# . Whatsample size do they need to detect this difference at 80% power, with alevel of significance of .05 using a two-tailed independent t-test?

Care Research & Statistics

Assignment
9B

Exercise
on Power and Sample Size

• See the article link below and

.pdf” href=”https://llu.instructure.com/courses/1029213/files/46203369/preview”>Article on Power and Sample Size  1.
Researchers using the Roland-Morris Disability Questionnaire as its tool for
collecting disability want to compare two treatment groups. They believe
that a 2.5 group difference would be important to them. The literature
implies that the common standard deviation for the groups for this questionnaire
is 3.7 points.

a. What
sample size do they need to detect this difference at 80% power, with a
level of significance of .05 using a two-tailed independent t-test?

b. How
would you adjust these sample sizes if you expect a 15% dropout rate?

2. We wish
to compare the walking speed (in Meters per second) of two groups of elderly
subjects (sedentary subjects and exercises). We feel that a difference of
0.2 meters per second would be an important difference to pick up. Pilot
study data on a group of sedentary individuals showed a standard deviation of
.24 M/sec.

a. What
sample size would be needed for this difference to be significant at the 5%
level of significance with 80% power?

3. In
comparing the effectiveness of sleep-inducing drugs with samples of size 5 each
of the groups, the researchers found a mean of 5.3 hours with the standard drug
and a mean of 6.1 with the experimental drug. The common standard
deviation was .70 hours. The difference was clinically important, but was

a. What is
the power of picking up this difference (at the .05 level of significance)?

4. To
understand the placebo effect in patients with Parkinson’s disease, scientists
want to measure activity at a key point in the brain when patients receive a
placebo that they think is an active drug and also when no treatment is given.

a. If the
smallest difference of important is .316 and the standard deviation of the
differences is expected to be .281, what sample size would be needed to pick up
this difference with 80% power at the 5% level of significance?

b.How would
the sample size change if you wanted 90% power?

5. We want
to do a study which will look at the effects of a low-cholesterol diet over a
three month period. A change of 20.0 mg/dL in total cholesterol would be
considered clinically important. From a pilot study we found that the
standard deviation of the change variable is 35.0 mg/dL. We would also
like to see if we can detect as significant a 3.0 mg/dL change in HDL cholesterol
which from the same pilot study has an estimated standard deviation of 8.5
mg/DL. (Use a 5% level of significance and power of 80%)

a. What
sample size would we need to detect the change in total cholesterol?

b. What
sample size would we need to detect the change in HDL cholesterol?

c. If we
expected a dropout rate of 12%, what sample size should we choose to find the
effect sizes we want to be significant for both variables at the 5% level of
significance?