Strategies for Managing Carryover Effects, Explained

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Strategies for Managing Carryover Effects

Research Methods in Psychology · Chapter 13: Factorial, Within-Subject, and Small-n DesignsSection 13.6 · lesson 82 of 949 min · free with a free account

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In this lesson

Counterbalancing, randomization, and the discipline of order.

  • Define carryover and say why it threatens within-subject work
  • Distinguish symmetric from asymmetric carryover
  • Apply complete counterbalancing for small designs
  • Construct a Latin square for larger ones

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Everything said in the video, section by section (1,223 words). Read along, or search it.

Factorial, Within-Subject, and Small-n Designs

Strategies for Managing Carryover Effects

The previous section ended with a promise, and this section keeps it. Within-subject designs are powerful because each participant sees every condition. They are fragile for exactly the same reason. By the end you will define carryover effects and explain why they threaten these designs. You will distinguish symmetric from asymmetric carryover, and see why the difference matters. You will apply complete counterbalancing for small numbers of conditions. You will construct a Latin square for partial counterbalancing of larger designs. And you will choose between strategies based on the structure of your experiment.

The Definition

What Carryover Means

A carryover effect is any influence of one condition on subsequent conditions. Some carryover takes obvious forms. A participant who has learned to solve a particular type of problem cannot unlearn it. There is no returning them to a state of innocence for a later condition. Other carryover is much subtler, and easier to overlook. The mood induced by one task, carried into the next. The fatigue accumulated over a long session. The expectations built up by a sequence of similar manipulations. All of these can leak from one condition into the next. And once they leak, they contaminate the comparison between the conditions.

The Threat

Confounded, and Undetectable Afterward

Carryover threatens within-subject designs for a specific structural reason. It produces differences between conditions that have nothing to do with the manipulation. Watch how the confound actually forms. Suppose condition B is always presented after condition A. Then any influence of A on B is confounded with the B versus A comparison. The two are inseparable in the data you collect. And here is the part that makes carryover different from many other threats. Detecting this confound after the fact is impossible. No analysis can pull apart two things that never varied independently. So it must be prevented by design, before a single participant arrives.

Form One

Symmetric Carryover

Carryover comes in two structurally different forms. The distinction matters, because it decides how much the design can do about it. Symmetric carryover affects every condition equally, regardless of what came before. Fatigue is often roughly symmetric. Any condition presented late in a session is performed under fatigue. The size of the effect depends on the position, not on the specific preceding condition. That property is what makes symmetric carryover tractable. It can be neutralized by counterbalancing. If every condition appears equally often in every position, the average influence is equal. And the manipulation comparison is preserved intact.

Form Two

Asymmetric Carryover

Asymmetric carryover is the harder case. Its magnitude depends on which specific condition came before. Take a learning manipulation as an example. It may carry forward strongly when the next condition uses related material. And barely at all when the next condition uses unrelated material. Now see why counterbalancing cannot rescue you here. The size of the carryover depends on the sequence, rather than the position. So balancing positions does not balance the influence. When asymmetric carryover is severe, a within-subject design may not be appropriate at all. At that point the right move is to reconsider the architecture, not the counterbalancing.

Strategy One

Complete Counterbalancing

The strongest counterbalancing strategy is the complete one. Complete counterbalancing presents every possible order of conditions across participants. With two conditions, there are two orders. A then B, and B then A. With three conditions, six orders. With four conditions, twenty four. The total number of orders is the factorial of the number of conditions. And the balance you get in return is perfect. Every condition appears in every position. And every condition both precedes and follows every other condition equally often. That second property is the one asymmetric carryover cares about.

The Limitation

Scale Defeats Completeness

With small numbers of conditions, complete counterbalancing is straightforward. Then the factorial takes over, and the strategy becomes impossible. With six conditions, complete counterbalancing requires seven hundred and twenty orders. That is more than most studies can possibly run. And it would require at least that many participants to use each order once. So researchers turn to partial counterbalancing strategies instead. The goal is to achieve most of the benefit with a fraction of the orders. Which raises the obvious question. Which part of the benefit are you willing to give up?

