How many possible orders for full counterbalancing are there in a study with four conditions?

I. Key Points

Researchers choose to use a repeated measures design in order to (1) conduct an experiment when few participants are available, (2) conduct the experiment more efficiently, (3) increase the sensitivity of the experiment, and (4) study changes in participants' behavior over time.

Repeated measures designs cannot be confounded by individual differences variables because the same individuals participate in each condition (level) of the independent variable.

Participants' performance in repeated measures designs may change across conditions simply because of repeated testing (not because of the independent variable); these changes are called practice effects.

Practice effects may threaten the internal validity of a repeated measures experiment when the different conditions of the independent variable are presented in the same order to all participants.

The two types of repeated measures designs, complete and incomplete, differ in the specific ways they control for practice effects.

Balancing Practice Effects in the Complete Design

Practice effects are balanced in complete designs within each participant using block randomization or ABBA counterbalancing.

In block randomization, all of the conditions of the experiment (a block) are randomly ordered each time they are presented.

In ABBA counterbalancing, a random sequence of all conditions is presented, followed by the opposite of the sequence.

Block randomization is preferred over ABBA counterbalancing when practice effects are not linear, or when participants' performance can be affected by anticipation effects.

Balancing Practice Effects in the Incomplete Design

Practice effects are balanced across subjects in the incomplete design rather than for each subject, as in the complete design.

The rule for balancing practice effects in the incomplete design is that each condition of the experiment must be presented in each ordinal position (first, second, etc.) equally often.

The best method for balancing practice effects in the incomplete design with four or fewer conditions is to use all possible orders of the conditions.

Two methods for selecting specific orders to use in an incomplete design are the Latin Square and random starting order with rotation.

Whether using all possible orders or selected orders, participants should be randomly assigned to the different sequences.

Describing the Results

Data analysis for a complete design begins with computing a summary score (e.g., mean, median) for each participant.

Descriptive statistics are used to summarize performance across all participants for each condition of the independent variable.

Confirming What the Results Reveal

The general procedures and logic for null hypothesis testing and for confidence intervals for repeated measures designs are similar to those used for random groups designs.

Differential transfer occurs when the effects of one condition persist and influence performance in subsequent conditions.

Variables that may lead to differential transfer should be tested using a random groups design because differential transfer threatens the internal validity of repeated measures designs.

Differential transfer can be identified by comparing the results for the same independent variable when tested in a repeated measures design and in a random groups design.

II. Glossary

repeated measures designs Research designs in which each subject participates in all conditions of the experiment (i.e., measurement is repeated on the same subject).

sensitivity Refers to the likelihood in an experiment that the effect of an independent variable will be detected when that variable does, indeed, have an effect; sensitivity is increased to the extent that error variation is reduced (e.g., by holding conditions constant rather than balancing them).

practice effects Changes that participants undergo with repeated testing. Practice effects are the summation of both positive (e.g., familiarity with a task) and negative (e.g., boredom) factors associated with repeated measurement.

counterbalancing A control technique for distributing (balancing) practice effects across the conditions of a repeated measures design. How counterbalancing is accomplished depends on whether a complete or an incomplete repeated measures design is used.

differential transfer Potential problem in repeated measures designs when performance in one condition differs depending on the condition preceding it.

Counterbalancing is a technique used to deal with order effects when using a repeated measures design. With counterbalancing, the participant sample is divided in half, with one half completing the two conditions in one order and the other half completing the conditions in the reverse order. E.g., the first 10 participants would complete condition A followed by condition B, and the remaining 10 participants would complete condition B and then A. Any order effects should be balanced out by this technique.

How many groups of participants would be needed to fully counterbalance four treatment conditions?

How many different orders would you need for complete counterbalancing in a repeated measures design with one factor that has 7 levels?

What is full counterbalancing in psychology?

How is counterbalancing calculated?