Basic Analysis and Graphing - SAS

244 Comparing Paired Data Chapter 8
Statistical Details for the Matched Pairs Platform
Figure 8.6 Example of Transforming to Difference by Mean, Rotated by 45 Degrees
Before rotation, the axes
represent y 1 and y 2 .
1 1
– 1 1
y 1
y 2
+ y
= 1
y 2
y 2
– y 1
After rotation, the axes represent
a sum and difference.
y 2
y 2 – y 1
y 2 + y 1
y 2
y 1
y 1
mean difference
and 95% CI
region where
y 1 < y 2 .
line where
y 1 = y 2 .
y 2 – y 1
y 2 + y 1
region where
y 1 > y 2 .
2
rescaled to mean
of responses
Correlation of Responses
In most cases where the pair of measurements is taken from the same individual at different times, they are
positively correlated. However, if they represent competing responses, the correlation can be negative.
Figure 8.7 shows how the positive correlation of the two responses becomes the small variance on the
difference (the y-axis). If the correlation is negative, the ellipse is oriented in the other direction and the
variance of the rotated graph is large on the y-axis.