’ effect?  this is the alpha (α) level selected for the study • α level is balanced bw 2 unwanted outcomes: 1. false-positive study (type I error): wrongly concluding there is an effect 2. false-negative study: wrongly concluding there isn’t an effect • possible study outcomes: the truth + – false- true- + positive positive study (type I error) result false- – negative true- negative (type II error) • 2 explanations for ‘not significant’: 1. there truly is no effect (though we can’t determine this directly) 2. there is a true effect, but the study didn’t
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