invest_3ed.pdf

# Q explain what it means to say that the f statistic

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(q) Explain what it means to say that the F -statistic is more powerful than the MAD statistic. The applet conducts a randomization test based on the F -statistic as well as the MAD statistic. (r) Use the pull-down Statistic menu to the F - statistic , and the null distribution changes from the MAD statistic to the F -statistic. Report the observed value of the F -statistic, which appears on the left side of the applet. (s) Use the simulation results, and the observed value of the F -statistic, to determine an empirical p- value.

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Chance/Rossman, 2015 ISCAM III Exploration 348 (t) Check the box by Show ANOVA Table , and the applet reports more output including the p-value based on the F -distribution. Report this p-value. Is the empirical p-value from (s) close to this theoretical p-value? Is the theoretical F -distribution, which is now overlaid on the simulated null distribution, a reasonable match? (u) You have now calculated a p-value in three different ways, two using simulations of randomization tests (with the MAD and F -statistics) methods and one based on the theoretical F -distribution. Are the p-values all similar? Do they all lead to the same conclusion about the strength of evidence that handicap type affects perception of qualification?
Chance/Rossman, 2015 ISCAM III Investigation 5.5 349 Investigation 5.5: Restaurant Spending and Music A British study (North, Shilcock, & Hargreaves, 2003) examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate classical music, popular music, and silence on successive nights over 18 days. The following summary statistics were reported: Classical music Pop music No Music Mean £24.13 £21.91 £21.70 SD £2.243 £2.627 £3.332 Sample size n 1 = 120 n 2 = 142 n 3 = 131 N = 393 (a) Based on these summary statistics, calculate the overall (weighted) mean amount spent and the pooled standard deviation. Check the consistency of your calculations with the summary statistics reported above. Overall (weighted) mean: Pooled standard deviation: (b) State the null and alternative hypotheses corresponding to the researchers’ conjecture. (c) Based on the above summary statistics and part (a), calculate the F -statistic (by hand) and then use technology to determine the p-value (sketch and shade the corresponding randomization distribution): x In R: pf(x, df1, df2, lower.tail=FALSE) x In Minitab : Graph > Probability Distribution Plot, View Probability, Distribution: F (d) What additional information is necessary before you can continue to draw a conclusion from this p- value?

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Chance/Rossman, 2015 ISCAM III Investigation 5.5 350 Study Conclusions In this study, a larger average amount was spent while classical music was playing. With such a large test statistic and such a small p-value ( F = 31.48, p-value | 0), we have very strong evidence that the observed differences in the sample means could not have arisen by chance alone. However, we need to assess the technical conditions before we could know whether this inferential procedure is valid with these data. Although the equal standard deviation assumption seems reasonable (because 3.332/2.243 <
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