StatTutor Lesson - Cautions about Significance Tests

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Cautions about significance tests 2012
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      Question 1

      48

      Question 1.

      Fill in the blank: We have evidence against H0 whenever P-value is _________.

      A.
      B.

      Correct. We have evidence against the null hypothesis whenever P-value is smaller than α.
      Incorrect. We have evidence against the null hypothesis whenever P-value is smaller than α.
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      Question 2

      114

      Question 2.

      What value might a skeptical doctor select for α if she wants really strong evidence against the null hypothesis, H0: St. John’s Wort is not an effective alternative to Prozac?

      A.
      B.

      Correct. A skeptical doctor wants strong evidence for St. John’s Wort so would set α very small, like 0.01.
      Incorrect. A skeptical doctor wants strong evidence for St. John’s Wort so would set α very small, like 0.01.
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      Questions 3-4

      178

      Question 3.

      If the consequences of rejecting a correct H0 are very serious, which value should you select for α?

      A.
      B.

      Correct. If the consequences of rejecting a correct null hypothesis are very serious, set α very small, like 0.01.
      Incorrect. If the consequences of rejecting a correct null hypothesis are very serious, set α very small, like 0.01.
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      Questions 5-7

      236

      Question 5.

      What are the consequences of “not adding chlorine” when you should?

      A.
      B.

      Correct. If chlorine is not added when it should be, you increase the risk of spreading disease.
      Incorrect. If chlorine is not added when it should be, you increase the risk of spreading disease.
      2
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      Question 8

      278

      Question 8.

      If you would rather have a greater risk of skin irritation and a lower risk of disease, what value should you select for α?

      A.
      B.

      Correct. Selecting α of 0.01 leads us to reject H0 less often which lessens the risk of skin irritation, but increases the risk of disease. Selecting α of 0.10 leads us to reject H0 more often and add chlorine more often than perhaps we need to. This lessens the risk of disease, but increases the risk of skin irritation.
      Incorrect. Selecting α of 0.01 leads us to reject H0 less often which lessens the risk of skin irritation, but increases the risk of disease. Selecting α of 0.10 leads us to reject H0 more often and add chlorine more often than perhaps we need to. This lessens the risk of disease, but increases the risk of skin irritation.
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      Questions 9-11

      392

      Question 9.

      If P-value = 0.049 and α = 0.05, should you reject H0?

      A.
      B.

      Correct. Since P-value = 0.049 < α = 0.05, we reject H0.
      Incorrect. Since P-value = 0.049 < α = 0.05, we reject H0.
      2
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      Question 12

      448

      Question 12.

      True or false: P-value for a two-sided test is twice the P-value for a one-sided test.

      A.
      B.

      Correct. This is true because P-value for a two-sided test is the area in both tails whereas P-value for a one-sided test is the area in only one tail.
      Incorrect. This is true because P-value for a two-sided test is the area in both tails whereas P-value for a one-sided test is the area in only one tail.
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      Questions 13-14

      556

      Question 13.

      Observed effect equals x¯μ0. What happens to P-value as the value for x¯ gets farther and farther from μ0?

      A.
      B.

      Correct. As x¯ gets farther and farther from μ0, P-value gets smaller and smaller because the tail area gets smaller and smaller.
      Incorrect. As x¯ gets farther and farther from μ0, P-value gets smaller and smaller because the tail area gets smaller and smaller.
      2
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      Question 15

      586

      Question 15.

      When should we check for practical significance?

      A.
      B.
      C.
      D.

      Correct. Check for practical significance whenever sample size is really large.
      Incorrect. Check for practical significance whenever sample size is really large.
      2
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      Question 16

      639

      Question 16.

      With P-value = 0.0004 and α = 0.05, are these results statistically significant?

      A.
      B.

      Correct. Since P-value = 0.0004 < α = 0.05, these results are statistically significant.
      Incorrect. Since P-value = 0.0004 < α = 0.05, these results are statistically significant.
      2
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      Question 17

      662

      Question 17.

      Is statistical significance the same as practical significance?

      A.
      B.

      Correct. Statistical significance and practical significance are not the same.
      Incorrect. Statistical significance and practical significance are not the same.
      2
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      Question 18

      694

      Question 18.

      Is a one point difference (out of eighty points) between the two means big enough to justify investing time and money to improve the average test score of rural students?

      A.
      B.

      Correct. A one point difference is not worth investing time and money to improve the average score of rural students.
      Incorrect. A one point difference is not worth investing time and money to improve the average score of rural students.
      2
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      Question 19

      812

      Question 19.

      If a one point difference is not big enough to justify investing time and money to improve the average score of rural students, are these results practically significant?

      A.
      B.

      Correct. A difference that is not big enough to matter is not practically significant.
      Incorrect. A difference that is not big enough to matter is not practically significant.
      2
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      Questions 20-21

      870

      Question 20.

      How do you check x¯μ0 for statistical significance?

      A.
      B.

      Correct. For statistical significance, check to see if P-value is smaller than α.
      Incorrect. For statistical significance, check to see if P-value is smaller than α.
      2
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      Question 22

      934

      Question 22.

      True or false: “multiple analyses” is performing more than one test on one set of data.

      A.
      B.

      Correct. This is exactly what we mean by “multiple analyses.”
      Incorrect. This is exactly what we mean by “multiple analyses.”
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      Question 23

      1195

      Question 23.

      What are the consequences of multiple analyses?

      A.
      B.
      C.

      Correct. When performing multiple analyses, more than one null hypothesis is tested using the same data. Since they are all tested using the same data, more of these get rejected than should be.
      Incorrect. When performing multiple analyses, more than one null hypothesis is tested using the same data. Since they are all tested using the same data, more of these get rejected than should be.
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      Questions 24-25

      1326

      Question 24.

      What problem could occur when a sample size is very large?

      A.
      B.

      Correct. When the sample size is very large, a difference may be declared as statistically significant when it is not practically significant.
      Incorrect. When the sample size is very large, a difference may be declared as statistically significant when it is not practically significant.
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