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2. Does p > 0.05 mean that blockamine had no effect on the responses? AcceptedNo errorType II error RejectedType I errorNo error Hypothesis is actually: FalseTrue Hypothesis is:

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Dr Wocky takes his data to the company statistics expert — not a formally trained statistician, rather, a statistical enthusiast — and asks if he should start again. The expert initially asks Dr Wocky to state his hypothesis. The hypothesis was that agamine will be less effective in the presence of blockamine. After hearing it, the statistics enthusiast points out that the hypothesis is directional insofar as it says that the effect of agamine will be reduced by blockamine, rather than just changed in an unspecified way. He suggests that that makes the hypothesis one-sided and that a one-tailed statistic would therefore be appropriate. He points out that a two tailed p=0.063 implies a one- tailed p=0.0315, and suggests that Dr Wocky has already obtained a significant result. 3. Do you think that blockamine affected the response to agamine? 4. Do you think that a one-tailed test is ever appropriate?

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Wocky wonders whether the natural variability in the starting levels of mimsy (i.e. the baseline mimsy levels) have added substantially to the variability in the stimulated mimsy levels. He suspects that if the data was expressed as the change in mimsy levels elicited by agamine, rather than the absolute mimsy levels, then there might be less variability in the data. Thus he recalculated all of the data as change (i.e. responses): Figure 2: Responses to agamine in the absence (Control) and presence (+ Blockamine) of blockamine. Responses are expressed as change from the mimsy values immediately prior to the agamine application, and are shown as the mean ± SEM from 6 independent experimental units.

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The newly-expressed data do not look very different from the originals, but the change is ‘ significant ’ insofar as a Student ’ s t-test on the data now yields a statistically-significant effect, with a two-tailed statistic giving p=0.044 5. Do you think that blockamine affected the response to agamine? Dr Wocky decides to inspect his data more closely by plotting the baseline mimsy levels as well as the agamine-stimulated levels

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The results show that the baseline levels before and after pre- treatment with agamine are significantly different (p = 0.048). 6. Do you think that blockamine affected the response to agamine?

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It is hypothesised that there are chemical differences in the brains of people who died with Alzheimer ’ s disease (test group) as compared to those who died of other causes (control group). The levels of 10 different chemicals are measured in each subject in both groups, and results are as follows: Chemical typeControl group Alzheimer ’ s group 1 2 3 4 5 6 7 8 9 10 84 ± 5 99 ± 12 54 ± 4 29 ± 3 96 ± 7 43 ± 8 76 ± 4 32 ± 7 88 ± 5 63 ± 5 79 ± 5 93 ± 12 61 ± 4 34 ± 3 74 ± 5 36 ± 8 84 ± 4 26 ± 7 91 ± 5 68 ± 5 P-value > 0.05 0.016 > 0.05 Conclusion: There is a significant difference in the level of chemical type 5 in the brains of people with Alzheimer ’ s disease as compared to the rest of the population. Do you agree?

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Incidence of cancer in radiologists In 1959, it was noticed that the average age of onset of cancers in radiologists was significantly less (P < 0.05) than in the population as a whole. Conclusion: Radiologists are more likely to develop cancer, possible as a result of greater exposure to radioactivity. Is that conclusion reasonable?

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The great global warming swindle Fact: The average global temperature in 1998 was higher than any year since then. Therefore, the “ global warming ” theory is a myth. Is that conclusion reasonable?

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* Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: "There are three kinds of lies: lies, damned lies and statistics.” - Autobiography of Mark Twain

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Copyright © Cengage Learning. All rights reserved. 13 Linear Correlation and Regression Analysis.

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