A question about comparing symptom reduction over time and across
treatment groups. Each respondent is asked twice if they
experience symptoms (coded 1), at baseline and then at 6 months
later. They are randomly assigned to either the control or the
intervention group. The 2x2x2 table below shows the frequency
counts.
As can be seen in the margins of the table, 21% of the control
group show symptoms at baseline, then it reduced to 7% six months
later; and 48% of the intervention group show symptoms at
baseline, then only 4% at 6 month.
The question is, given the information below, how do I test if
the intervention group has a better improvement?
Intuitively, I imagine that a difference of 44% should be better
than a 14% difference in a sample of about 30 respondents. But
it is no so according to Levin & Serlin's method (J. of Stats
Education, 8 (2), 2000).
Levin and Serlin say that correlated proportions between two
groups can be tested by a simple 2x2 table using the frequency of
changes:
Control Intervention
------------------------------------
0 --> 1 (worse) 2 0
1 --> 0 (better) 6 12
----------------------------------------------------
A fisher.test(matrix(c(2,6,0,12), ncol=2)) shows a p-value of
0.15.
I'd appreciate suggestions to alternative methods, perhaps a test
of conditional independence in loglin()? But I am not sure how
to do that.
Yuelin Li.
--------- Table -------------
Control Group
(baseline by 6 months)
Frequency|
Percent |
Row Pct | 0| 1| Total
---------+--------+--------+
0 | 20 | 2 | 22
| 71.43 | 7.14 | 78.57
| 90.91 | 9.09 |
---------+--------+--------+
1 | 6 | 0 | 6
| 21.43 | 0.00 | 21.43
| 100.00 | 0.00 |
---------+--------+--------+
Total 26 2 28
92.86 7.14 100.00
Intervention Group
(baseline by 6 months)
Frequency|
Percent |
Row Pct | 0| 1| Total
---------+--------+--------+
0 | 14 | 0 | 14
| 51.85 | 0.00 | 51.85
| 100.00 | 0.00 |
---------+--------+--------+
1 | 12 | 1 | 13
| 44.44 | 3.70 | 48.15
| 92.31 | 7.69 |
---------+--------+--------+
Total 26 1 27
96.30 3.70 100.00
