Deck 14: Learning From Experiment Data

Question 1

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

Answer 1

a) The hypotheses would have to be worded in terms of treatment means or
proportions rather than population means or proportions.
b) For experiments, the individuals or objects are randomly assigned to treatments
For experiments, the number of individuals in the treatment groups is large or the
distributions of the response variable would be approximately normal in very
large treatment groups.
c) Conclusions would need to be worded in terms of treatment means. If random
sampling from a population preceded the random assignment to treatments, it
would be reasonable to generalize the conclusions about treatment effects to the
population.

Question 2

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

Answer 2

a) The hypotheses would have to be worded in terms of treatment means or
proportions rather than population means or proportions.
b) For experiments, the individuals or objects must be randomly assigned to
treatments, whereas in testing hypotheses using data from sampling, the samples
must be randomly selected.
For experiments, the number of individuals in the treatment groups must be large
or the distributions of the response variable would need to be approximately
normal in very large treatment groups. For data from sampling, the assumption is
that the samples are large or the population distributions are approximately
normal.
c) Conclusions would need to be worded in terms of treatment means or proportions.
If random sampling from a population preceded the random assignment to
treatments, it would be reasonable to generalize the conclusions about treatment
effects to the population.

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 not
regularly eat breakfast, and thus may have low blood glucose levels after fasting
at night. To investigate the potential for danger, 8 pilots were selected for study
in flight simulators. Each pilot participated in two trials and they tried a different
drink, either Drink A (high carbohydrate) or Drink B (low carbohydrate) in each
trial. The order in which the drinks were tried was determined at random. The
second trial was conducted 2 days after the first trial, so that any effects of the
first drink were eliminated. After consuming one of the drinks, the pilots were
subjected to a variety of attitude recovery tasks. (An attitude recovery task is one
where the pilot must return to wings-level flight.) The duration of self-illusory
motion (time between wings-level flight and the pilot to "feel" he or she has
returned to wings-level flight) are shown in the table below. Graphical displays
of the data indicate that it is reasonable to assume that the two "felt recovery
time" distributions are approximately normal. Do these data provide convincing evidence that the mean self-illusory motion time
differs for the two drinks? Provide appropriate statistical justification for your
conclusion.

Answer 3

Question 4

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

Question 5

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 regularly
eat breakfast, and thus may have low blood glucose levels after fasting at night. To
investigate the potential for danger, 8 pilots were selected for study in flight
simulators. Each pilot participated in two trials and they tried a different drink, either
Drink A (high carbohydrate) or Drink B (low carbohydrate) in each trial. The order in
which the drinks were tried was determined at random. The second trial was
conducted 2 days after the first trial, so that any effects of the first drink were
eliminated. After consuming one of the drinks, the pilots were subjected to a variety
of attitude recovery tasks. (An attitude recovery task is one where the pilot must
return 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.

Question 6

The Internet is increasingly available to the general public, and this has not gone
unnoticed by those who construct and give surveys. Researchers are using electronic
surveys more and more, which naturally leads to questions about the usefulness of
electronic surveys compared to traditional mail and telephone surveys. One very
important aspect of surveys is the response rate. To study the difference in response
rates between electronic and postal surveys, 377 college faculty members randomly
selected from a list of members in a single professional membership, the Mid-South
Educational Research Association. Each person was assigned at random to either
receive the survey by the U. S. Postal Service (USPS) or by email. There were 189
people in the USPS group and 188 people in the email group. Each group was sent a
follow-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 delivered
surveys were returned, and 42 of the electronic surveys were returned.
(a) Construct and interpret a 95% confidence interval for the difference in
proportions of surveys returned before being sent a follow-up notice for the mail
and the email survey.
(b) In the context of this study, discuss the statistical significance and practical
significance of the results.
(c) To whom do you feel the results of this study can be generalized? Justify your
response in a few sentences.

Question 7

Osteoarthritis of the knee is a degenerative disease causing joint pain, stiffness, and
decreased function. Usual treatment is a combination of physical therapy,
medication, and arthroscopic surgery. The arthroscopic surgery involves removal of
cartilage fragments and calcium crystals, or the smoothing of bones to eliminate
difficulties with joint motion. Arthroscopic surgery is widely used, but it is not clear
how, or even if it works. In a recent study patients were randomly assigned to two
treatment groups. Patients in the arthroscopic surgery group received standard
arthroscopic treatment plus physical therapy and medicine. Patients in the other
group received only physical therapy and medicine. Two years after treatment the
patients were evaluated using standard scales for pain, stiffness, and physical
function. Higher scores indicate increased pain, increased stiffness, and decreased
physical function. Physical function data from the study are summarized below.
Graphical displays of the data indicate that it is reasonable to assume that the two
physical function score distributions are approximately normal.

Question 8

Osteoarthritis of the knee is a degenerative disease causing joint pain, stiffness, and
decreased function. Usual treatment is a combination of physical therapy,
medication, and arthroscopic surgery. The arthroscopic surgery involves removal of
cartilage fragments and calcium crystals, or the smoothing of bones to eliminate
difficulties with joint motion. Arthroscopic surgery is widely used, but it is not clear
how, or even if it works. In a recent study patients were randomly assigned to two
treatment groups. Patients in the arthroscopic surgery group received standard
arthroscopic treatment plus physical therapy and medicine. Patients in the other
group received only physical therapy and medicine. Two years after treatment the
patients were evaluated using standard scales for pain, stiffness, and physical
function. Higher scores indicate increased pain, increased stiffness, and decreased
physical function. Pain score data from the study are summarized below. Graphical
displays of the data indicate that it is reasonable to assume that the two pain score
distributions are approximately normal. (a) What null hypothesis and alternative hypothesis might be used in this setting to
compare 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 the
difference between the two treatments? Be sure to give your answer in the context
of this study.