What are carry-over effects?
 

A carryover effect is an effect that "carries over" from one experimental condition to another. Whenever subjects perform in more than one condition (as they do in within-subject designs) there is a possibility of carryover effects. For example, consider an experiment on the effect of rate of presentation on memory. Subjects are presented with a list of words and asked to recall as many words as they can. In one condition, the words are presented one word per second; in the other condition, the words are presented two words per second. The question is whether or not having performed in one condition affects performance in the second condition. Perhaps learning the first list of words will interfere with learning the second list because it will be hard to remember which words were in each list. Or maybe the practice involved learning one list will make it easier to learn a second list. In either case, there would be a carryover effect: performance on the second list would be affected by the experience of being given the first list. Assume two experimental conditions: A1 and A2.

Half the subjects perform in Condition A1 first and then in A2; the other subjects perform in Condition A2 first and then in A1. The following table of means shows "symmetric carryover effects."
 

                 Condition


Order             A1          A2
A1 given first     8
A2 given first                 5
 
A1 given second    10
A2 given second                7 

First notice that performance in Condition A1 is three points better than performance in Condition A2.

Now consider the carryover effects by comparing the performance in Condition A1 when A1 was given first with performance in Condition A1 when A1 was given second. The table shows that performance in Condition A1 was two points better when it was given second (10) than when it was given first (8). Now, notice that the carryover effect is the same for Condition A2: Performance in A2 was two points better when it was performed second (7) than when it was performed first (5). Therefore, performing in Condition A1 prior to performing in Condition A2 raises performance in Condition A2 by two points. Analogously, performing in Condition A2 prior to performing in Condition A1 raises performance in Condition A1 by two points. The carryover effects are thus symmetric.

Carryover effects can also be asymmetric. Consider the following table of means.

                 Condition


Order             A1          A2
A1 given first     8
A2 given first                 5
 
A1 given second    10
A2 given second               15 


Notice that performance in condition A1 is only two points (10 - 8) better if it follows condition A2 than if it is performed first. Compare this with performance in Condition A2which is 10 (15 - 5) points better if it follows condition A1 than if it is performed first.

The presence of asymmetric carryover effects makes it difficult to interpret the data. In the example, A1 when performed first is three points higher than A2 when A2 is performed first. However, A1 when performed second is five points lower than A2 when A2 is performed second.
 

Reference:
http://davidmlane.com/hyperstat/