Statistical Details for the Correlation of Responses

It is important to know the correlation between pairs of measurements when performing an analysis in the Matched Pairs platform. In most cases, if the pair of measurements is taken from the same individual at different times, the measurements are positively correlated. However, if the measurements represent competing responses, the correlation can be negative.

Figure 20.7 shows how the positive correlation of the two responses becomes the small variance on the difference (the vertical 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 vertical axis.

Figure 20.7 Examples of Positive Correlation Before and After Rotation