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corotto f wise use null hypothesis tests practitioner s handbook 2022

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Textbook in PDF format Wise Use of Null Hypothesis Tests: A Practitioner's Handbook provides readers with the foundational knowledge needed to devise and successfully validate their research. This volume provides the conceptual background needed to fully understand this methodology, including how to determine a null hypothesis, which test is most appropriate, T Tests, common misconceptions, and research study design. Written by a neurobiologist for the neuroscientist, readers will have a better understanding of null hypothesis tests in their journey to better quality research and publishing validated, significant results. Epigraph About the author What makes this book different? This is not a mathematics book Conventional books get it wrong Ronald Fisher got it right, and his method is simple What conventional books leave out How to use this book The conventional method is a flawed fusion Three statisticians, two methods, and the mess that should be banned Wise use and testing nulls that must be false Null hypothesis testing in perspective Notes The point is to generalize beyond our results Samples and populations Real and hypothetical populations Randomization Know your population, and do not generalize beyond it Notes Null hypothesis testing explained The effect of sampling error The logic of testing a null hypothesis We should know from the start that many null hypotheses cannot be correct The traditional explanation of how to use p What use of α accomplishes The flawed hybrid in action Criticisms of the flawed hybrid We should test nulls in a way that answers the criticisms How to use p and α Mouse preference, done right this time More p-values in action What were the nulls and predictions? What if p=? A radical but wise way to use p or ? p or P? Notes How often do we get it wrong? Distributions around means Distributions of test statistics Null hypothesis testing explained with distributions Type I errors explained Probabilities before and after collecting data The null’s precision explained The awkward definition of p explained Errors in direction Power and errors in direction Manipulating power to lower p-values Increasing power with one-tailed tests Power and why we should we set α to or higher Power, estimated effect size, and type M errors How can we know a population’s distribution? Notes Important things to know about null hypothesis testing Examples of null hypotheses in proper statistics books and what they really mean Categories of null hypotheses? What if is important to accept the null? Never do this Null hypothesis testing as never explained before Effect size: what is it and when is it important? We should provide all results, even those not statistically “significant” Notes Common misconceptions Null hypothesis testing is misunderstood by many Statistical “significance” means a difference is large enough to be important—wrong! p is the probability of a type I error—wrong! If results are statistically “significant,” we should accept the alternative hypothesis that something other than the n If results are not statistically “significant,” we should accept the null hypothesis—wrong! Based on p we should either reject or fail to reject the null hypothesis—often wrong! Null hypothesis testing is so flawed that we should use confidence intervals instead—wrong! Power can be used to justify accepting the null hypothesis—wrong! The null hypothesis is a statement of no difference—not always The null hypothesis is that there will be no significant difference between the expected and observed values—very, ver A null hypothesis should not be a negative statement—wrong! Notes The debate over null hypothesis testing and wise use as the solution The debate over null hypothesis testing Communicate to educate Plan ahead Test nulls when appropriate, not promiscuously Strike the right balance between what is conventional and what is best Think outside of the null hypothesis test Encourage our audience to draw their own conclusions Allow ourselves to draw our own conclusions Strike the right balance when providing our results Know the misconceptions and do not fall for them Do not say that two groups “differ” or “do not differ” Provide all results somehow Other reformed methods of null hypothesis testing Notes Simple principles behind the mathematics and some essential concepts Why different types of data require different types of tests Simple principles behind the mathematics Numerical data exhibit variation Nominal data do not exhibit variation How to tell the difference between nominal and numerical data Simple principles behind the analysis of groups of measurements and discrete numerical data Variance: a statistic of huge importance Incorporating sample size and the difference between our prediction and our outcome Drawing conclusions when we knew all along that the null must be false Degrees of freedom explained Other types of t tests Analysis of variance and t tests have certain requirements Do not test for equal variances unless … Simple principles behind the analysis of counts of observations within categories Counts of observations within categories When the null hypothesis specifies the prediction When there is only one degree of freedom When the null hypothesis does not specify the prediction Interpreting p when the null hypothesis cannot be correct × Designs and other variations The problem with chi-squared tests The reasoning behind the mathematics Rules for chi-squared tests Notes nine The two-sample t test and the importance of pooled variance Comparing more than two groups to each other If we have three or more samples, most say we cannot use two-sample t tests to compare them two samples at a time Analysis of variance The price we pay is power Comparing every group to every other group Comparing multiple groups to a single reference, like a control Is all of this a load of rubbish? Notes Assessing the combined effects of multiple independent variables Independent variables alone and in combination No, we may not use multiple t tests We have a statistical main effect: now what? We have a statistical interaction: things to consider We have a statistical interaction and we want to keep testing nulls Which is more important, the main effect or the interaction? Designs with more than two independent variables Use of analysis of variance to reduce variation and increase power Notes Comparing slopes: analysis of covariance Analysis of covariance Use of analysis of covariance to reduce variation and increase power More on the use of analysis of covariance to reduce variation and increase power Use of analysis of covariance to limit the effects of a confound Note When data do not meet the requirements of t tests and analysis of variance When do we need to take action? Floor effects and the square root transformation Floor and ceiling effects and the arcsine transformation Not as simple as a floor or ceiling effect—the rank transformation Making analysis of variance sensitive to differences in proportion—the logarithmic transformation Nonparametric tests Transforming data changes the question being asked Notes Reducing variation and increasing power by comparing subjects to themselves The simple principle behind the mathematics Repeated measures analysis of variances Multiple comparisons tests on repeated measures When subjects are not organisms When repeated does not mean repeated over time Pretest-posttest designs illustrate the danger of measures repeated over time Repeated measures analysis of variance versus t tests The problem with repeated measures The requirement for sphericity Correcting for a lack of sphericity Multiple comparisons tests when there is a lack of sphericity The multivariate alternative to correction Notes What do those error bars mean? Confidence intervals Testing null hypotheses in our heads Plotting confidence intervals Error bars and repeated measures Plot comparative confidence intervals to make the overlap myth a reality Notes Appendix A Philosophical objections Decades of bitter debate We want to know when we are wrong, not how often Setting α to does not mean that % of all null-based decisions are wrong There are better ways to analyze and interpret data The fallacy of affirming the consequent Some say our method cannot be used to determine direction The return of one-tailed tests Kaiser’s absurd directional two-tailed tests Invoking power to justify Kaiser’s directional two-tailed tests Fisher did not follow Kaiser’s rules Still not convinced? Notes Appendix B How Fisher used null hypothesis tests Why follow my advice? Fisher tested for direction Others did too Fisher believed α should vary according to the circumstances Fisher came close to saying there should be no α at all In practice, Fisher did not categorize outcomes Fisher’s language answers many criticisms of null hypothesis testing Except for Fisher’s use of “significant” Fisher’s inconsistency explained Fisher’s thinking expressed in one word We have come a long way since Fisher, but the wrong way? Notes Appendix C The method attributed to Neyman and Pearson Neyman and Pearson with Pearson Neyman and Pearson without Pearson An important limitation Alternatives are always infinitely numerically precise The method step-by-step The method’s influence on the flawed hybrid The method’s fate in the world of the flawed hybrid Power spreads its wings Neyman et al’s method has no place in science Notes Back Cover

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corotto f wise use null hypothesis tests practitioner s handbook 2022