Advice blood choleste rol advice blood cholesterol

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Advice Blood choleste rol Advice Blood cholesterol Subj. Type Before After Subj. Type Before After 1 A 421 346 11 B 307 283 2 B 297 290 12 A 444 387 3 B 278 259 13 B 317 303 4 B 220 196 14 A 261 217 5 A 542 530 15 A 224 207 6 A 333 287 16 B 467 415 7 B 267 241 17 B 213 186 8 A 344 306 18 A 244 228 9 A 426 374 19 B 312 273 10 A 331 280 Blood cholesterol readings appear normally distributed, for each advice type, so means and standard deviations are appropriate summaries. (Check this by drawing a histogram of the 19 “Before” readings, and of the 19 “Before minus After” differences.) Summary statistics: Choleste rol – Before Choleste rol – After Cholesterol – Difference Advice N Mean SD Mean SD Mean SD A 10 357.0 101.0 316.2 98.2 40.8 20.3 B 9 297.6 74.1 271.8 67.2 25.8 13.3 Examination of the means suggests that the blood cholesterol is reduced using both advice types, but Advice Type A may result in a greater reduction than Advice Type B. a) Carry out a paired t-test to assess the Before to After change, ignoring advice type. H o : Mean difference (µ d ) = 0 H a : Mean difference (µ d ) ≠ 0 Difference of sample means = 33.68, Std Error of the difference = 4.26 t-stat = 7.91, P-value < .0001 Conclusion: There is strong evidence that dietary advice, ignoring type, reduces cholesterol. b) Carry out a two-sample t-test to compare the Before-to-After change for Type A to the corresponding change for Type B. H o : Mean difference of Type A – Mean difference of Type B (µ d(A) - µ d(B) ) = 0 H a : Mean difference of Type A – Mean difference of Type B (µ d(A) - µ d(B) ) ≠ 0 Difference of sample means = 40.8 – 25.8 = 15.0, Pooled Std Dev = 17.4 t-stat = 1.88 , P-value = .077 (two-tailed) 12
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Conclusion: There is some evidence that Type A provides greater reduction in blood cholesterol than Type B, but the sample size is too small to make a definitive conclusion. Further testing is warranted, however. 13
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c) An optional analysis would be to check whether the random assignment to the two groups did in fact give two comparable groups. If the two groups really are comparable then the Before cholesterol levels in both groups should be similar. A two-sample t-test to compare the means of the two groups using the “Before” data gives a t-stat = 1.45, with a P-value = 0.17, indicating that there is no evidence of a difference in starting cholesterol. Here is how the spreadsheet looks in Excel, and what the output would look like. Subjec t Atyp e Type Before After Diff Type Before After Diff 1 A 1 421 346 75 1 421 346 75 2 B 2 297 290 7 1 542 530 12 3 B 2 278 259 19 1 333 287 46 4 B 2 220 196 24 1 344 306 38 5 A 1 542 530 12 1 426 374 52 6 A 1 333 287 46 1 331 280 51 7 B 2 267 241 26 1 444 387 57 8 A 1 344 306 38 1 261 217 44 9 A 1 426 374 52 1 224 207 17 10 A 1 331 280 51 1 244 228 16 11 B 2 307 283 24 2 297 290 7 12 A 1 444 387 57 2 278 259 19 13 B 2 317 303 14 2 220 196 24 14 A 1 261 217 44 2 267 241 26 15 A 1 224 207 17 2 307 283 24 16 B 2 467 415 52 2 317 303 14 17 B 2 213 186 27 2 467 415 52 18 A 1 244 228 16 2 213 186 27 19 B 2 312 273 39 2 312 273 39 t-Test: Paired Two Sample for Means t-Test: Two-Sample Assuming Equal Variances Before After Type 1 Type 2 Mean 328.8 295.2 Mean 40.8 25.8 Variance 8464.0 7348.3 Variance 413.1 175.9 Observations 19 19 Observations 10 9 Pearson Corr, 0.981 Pooled Variance 301.5 Hypo. Mean Diff. 0 Hypo. Mean Diff 0 df 18 df 17 t Stat 7.91 t Stat 1.88 P(T<=t) one-tail 0.00 P(T<=t) one-tail 0.04 t Critical one-tail 1.73
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