The Role of Confidence Intervals in Research

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Chapter 20

• The Role of Confidence Intervals in Research

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Thought Questions
1.a, page 351
In this chapter, Example 1 compares weight loss
(over one year) in men who diet but do not
exercise and vice versa. The results show that a
95 confidence interval for the mean weight loss
for men who only diet extends from 13.4 to 18.0
pounds...
a. Do you think this means that 95 of all men
who diet will lose between 13.4 and 18.0 pounds?
Explain.
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Thought Questions
1.b, page 351
a 95 confidence interval for the mean weight
loss for men who only diet extends from 13.4 to
18.0 pounds. A 95 confidence interval for the
mean weight loss for men who exercise but do not
diet extends from 6.4 to 11.2 pounds.
b. On the basis of these results, do you think
you can conclude that men who diet without
exercising lose more weight, on average, than men
who exercise but do not diet?
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Thought Questions
2, page 351
The first confidence interval in Question 1 was
based on results from 42 men. The confidence
interval spans a range of almost 5 pounds. If
the results had been based on a much larger
sample, do you think the confidence interval for
the mean weight loss would have been wider, more
narrow or about the same? Explain your reasoning.
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Thought Questions
3, page 351
In Question 1, we compared average weight loss
for dieting and for exercising by computing
separate confidence intervals for the two means
and comparing the intervals. What would be a
more direct value to examine, in order to make
the comparison between the two methods?
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Case Study I
Exercise and Pulse Rates
Hypothetical
Is the mean resting pulse rate of adult subjects
who regularly exercise different from the mean
resting pulse rate of those who do not regularly
exercise?
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Case Study I Results
Exercise and Pulse Rates
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The Rule for Sample Means
If numerous samples of size n are taken, the
frequency curve of the sample means from the
various samples will be approximately
bell-shaped. The mean of those sample means will
be m (the population mean). The standard
deviation will be
We dont know the value of ? !
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Standard Error of the (Sample) Mean

• SEM standard error
• (standard deviation from the sample)
• divided by
• (square root of the sample size)

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Case Study I Results
Exercise and Pulse Rates

• Typical deviation of an individual pulse rate
  (for Nonexer.) 9.0
• Typical deviation of a mean pulse rate 1.6.

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Case Study I Confidence Intervals
Exercise and Pulse Rates

• 95 C.I. for the population mean
• sample mean 2 (standard error)

• Exercisers 66 3.2 (62.8, 69.2)
• Nonexercisers 75 3.2 (71.8, 78.2)
• Do you think the population means are different?

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Careful Interpretation of a Confidence Interval

• 95 of all samples of size 29 from the population
  of exercisers should yield a sample mean within
  two standard errors of the population mean.
• Thus, we feel that plausible values for the
  population of exercisers mean resting pulse rate
  are between 62.8 and 69.2.
• This does not mean that 95 of all people who
  exercise regularly will have resting pulse rates
  between 62.8 and 69.2.

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Case Study I Confidence Intervals
Exercise and Pulse Rates

• 95 C.I. for the difference in population means
  (nonexercisers minus exercisers)
• (difference in sample means)
  2 (measure of variability)
• Difference in sample means 9
• 95 confidence interval (4.4, 13.6)
• you dont need to know how to calculate it!
• interval does not include zero (? means are
  different)

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Case Study II
An Experiment Testing a Vaccine for Those with
Genital Herpes
Adler, T., (1994) Therapeutic vaccine fights
herpes. Science News, Vol. 145, June 18, p. 388.
Does a new vaccine prevent the outbreak of herpes
in people already infected?
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Case Study II Sample
An Experiment Testing a Vaccine for Those with
Genital Herpes

• 98 men and women aged 18 to 55
• Experience between 4 and 14 outbreaks per year
• Experiment
• Double-blind experiment
• Randomized to vaccine or placebo

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Case Study II Report
An Experiment Testing a Vaccine for Those with
Genital Herpes
The vaccine was well tolerated. gD2 recipients
reported fewer recurrences per month than placebo
recipients (mean 0.42 sem 0.05 vs 0.55
0.05)
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Case Study II Confidence Intervals
An Experiment Testing a Vaccine for Those with
Genital Herpes

• 95 C.I. for popn mean recurrences
• Vaccine group 0.42 2(0.05) (.32, .52)
• Placebo group 0.55 2(0.05) (.45, .65)
• 95 C.I. for the difference in population means
• Difference 0.13, SE 0.07 (given)
• C.I. (-0.01, 0.27) (contains 0 ? means not
  different)

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Case Study III
Relationship between breast cancer and induced
abortion
Daling, et. al., (1994) Risk of breast cancer
among young women relationship to induced
abortion. Journal of the National Cancer
Institute, Vol. 86, No. 21, pp. 1584-1592.
Is the risk of breast cancer among women who have
had an induced abortion different from the risk
among those who have not?
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Case Study III Sample
Relationship between breast cancer and induced
abortion

• 845 breast cancer cases were identified in
  Washington State from 1983 to 1990.
• 910 control women were identified using
  random-digit dialing in the same area.
• Women born prior to 1944 were excluded.

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Case Study III Results
Relationship between breast cancer and induced
abortion

• The relative risk for breast cancer was 1.5, with
  the higher risk for women who had a induced
  abortion.
• A 95 confidence interval for the relative risk
  was 1.2 to 1.9. (given)
• Note the confidence interval does not contain the
  value one (? risks are different)

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Case Study III Results
Relationship between breast cancer and induced
abortion

• No increased risk was found for women who had
  spontaneous abortions the relative risk was 0.9.
• A 95 confidence interval for the relative risk
  was 0.7 to 1.2. (given)
• Note the confidence interval does contain the
  value one (? risks are not different)

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Key Concepts

• Compute confidence intervals for means based on
  one sample
• Interpret confidence intervals for means
• Interpret confidence intervals in general (e.g.,
  difference between two means, or relative risk)