Deck 14: Learning From Experiment Data

Question 1

Osteoarthritis of the knee is a degenerative disease causing joint pain, stiffness, anddecreased function. Usual treatment is a combination of physical therapy,medication, and arthroscopic surgery. The arthroscopic surgery involves removal ofcartilage fragments and calcium crystals, or the smoothing of bones to eliminatedifficulties with joint motion. Arthroscopic surgery is widely used, but it is not clearhow, or even if it works. In a recent study patients were randomly assigned to twotreatment groups. Patients in the arthroscopic surgery group received standardarthroscopic treatment plus physical therapy and medicine. Patients in the othergroup received only physical therapy and medicine. Two years after treatment thepatients were evaluated using standard scales for pain, stiffness, and physicalfunction. Higher scores indicate increased pain, increased stiffness, and decreasedphysical function. Pain score data from the study are summarized below. Graphicaldisplays of the data indicate that it is reasonable to assume that the two pain scoredistributions are approximately normal.
(a) What null hypothesis and alternative hypothesis might be used in this setting tocompare mean pain rating for the two treatments?
(b) For your hypotheses in part (a), what is the associated P-Value?
(c) Given your results in parts (a) and (b), what would you conclude about thedifference between the two treatments?
Be sure to give your answer in the contextof this study.

Answer 1

Either a one-tailed or two-tailed test is appropriate.
For the one-tailed test, the alternative hypothesis is that the mean for the arthroscopic pain scores is less than the mean for the non-arthroscopic pain scores.
a)
b) The associated P-value is 0.8121.
c) Since the P-value is greater than .05, we do not have sufficient evidence to conclude that the arthroscopic surgery results in a smaller mean pain level than physical therapy and medicine.
For the two-tailed test, the alternative hypothesis is that the mean arthroscopic pain
level is different from the mean non-arthroscopic pain level
a)
b)The associated P-value is 0.3758
c)Since the P-value is very large, there is no statistically significant difference
between the treatment means. We do not have sufficient evidence to conclude
that the mean pain level for arthroscopic surgery treatment is different from the
mean pain level of the physical therapy and medicine treatment

Question 2

Osteoarthritis of the knee is a degenerative disease causing joint pain, stiffness, anddecreased function. Usual treatment is a combination of physical therapy,medication, and arthroscopic surgery. The arthroscopic surgery involves removal ofcartilage fragments and calcium crystals, or the smoothing of bones to eliminatedifficulties with joint motion. Arthroscopic surgery is widely used, but it is not clearhow, or even if it works. In a recent study patients were randomly assigned to twotreatment groups. Patients in the arthroscopic surgery group received standardarthroscopic treatment plus physical therapy and medicine. Patients in the othergroup received only physical therapy and medicine. Two years after treatment thepatients were evaluated using standard scales for pain, stiffness, and physicalfunction. Higher scores indicate increased pain, increased stiffness, and decreasedphysical function. Physical function data from the study are summarized below.Graphical displays of the data indicate that it is reasonable to assume that the twophysical function score distributions are approximately normal.
(a) What null hypothesis and alternative hypothesis might be used in this setting tocompare mean pain rating for the two treatments?
(b) For your hypotheses in part (a), what is the associated P-Value?
(c) Given your results in parts (a) and (b), what would you conclude about thedifference between the two treatments?
Be sure to give your answer in the contextof this study.

Answer 2

Either a one-tailed or two-tailed test is appropriate. For the one-tailed test, the alternative hypothesis is that the mean for the arthroscopic physical function scores is greater than the mean for the non-arthroscopic physical function scores.
a)
b) The associated P-value is 0.0568.
c) Since the P-value is greater than .05, we do not have sufficient evidence to conclude that the arthroscopic surgery results in a greater mean physical function score than physical therapy and medicine.

For the two-tailed test, the alternative hypothesis is that the mean arthroscopic physical function score is different from the mean non-arthroscopic physical function scores.
a)
b) The associated P-value is 0.1137.
c) Since the P-value is greater than .05, there is no statistically significant difference between the treatment means.We do not have sufficient evidence to conclude that the mean physical function score for arthroscopic surgery treatment is different from the mean physical function score of the physical therapy and medicine treatment.

