1. In a recent review of acupuncture (journal of Anesthesia and Analgesia, 2013)
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Question
1. In a recent review of acupuncture (journal of Anesthesia and Analgesia, 2013), the effects were referred to as “theatrical placebo,” since in many well controlled studies, the average reported pain relief with acupuncture is not statistically different from a placebo (or a pretend acupuncture session). In other words, pvalues from these comparison tests are large enough that the sample average differences cannot be distinguished from natural sampling variability. Advocates of acupuncture will often claim (well, if they knew statistical terminology) that what is happening in these cases is an error of:
a. Type I
b. Type II
c. Type III
d. Type Natural Variability
e. Indistinguishability Error
2. When a careful hypothesis is performed and the pvalue for the test is very small, this means:
a. The null hypothesis is correct.
b. The test was performed correctly.
c. There is evidence in favor of the alternative hypothesis, but a type I error may be occurring.
d. The alternative hypothesis is correct.
e. There is evidence in favor of the null hypothesis, but natural variability may be occurring.
f. There is evidence in favor of the alternative hypothesis, but a type II error may be occurring.
3. Suppose that an epidemiological researcher has made many comparisons from a single large data set, and discovered that out of 50 comparisons between life expectancies among different groups, 2 of them have small enough pvalues to reject the null that there is no average difference. However, type I error says that she could be simply
a. Not considering a large enough sample size to reject all the null hypotheses in all cases.
b. Rejecting the null hypothesis when in fact there was no difference. Pvalues will sometimes be small even if Ho is true just from sampling variability, especially when there are so many tests considered.
c. Calculating her test statistics incorrectly by entering her data with the wrong values.
d. Rejecting the alternative hypothesis for the other 48 comparisons with large pvalues, when in fact those comparisons showed no difference.
e. Accepting that her study can only show correct results 2 out of every 50 comparisons.
4. Label clearly whether EACH the following statements are true or false.
T/F The p-value of a hypothesis test tells you how likely it is that the alternative hypothesis is true.
T/F Large p-values do not give evidence to reject the null hypothesis.
T/F If you reject the null hypothesis, you know the alternative hypothesis must be true.
T/F If you fail to reject the null hypothesis, this means the null hypothesis must be true.
T/F Small p-values give you evidence in favor of the alternative hypothesis
5. Suppose the p-value in a hypothesis test is larger than the significance level. This means:
a. Ho is obviously correct.
b. Ho is obviously wrong.
c. There is not enough evidence to reject Ha.
d. There is not enough evident to reject Ho.
e. Ha is obviously correct.
f. Ha is obviously wrong.
g. There is a large significance in the data.
Explanation / Answer
1.
Advocates of acupuncture will often claim (well, if they knew statistical terminology) that what is happening in these cases is an error of Natural Variability (Option D) .
2.
The p-value is defined as the probability of obtaining a result equal to or "more extreme" than what was actually observed, assuming that the null hypothesis is true.
P values address only one question: how likely are your data, assuming a true null hypothesis? It does not measure support for the alternative hypothesis.
So, There is evidence in favor of the alternative hypothesis, but a type I error may be occurring. (Option C) Natural Variability Error is unlikely since the p values are not large.
3.
Since the p value is small only for 2 out of 50 samples.
b. Rejecting the null hypothesis when in fact there was no difference. Pvalues will sometimes be small even if Ho is true just from sampling variability, especially when there are so many tests considered.
4.
The p-value of a hypothesis test tells you how likely it is that the alternative hypothesis is true. P values address only one question: how likely are your data, assuming a true null hypothesis? It does not measure support for the alternative hypothesis. Hence , False
Large p-values do not give evidence to reject the null hypothesis. True (A Confidence should also be specified to reject the null)
If you reject the null hypothesis, you know the alternative hypothesis must be true.(False, rejecting a null does not imply that alternative hypothesis is true.)
If you fail to reject the null hypothesis, this means the null hypothesis must be true. (False, it just means that your experiment did not have enough evidence to reject the null)
Small p-values give you evidence in favor of the alternative hypothesis. True but you still cannot say that the alternative hypothesis is correct.
5. Suppose the p-value in a hypothesis test is larger than the significance level.
from the definition it follows that There is not enough evidence to reject H0. (Option D)
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