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Exam 24: Significance, Importance, and Undetected Differences

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Question 21

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Explain how the public can be misled by the results of a "very large study." (Assume data quality is not an issue.)

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Very large sample sizes are ve...

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Question 22

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Suppose you read the following headline: "Taking an aspirin a day can cut your risk of heart attack by almost half!" Suppose the news report goes on to tell you that the research is based on a very large well-designed randomized experiment with a p-value less than 0.0001.Assume this information is technically correct, given the results of the study.Which of the following statistics could actually represent the results of this study?

A) The rates of heart attack were 9.4 per thousand for the aspirin group and 17.1 per thousand for the placebo group (non aspirin) .
B) 94 people in the aspirin group had a heart attack, compared to 171 people in the non-aspirin group.
C) The risk of a heart attack for the aspirin group was 45% of the risk of a heart attack for the non-aspirin group.
D) Any of the above could have been possible.

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Question 23

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Suppose you got a p-value with a small study that was less than .05.Had you gotten the same sample results with a larger study done in a similar way, the p-value from the larger study would have been _______________ (choose: less than, greater than, equal to) the p-value from the smaller study.

What two pieces of information do you get from a confidence interval that can help you evaluate whether or not statistically results are really important to you?

Explain how the results of a very small study can be misleading.(Assume data quality is not an issue.)

Choosing beforehand to conduct a two-sided alternative will make it __________to detect a real difference in one single direction (choose: harder, easier, just as hard or easy).

Which of the following statements is false?

Suppose a researcher conducted a 2-sided hypothesis test for a population mean (significance level .05) and his test statistic was +1.84.(The significance level was .05.) He knows this test statistic is not large enough to reject the null hypothesis, because the test statistic was not greater than 1.96.Then he realizes that if he had done a one-sided test to begin with (alternative hypothesis ">" ) his results would have been statistically significant, because his test statistic was greater than 1.65.At this point, he decides to change to a one-sided hypothesis test, and reports his results as being statistically significant.Is this acceptable? Why or why not.

The natural variability in the population can affect a test's ability to detect a difference or relationship in the population that actually does exist.Explain how this is taken into account in the formula for the test statistic for testing a population mean.

When it comes to sample size, "results may be smaller (less significant) than they appear" is a good way to describe one of the possible problems with a hypothesis test.Explain how this can happen.

Which of the following statements must be true regarding a p-value of .0001?

Suppose you examined a possible relationship between gender and opinion on an issue in a population using two different studies.The percentages found were exactly the same for both studies, but one study had a much larger sample size than the other.Which of the following is not a possible outcome in this scenario?

What information can a confidence interval provide that a p-value alone cannot?

Suppose a chi-square statistic testing for a relationship between two variables was found to be 1.746, with p-value 0.19.What happens to the chi-square statistic and the resulting p-value if you triple the sample size?

Suppose a study found a strongly statistically significant relationship between two variables.From the p-value for this study you __________ (choose: could, could not) find the probability that there is a relationship between these two variables in the population.

Which of the following conclusions should make you suspicious as an educated consumer of statistical information?

Suppose a study found a strongly statistically significant relationship between two variables.The test statistic and the p-value for this study __________ (choose: would, would not) provide information about the magnitude of the effect.

The simplest and most conservative method for handling type 1 error probabilities in multiple comparisons is the _____________________ method.