Question 3

Proper nutrition is essential for aircraft pilots, given the demands of their job.Previous studies have indicated that United States Air Force pilots do notregularly eat breakfast, and thus may have low blood glucose levels after fastingat night. To investigate the potential for danger, 8 pilots were selected for studyin flight simulators. Each pilot participated in two trials and they tried a differentdrink, either Drink A (high carbohydrate) or Drink B (low carbohydrate) in eachtrial. The order in which the drinks were tried was determined at random. Thesecond trial was conducted 2 days after the first trial, so that any effects of thefirst drink were eliminated. After consuming one of the drinks, the pilots weresubjected to a variety of attitude recovery tasks. (An attitude recovery task is onewhere the pilot must return to wings-level flight.) The duration of self-illusorymotion (time between wings-level flight and the pilot to "feel" he or she hasreturned to wings-level flight) are shown in the table below. Graphical displaysof the data indicate that it is reasonable to assume that the two "felt recoverytime" distributions are approximately normal. Do these data provide convincing evidence that the mean self-illusory motion timediffers for the two drinks?
Provide appropriate statistical justification for yourconclusion.

Answer 3

Since the P-value is very large, we cannot reject the null hypothesis.There is not sufficient evidence of a difference in mean felt recovery times to wings level between drinks A and B.

Question 4

The Internet is increasingly available to the general public, and this has not goneunnoticed by those who construct and give surveys. Researchers are using electronicsurveys more and more, which naturally leads to questions about the usefulness ofelectronic surveys compared to traditional mail and telephone surveys. One veryimportant aspect of surveys is the response rate. To study the difference in responserates between electronic and postal surveys, 377 college faculty members randomlyselected from a list of members in a single professional membership, the Mid-SouthEducational Research Association. Each person was assigned at random to eitherreceive the survey by the U. S. Postal Service (USPS) or by email. There were 189people in the USPS group and 188 people in the email group. Each group was sent afollow-up notice two weeks after the initial mailing. Forty-eight of the USPSdelivered surveys were returned before the follow-up notice, and 24 of the electronicsurveys were returned before the follow-up notice.
(a) Construct and interpret a 95% confidence interval for the difference inproportions of surveys returned before being sent a follow-up notice for the mailand the email survey.
(b) In the context of this study, discuss the statistical significance and practicalsignificance of the results.
(c) To whom do you feel the results of this study can be generalized?
Justify yourresponse in a few sentences.

Question 5

The Internet is increasingly available to the general public, and this has not goneunnoticed by those who construct and give surveys. Researchers are using electronicsurveys more and more, which naturally leads to questions about the usefulness ofelectronic surveys compared to traditional mail and telephone surveys. One veryimportant aspect of surveys is the response rate. To study the difference in responserates between electronic and postal surveys, 377 college faculty members randomlyselected from a list of members in a single professional membership, the Mid-SouthEducational Research Association. Each person was assigned at random to eitherreceive the survey by the U. S. Postal Service (USPS) or by email. There were 189people in the USPS group and 188 people in the email group. Each group was sent afollow-up notice two weeks after the initial mailing. Each group was sent a follow-up notice two weeks after the initial mailing. Eighty-four of the USPS deliveredsurveys were returned, and 42 of the electronic surveys were returned.
(a) Construct and interpret a 95% confidence interval for the difference inproportions of surveys returned before being sent a follow-up notice for the mailand the email survey.
(b) In the context of this study, discuss the statistical significance and practicalsignificance of the results.
(c) To whom do you feel the results of this study can be generalized?
Justify yourresponse in a few sentences.

Question 6

Testing hypotheses about differences in experimental treatments requires somemodifications to the procedures for testing hypotheses about differences in populationcharacteristics.
a) How are the hypotheses different?
b) How are the conditions different?
c) How are the conclusions different?

Question 7

Testing hypotheses about differences in experimental treatments requires somemodifications to the procedures for testing hypotheses about differences in populationcharacteristics.
a) How are the hypotheses different?
b) How are the conditions different?
c) How are the conclusions different?

Question 8

Proper nutrition is essential for aircraft pilots, given the demands of their job.Previous studies have indicated that United States Air Force pilots do not regularlyeat breakfast, and thus may have low blood glucose levels after fasting at night. Toinvestigate the potential for danger, 8 pilots were selected for study in flightsimulators. Each pilot participated in two trials and they tried a different drink, eitherDrink A (high carbohydrate) or Drink B (low carbohydrate) in each trial. The order inwhich the drinks were tried was determined at random. The second trial wasconducted 2 days after the first trial, so that any effects of the first drink wereeliminated. After consuming one of the drinks, the pilots were subjected to a varietyof attitude recovery tasks. (An attitude recovery task is one where the pilot mustreturn to wings-level flight.) The times to recovery are shown in the table below.Graphical displays of the data indicate that the t-procedure is appropriate. Do these data provide convincing evidence that the mean attitude recovery timediffers for the two drinks?
Provide appropriate statistical justification for yourconclusion.