invest_3ed.pdf

# A pase the talley5k2013txt data file into the

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of assessing the statistical significance of our results. (a) Pase the Talley5K2013.txt data file into the Analyzing Two Quantitative Variables applet. Press Use Data and make sure age is used as the explanatory variable (if not press the (response, explanatory) button to toggle their roles). Remove the outlier and check the Show Regression Line box and confirm the equation. Another way to investigate whether the association observed in these sample data could have arisen by chance is a randomization test that shuffles the outcomes for one of the variables and reexamines the correlation coefficient and/or sample slope for the shuffled or re-randomized data. (b) Check the Show Shuffle Options box. Press the Shuffle Y-values box. Select the Plot radio button. Describe the blue line that appears. Is the association as strong as the one that we found in the actual data? How are you deciding? (c) Press the Shuffle Y-values button 5-10 more times. Do you ever find a negative association? Are any of the associations as strong as the one observed by the student group? What pattern is beginning to emerge in the blue regression lines on the scatterplot? (d) Change Number of Shuffles to some large number (like 1000 or the difference between how many you have done so far and 1000) and press the Shuffle Y-values button. Describe the shape, center, and variability of the resulting distribution of re-randomized slopes. How does this distribution compare to the one you found in Investigation 5-10(k)? (e) Use the applet to estimate the p-value by using the Count Samples box: choosing to count “beyond” (for the two-sided p-value) and specifying the observed sample slope. Press Count .

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Chance/Rossman, 2015 ISCAM III Investigation 5.11 390 You should see many similarities between these distributions (from random sampling and random shuffling). So let’s again consider applying the t -probability model to the standardized statistics. (f) Use the standard deviation for the slopes found in (d) and standardize the value of the observed sample slope. (g) Now select the radio button for t -statistic . Use the applet to estimate the p-value corresponding to the observed t -statistic. How does it compare to the p-value you found in the previous Investigation? (h) Check the box to Overlay t- distribution . Does it appear to be a reasonable model of the shuffled t - statistics distribution? (i) Check the Regression Table box to confirm your calculations. Discussion: It is interesting to compare these two analysis approaches. In Investigation 5.10, we modeled repeated random sampling from a population but this required us to make certain assumptions about the data in the population (which we will spell out in more detail in the next Investigation). In Investigation 5. 11, we didn’t make any assum ptions about a larger population; instead we modeled what the sample data could look like if the observed response values had been randomly paired, over and over again, with the observed explanatory variable values. This approach is sometimes referred to as “conditioning on the observed data.”
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