Chapter 23 Notes
Chapter 23 Notes STAT 1350 Intro to Stats
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This 2 page Class Notes was uploaded by Katie Catipon on Tuesday April 14, 2015. The Class Notes belongs to STAT 1350 Intro to Stats at Ohio State University taught by Alice Miller in Spring2015. Since its upload, it has received 115 views. For similar materials see Intro to Stats in Statistics at Ohio State University.
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Date Created: 04/14/15
Chapter 23 Use and Abuse of Statistical Inference Two major types of statistical inference con dence intervals and signi cance tests To use inference wisely understand the data and the questions you want to answer and t the method to its setting For con dence intervals and signi cance tests for a population proportion p Data must be an SRS from the population of interest These methods aren t correct for sample designs more complex than an SRS Population size is much larger than sample size Sample size is reasonably large so than sample distribution of the sample proportion p hat is close to Normal Note Con dence intervals and tests ignore sources of error such as dropouts and nonresponse Con dence levels Con dence interval estimates the unknown value of a parameter and also tells us how uncertain that estimate is All con dence levels say how often the method catches the true parameter when sampling many times This is not the same as saying whether this speci c data set gives us an interval that contains the true value of the parameter Trade off between con dence level and size of interval 99 con dence level will provide a larger interval than a 95 con dence level Larger sample narrower interval Length of con dence level for p goes down in proportion to the square root of the sample size the cut an interval in half sample size must be increased 4x Con dence intervals are more informative than signi cance test because they estimate a population parameter and are easier to interpret It is good practice to give them whenever possible Statistical signi cance Signi cance tests help us weigh the evidence that the data yields in support of what we were looking for To do this we ask what would happen if the claim was nottrue null hypothesis Signi cance test answers the null hypothesis by giving the Pvalue tells us how unlikely data as or more extreme than ours would be if the null hypothesis were true Very unlikely data is strong evidence that the null hypothesis is incorrect Although we usually don t know if the hypothesis is true for this speci c population Resulting statement example quotData as or more extreme than these would occur only 5 of the time if the hypothesis were truequot This is less straightforward than a con dence interval Larger samples make signi cance test more sensitive Smaller samples make them less sensitive Small effects will often be hidden behind the chance variation in a sample Test measures only the strength of the evidence against the null hypothesis It says nothing about how big or important the effect we seek in the population really is A nding can be statistically signi cance without being practically important Lack of signi cance does not mean that there is no effect only that we do not have food evidence for that effect Small samples often miss important effects that are really present in the population Pvalue of a signi cance test depends strongly on sample size and truth of the population It is bad practice to report a naked Pvalue one by itself wout also giving the sample size and a statistics that describes the sample outcome There is no sharp border between signi cant and insigni cant only increasingly strong evidence as the Pvalue decreases
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