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Chancerossman 2015 iscam iii chapter 1 summary 129

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Chance/Rossman, 2015 ISCAM III Chapter 1 Summary 129 CHAPTER 1 SUMMARY In this chapter, you have focused on making inferences based on a representative sample from a random process that can be repeated indefinitely under identical conditions or from a finite population, for a single binary variable. You have learned how to model the chance variation in the binary outcomes that arise from such a sampling process. x You utilized simulation as a powerful tool for assessing the behavior of the outcomes and estimating the likelihood of different results for the sample proportion. In particular, you saw you could estimate the p-value of a test to measure how unlikely we are to get a sample proportion at least as extreme as what was observed under certain conjectures (the null hypothesis) about the process or population from which the sample was drawn. x Then you used the binomial distribution to calculate one-sided and two-sided p-values exactly. x As a third alternative for estimating p-values and confidence intervals, you considered the normal approximation to the binomial distribution (the Central Limit Theorem for a sample proportion). In this case, we also found z -score values ( test statistics ). These are informative in accompanying p-value calculations to provide another assessment of how unusual an observation is. We often flag an observation as surprising or unusual if the |z-score| value exceeds 2. In each case, when the p-value is small, we have evidence that the observed result did not happen solely due to the random chance inherent in the sampling process (a “statistically significant result”). The smaller the p-value, the stronger the evidence against the null hypothesis. Still, we must keep in mind that we are merely measuring the strength of evidence ± we may be making a mistake whenever we decide whether or not to reject a null hypothesis. If we decide the observed result did not happen by chance and so reject the null hypothesis, there is still a small probability that the null hypothesis is true and that the observed result did occur by chance (the probability of committing a Type I error ). If we decide the result did happen by chance, there is still a probability that something other than random chance was involved (a Type II error ). It is important to consider the probabilities of these errors when completing your assessment of a study. In particular, the sample size of the study can influence the probability of a Type II error and the related idea of power , which is the probability of correctly rejecting a null hypothesis when it is false. You began your study of confidence intervals as specifying an interval of plausible values for the process probability based on what you observed in the sample. These were the hypothesized parameter values that generated two-sided p-values above the level of significance D . In other words, they were the parameter values for which your sample result would not be surprising. When the sample size is

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