Question

What source of variation is found in an ANOVA summary table for a withinsubjects design that is not in in an ANOVA summary table for a between subjects design. What happens to this source of variation in a between- subjects design?

Short answer

'Subjects' variation in within-subjects design is absent in between-subjects design; it becomes part of the error term.

Step-by-step solution

Identify Source of Variation

In an ANOVA summary table for a within-subjects design, the source of variation that is present but not in a between-subjects design is the 'subjects' or 'individuals' source of variation.

Explain the Role of 'Subjects' Variation

In a within-subjects design, the 'subjects' variation accounts for differences between individual participants that might influence the dependent variable, separate from the treatment effects. This allows one to control for these differences by analyzing how the same individuals respond across different conditions.

Consider 'Subjects' in Between-Subjects Design

In a between-subjects design, there is no 'subjects' source of variation because each participant experiences only one condition. Differences due to individual participants are treated as random error, rather than being explicitly modeled within the ANOVA. These differences contribute to the error term in between-subjects designs.

Key concepts

Within-Subjects Design

In a within-subjects design, participants are tested under all conditions of the experiment, making it a powerful tool for detecting treatment effects. This type of experimental design allows researchers to compare how the same individual behaves across different treatments. By doing so, it helps to control for inter-participant variability, since each person serves as their own control.

• Each participant experiences every level of the independent variable.
• This design minimizes the variance caused by individual differences.
• It increases the statistical power of the study.

The trade-off, however, is the potential for order effects, where the sequence of conditions affects the results. Counterbalancing is often used to mitigate these effects.

Between-Subjects Design

In contrast, a between-subjects design involves different participants assigned to separate groups, with each group experiencing only one condition. This design is straightforward in terms of setup and analysis but may require a larger sample size to achieve similar statistical power as a within-subjects design.

• Each participant is exposed to only one level of the independent variable.
• Random assignment is crucial to control for individual differences.
• It avoids issues like order effects common in within-subjects designs.

Since individual differences are not controlled as in the within-subjects design, they are included in the error term of the ANOVA. This means that variations among subjects are treated as random noise.

Source of Variation

In ANOVA, understanding the source of variation helps in identifying where the differences in your data come from. One important source of variation exclusive to within-subjects designs is the 'subjects' or 'individuals' source of variation.

• This accounts for discrepancies among participant responses that aren't related to the treatment conditions.
• It separates personal differences from treatment effects.

In a between-subjects design, any differences due to individual characteristics are not captured as a separate source. Instead, they contribute to the overall error term. By not isolating these differences, the analysis may have reduced sensitivity in detecting treatment effects. This is a key difference when interpreting ANOVA results between these two designs.