Exam 14: Learning From Experiment Data

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?

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Question 1

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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.

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.

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a) Assumption check: Subjects were randomly assigned to treatment groups and there are at least 10 responses and at least 10 non-responses in each treatment groups.Thus, the large sample procedure (z) is appropriate.
I am 95% confident that the difference in proportions of response between the USPS and email treatments is between 0.1285 and 0.3136.
b) The confidence interval does not contain 0.It appears that the response rate is greater for the USPS.A difference in response rates that is between about 13 and 31 percentage points is large and would be of practical significance.
c) It would be appropriate to generalize to the people in the professional organization, because the sample was a random sample from this population. However, the surveys were sent to college faculty in a single professional organization.College faculty are highly educated and probably use the Internet more than most; generalizing the results of this experiment beyond this group would not be appropriate.

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.

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Question 3

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a)
b) The confidence interval does not contain 0.It appears that the response rate is greater for the USPS.A difference in response rates that is between about 5 and 20 percentage points is large and would be of practical significance.
c) It would be appropriate to generalize to the people in the professional organization, because the sample was a random sample from this population. However, the surveys were sent to college faculty in a single professional organization.College faculty are highly educated and probably use the Internet more than most; generalizing the results of this experiment beyond this group would not be appropriate.