Errors in Statistics

[...]... three ways for coping with individual-to-individual and observer-to-observer variation: 1 Controlling Making the environment for the study—the subjects, the manner in which the treatment is administered, the manner in which the observations are obtained, the apparatus used to make the measurements, and the criteria for interpretation—as uniform and homogeneous as possible 2 Blocking A clinician might stratify... fundamental principle is also applicable to both experiments and surveys: Collect exact values whenever possible Worry about grouping them in interval or discrete categories later A long-term study of buying patterns in New South Wales illustrates some of the problems caused by grouping prematurely At the beginning of the study, the decision was made to group the incomes of survey subjects into categories,... are testing a binomial hypothesis p = 1/2 against the alternatives p £ 2/3, we would assume that p = 2/3 If the data do not come from one of the preceding distributions, then we might use a bootstrap to estimate the power and significance level In preliminary trials of a new device, the following test results were observed: 7.0 in 11 out of 12 cases and 3.3 in 1 out of 12 cases Industry guidelines specified... testing is the Neyman–Pearson Lemma To get a feeling for the working of this lemma, suppose we are testing a new vaccine by administering it to half of our test subjects and giving a supposedly harmless placebo to each of the remainder We proceed to follow these subjects over some fixed period and to note which subjects, if any, contract the disease that the new vaccine is said to offer protection against... premature drawing of conclusions in Chapter 5 Be sure to incorporate provisions for sampling nonresponders in your sample design and in your budget Sample from the Right Population Be sure you are sampling from the population as a whole rather than from an unrepresentative subset of the population The most famous blunder along these lines was basing the forecast of Landon over Roosevelt in the 1936 U.S... one position in space, one container of gas means one volume and pressure to be recorded, and one runner on one fixed race course means one elapsed time In a clinical trial, each individual patient corresponds to a single set of observations or does she? Suppose we are testing the effects of a topical ointment on pinkeye Is each eye a separate experimental unit, or each patient? It is common in toxicology... the topical ointment, while more precise results might be obtained by treating only one eye with the new ointment and recording the subsequent difference in appearance between the treated and untreated eyes, each patient still yields only one observation, not two Identically Distributed Observations If you change measuring instruments during a study or change observers, then you will have introduced... conducted in accordance with regulatory agency guidelines From the regulatory agency’s perspective, the principal hypothesis H is that the new vaccine offers no protection Our alternative hypothesis A is that the new vaccine can cut the number of infected individuals in half Our task before the start of the experiment is to decide which outcomes will rule in favor of the alternative hypothesis A and which in. .. will fail to contain a single member of that minority at least 28% of the time Groups to be compared may differ in other important ways even before any intervention is applied These baseline imbalances cannot be attributed to the interventions, but they can interfere with and overwhelm the comparison of the interventions One good after-the-fact solution is to break the sample itself into strata (men,... we are boring,5 and managers hate us because all our suggestions seem to require an increase in the budget But controls will save money in the end Blinding is essential if our results are to have credence, and care in treatment allocation is mandatory if we are to avoid bias Randomize Permitting treatment allocation by either experimenter or subject will introduce bias Controls To guard against the . determine which members are to be included in the sample. Surveys and Long-Term Studies Being selected at random does not mean that an individual will be willing to participate in a public opinion. then replicate again. Persi Diaconis [1978] spent some years as a statistician investigating paranormal phenomena. His scientific inquiries included investigating the powers linked to Uri Geller,. hypothesis testing is the Neyman–Pearson Lemma. To get a feeling for the working of this lemma, suppose we are testing a new vaccine by administering it to half of our test subjects and giving a supposedly