Download Homework assignments for MCBS Biostatistics I

Exercise for Weekly GCRC Workshop
March 31, 2006
Instructor: Ayumi Shintani, Ph.D., M.P.H.
3.3
Datasets paired1.sav and paired2.sav contain hypothetical data of a randomized
clinical trial assessing pre- and post- measures of a continuous outcome variable
comparing between two groups (GROUP: coded as 0 and 1).
3.3.a Compute power of Student t-test comparing post measurement (POST) between the
two groups using paired1.sav.
Answer: 32%. Explanation: SPSS was used to find the SD (mean = 0.99107) and difference
of the means (0.21167). PS was then used to calculate the power, which was found to be
32% assuming an alpha of 0.05.
Group Statistics
post
group
.00
1.00
N
100
100
Mean
-.0248
.1869
Std.
Deviation
1.01013
.97201
Std. Error
Mean
.10101
.09720
Independent Samples Test
Levene's Test for
Equality of
Variances
F
post
Equal
variances
assumed
Equal
variances
not assumed
1.367
Sig.
.244
t-test for Equality of Means
t
df
Sig. (2tailed)
Mean
Differenc
e
Std.
Error
Differenc
e
95% Confidence
Interval of the
Difference
Lower
Upper
-1.510
198
.133
-.21167
.14018
-.48811
.06478
-1.510
197.70
8
.133
-.21167
.14018
-.48812
.06478
3.3.b Compute power of Student t-test comparing change between pre and post
measurements between the two groups using paired1.sav.
Answer: 18.4%. Explanation: SPSS was used to find the SD (mean = 0.93924) and difference
of the means (0.14180). PS was then used to calculate the power, which was found to be
18.4% assuming and alpha of 0.05.
Group Statistics
diff
group
.00
1.00
N
Mean
.0350
.1768
100
100
Std.
Deviation
.88468
.99380
Std. Error
Mean
.08847
.09938
Independent Samples Test
Levene's Test for
Equality of
Variances
F
diff
Equal
variances
assumed
Equal
variances not
assumed
.678
Sig.
.411
t-test for Equality of Means
t
df
Sig. (2tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-1.066
198
.288
-.14180
.13305
-.40418
.12058
-1.066
195.381
.288
-.14180
.13305
-.40420
.12060
3.3.c Compute power of Student t-test comparing post measurement (POST) between the
two groups using paired2.sav.
Answer: 37%. Explanation: SPSS was used to find the SD (mean = 1.001855) and difference
of the means (0.23244). PS was then used to calculate the power, which was found to be
37% assuming and alpha of 0.05.
Group Statistics
post
group
.00
1.00
N
100
100
Mean
.0884
-.1441
Std.
Deviation
1.00786
.99585
Std. Error
Mean
.10079
.09958
Independent Samples Test
Levene's Test for
Equality of
Variances
F
post
Equal
variances
assumed
Equal
variances
not assumed
.014
Sig.
.908
t-test for Equality of Means
t
df
Sig. (2tailed)
Mean
Differenc
e
Std.
Error
Differenc
e
95% Confidence
Interval of the
Difference
Lower
Upper
1.641
198
.102
.23244
.14169
-.04696
.51185
1.641
197.97
2
.102
.23244
.14169
-.04696
.51185
3.3.d Compute power of Student t-test comparing change between pre and post
measurements between the two groups using paired2.sav.
Answer: 99.98%. Explanation: SPSS was used to find the SD (mean = 0.437545) and
difference of the means (0. 34510). PS was then used to calculate the power, which was
found to be 99.98% assuming and alpha of 0.05.
Group Statistics
diff
group
.00
1.00
N
100
100
Mean
.0124
-.3327
Std.
Deviation
.44961
.42548
Std. Error
Mean
.04496
.04255
Independent Samples Test
Levene's Test for
Equality of
Variances
F
diff
Equal
variances
assumed
Equal
variances
not assumed
.010
Sig.
.922
t-test for Equality of Means
t
df
Sig. (2tailed)
Mean
Differen
ce
Std.
Error
Differen
ce
95% Confidence
Interval of the
Difference
Lower
Upper
5.575
198
.000
.34510
.06190
.22302
.46717
5.575
197.40
1
.000
.34510
.06190
.22302
.46717
3.3.e Compare your findings in the above 4 power analyses, does the power improve using
change in both datasets? If the power improves in one dataset, and does not in the
other dataset, what do you think the difference between the 2 datasets in terms of SD
and correlation of pre and post that may explain the difference in improvement of the
power by using change?
Answer: The power improves in the first but not the second data set when using the change
in measurements. The main difference that explains the dramatic increase in power using
change in dataset2 is that the standard deviation is markedly lower with the change rather
than with the POST measurement. As the standard deviation approaches zero, the power
will increase. The smaller standard deviation is due to high correlation of data in pair2, while
data in pair1 might not highly correlated.