Strategy Two

The Latin Square

The standard answer is the Latin square. It is a partial counterbalancing scheme with one guarantee. Each condition appears exactly once in each ordinal position. With four conditions, the Latin square has four rows and four columns. Each row is one possible order of the conditions. And the columns are the four positions in the sequence. Participants are randomly assigned to one of the rows. Four orders instead of twenty four, for four conditions. Across the full sample, every condition is balanced across positions. Which neutralizes symmetric carryover effects, at a fraction of the cost.

Strategy Three

Balancing the Sequences Too

But a simple Latin square gives up something, and it is worth knowing what. It balances position, and it does not balance every pairwise sequence. Some condition pairs follow each other more often than others. For symmetric carryover that does not matter, because only position mattered. For asymmetric carryover it matters a great deal. So when asymmetric carryover is a concern, use a stronger construction. A balanced Latin square, or a digram-balanced square. Those ensure each condition is preceded by every other condition equally often. They are slightly more complex to construct. And they offer stronger protection exactly where the simple square is weakest.

The Honest Limit

Averaging Out Is Not Removing

Now an honest limit on everything in this section. Counterbalancing balances the average influence of order across conditions. It does not eliminate carryover from any individual participant's data. Read that sentence twice, because it is easy to slide past. When carryover is large or asymmetric, individual participants still show order effects. Even if those effects average out neatly across the sample. So for especially sensitive manipulations, researchers do more. They add washout intervals between conditions, long enough for effects to dissipate. They split the experiment across multiple sessions. Or they abandon the within-subject design altogether, in favor of between-subjects.

Choosing

Matching Strategy to Structure

Match the strategy to the structure of your experiment. With two to four conditions and feasible sample sizes, use complete counterbalancing. Administer every order, and take the perfect balance. With five or more conditions, and symmetric carryover, use a Latin square. It balances position with a manageable number of orders. With more conditions and asymmetric carryover, upgrade to a balanced Latin square. Or a digram-balanced design, which controls the sequences directly. When carryover is severe enough that counterbalancing cannot neutralize it, change tactics. Washout intervals, multiple sessions, or a between-subjects design. And with large stimulus sets in a single session, randomize order per participant. Then record stimulus position, so you can account for it in the analysis.

Afterward

Report the Order Check

One thing remains, and it happens after the data are in. Even when counterbalancing has been applied, order effects can be tested directly. Include position as a factor in the analysis. That lets you determine whether the manipulation effect varies across positions. And it confirms that the counterbalancing actually did its work. Studies that skip this check leave readers stranded. There is no way to evaluate whether the design succeeded. It is an omission that careful peer review increasingly catches. The principle behind every strategy in this section is the same. Order is never neutral. The design must either neutralize its influence, or measure it explicitly. Treating order as if it does not matter is the most common reason these studies fail.

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FAQ

Questions students ask us

About Strategies for Managing Carryover Effects

What is a carryover effect in research?
A carryover effect is any influence of one condition on the conditions that follow it in a within-subjects design. Some carryover is obvious, such as a participant who has learned to solve a type of problem and cannot unlearn it. Subtler forms include mood carried from one task, fatigue that builds over a session, and expectations built by a sequence of manipulations. If one condition always comes first, its carryover is confounded with the comparison and cannot be separated afterward.
What is the difference between symmetric and asymmetric carryover?
Symmetric carryover affects every condition equally, depending on position rather than on which condition came before; fatigue is a common example. Counterbalancing can neutralize it because every condition appears equally often in each position. Asymmetric carryover depends on which specific condition came before, such as learning that carries strongly into related material. Balancing positions does not balance that influence, so severe asymmetric carryover may call for a different design.
How many orders does complete counterbalancing require?
Complete counterbalancing requires the factorial of the number of conditions: two orders for two conditions, six for three, 24 for four, and 720 for six. Every condition then appears in every position and precedes and follows every other condition equally often. Because the number grows so fast, complete counterbalancing is practical mainly for two to four conditions, and larger designs use partial counterbalancing such as a Latin square.
What is a Latin square in counterbalancing?
A Latin square is a partial counterbalancing scheme in which each condition appears exactly once in each ordinal position. With four conditions it uses four orders instead of 24, and participants are randomly assigned to the rows. This neutralizes symmetric carryover but does not balance every sequence. When asymmetric carryover is a concern, a balanced, or digram-balanced, Latin square ensures each condition is preceded by every other condition equally often.

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