Question

FROM DATA TO DECISION Critical Thinking: Is the pain medicine Duragesic effective in reducing pain? Analyzing the Results 1. Correlation Use the given data to construct a scatterplot. Listed below are measures of pain intensity before and after using the drug Duragesic (fentanyl) (based on data from Janssen Pharmaccutical Products, L.P.). The data are listed i order by row, and corresponding measures are f subject before and after treatment. For example, the first subject had a measure of 1.2 before treatment and a measure of 0.4 after treatment. Each pair of measurements is from then use the methods of Section 10-1 to test for a linear correlation between the pain intensity before and after treat- nment. If there does appear to be a linear correlation, can we conclude that the drug treatment is effective? rom the same 2. Regression Use the given data to find the equation of the regression line. Let the response ) variable be the pairn one subject, and the intensity of pain was measured using the intensity after treatment. What would be the equation of the regression line for a treatment having absolutely no effect? standard visual analog score. A higher score corresponds to higher pain intensity 3. Two Independent Samples The methods of Section 9-2 can be used to test the claim that two popula- Pain Intensity Before Duragesic Treatment tions have the same mean. Identify the specific claim that the treatment is effective, then use the methods of Section 9-2 to 1.2 1.3 1.5 1.6 8.0 3.4 3.5 2.8 2.6 2.2 3.0 7.1 2.32.1 3.4 6.4 5.0 4.2 2.8 3.9 test that claim. The methods of Section 9-2 are based on the 5.2 6.9 6.9 5.0 5.5 6.0 5.5 8.6 9.4 10.0 requirement that the samples are independent. Are they inde- pendent in this case? 7.6 4. Matched Pairs The methods of Section 9-3 can be used to test a claim about matched data. Identify the specific claim that the treatment is effective, then use the methods of Pain Intensity After Duragesic Treatment 0.4 1.4 1.8 2.9 6.0 1.4 0.7 3.9 0.9 1.8 Section 9-3to test that claim. 0.9 9.3 8.0 6.8 2.3 0.4 0.7 1.2 4.5 20 1.6 2.0 2.0 6.8 6.6 4.1 4.6 2.9 5.4 4.8 5. Best Method? Which of the preceding results is best for determining whether the drug treatment is effective in reduc- ing pain? Based on the preceding results, does the drug appear to be effective? 4.1

Answer 1

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RGui (32-bit) File Edit View Misc Packages Windows Help WP sample estimates: cor 0.3044342 > #to obtain linear regression between 'x' and 1 > summary(im(yx)) Call: lm (formula = y x) Residuals: 3Max -3.4087 -1.8595 -0.6188 1.1087 5.4074 10 Median Min Coefficients: Estimate Std. Error t value Pr t) (Intercept) 1.9103 0.9111 2.097 .0448 0.2966 0.1723 1.721 0.0959. signif. codes : 0 , , 0.001 ikk, O.01 r*n О.05., 0.1 ' , 1 Residual standard error: 2.37 on 29 degrees of freedom Multiple R-squared: 0.09268, Adjusted R-squared: 0.06139 F-statistic: 2.962 on 1 and 29 DF, p-value: 0.09588

RGui (32-bit) File Edit View Misc Packages Windows Help to test whether treatment is effective under the consideration of independent samples test(xy alternativegreater, var.equalFALSE) Welch Two Sample t test data:x and y t-2.1881, df-59.959, p-value =0.01628 alternative hypothesis: true difference in means is greater than o 5 percent confidencel interval: 0.325738 Inf samp le estimates: an of x mean of me 4 674194 31296714 #to test whether treatment is effective under the consideration of matched data t.test (x y paired- TRUE· alternative= "greater" l aired t-te data: Tx and to 2.6234, lcernative hypotheshs: tue difterence th means = 30, p-value = O, P-value greater chah eoxtidatceine s pene Hs 95 percent confidence interval 0.4862328 Inf sample estimates:

data: x and y t= 2.1881, df= 59.959, p-value-0.01628 alternative hypothesis: true difference in means is greater than 0 95 percentconfidencel interval: 0.325738 Inf sample estimates: mean ofx mean of y 4 674194 3.296774 tto test whether treatment is effective under the consideration of matched data S t test (x. y, paired TRUE, alternative"greater" Paired t test data x and y iti : 2.6234, df = 30, p-value-, O. 006776 alternative hypothesis: true difference in means 1s greacer than o 95 percenti.confidence interval: 0- 4862828IE gample estimates: mean of the idifferences 1-377419

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