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d. Report (again) the observed class value of the statistic. (What proportion of students in your class put Timâs name on the left?) pÌ = e. Calculate how many standard deviations the observed class value of the statistic is from the hypothesized mean of the null distribution, 0.5. In other words, subtract the 0.5 from the observed value, and then divide by the standard deviation. This is the standardized statistic z = (observed statistic pÌ â 0.5) / SD of null distribution. f. Once you calculate this value, you interpret it as âhow many standard deviations the observed statistic falls from the hypothesized parameter value.â What strength of evidence against the null does your standardized statistic provide? g. How closely does your evaluation of strength of evidence based on the standardized statistic compare to the strength of evidence based on the p-value in #4c? Guidelines for evaluating strength of evidence from standardized values of statistics Standardizing gives us a quick, informal way to evaluate the strength of evidence against the null hypothesis: between -1.5 and 1.5: below -1.5 or above 1.5: below -2 or above 2: below -3 or above 3: little or no evidence against the null hypothesis; moderate evidence against the null hypothesis; strong evidence against the null hypothesis; very strong evidence against the null hypothesis. Step 5: Formulate conclusions. 6. Now, letâs step back a bit further and think about the scope of inference. We have found that in most classes, the observed data provide strong evidence that students do better than random guessing which face is Timâs and which is Bobâs. In that case, do you think that most students at your school would agree on which face is Timâs? Do you think this means that most people can agree on which face belongs to Tim? Furthermore, does this mean that all people do ascribe to the same facial prototyping? We will look more at the scope of inference in chapters 2 and 4. June 27, 2014 MAA PREP workshop 27