Final answer:
Effect sizes are classified as small, medium, or large based on Cohen's benchmarks. For r squared, values near 0.02 represent a small effect, near 0.13 a medium effect, and near 0.26 a large effect. Examples provided illustrate how effect sizes between 0.2 and 0.5 indicate a small effect, and those exceeding 0.8 indicate a large effect.
Step-by-step explanation:
The magnitudes of r squared (r²) for effect sizes can typically be categorized as small, medium, and large based on Cohen's benchmarks. A small effect size would have an r² around 0.02 (or Cohen's d of 0.2), a medium effect size would be around 0.13 (or Cohen's d of 0.5), and a large effect size would be around 0.26 (or Cohen's d of 0.8). These values are benchmarks and serve to give a rough estimate of the strength of a relationship; the greater the effect size, the stronger and more significant the relationship is assumed to be within the context of the studied phenomenon.
In Example 10.4, the effect size of 0.384 is between 0.2 and 0.5 (Cohen's standards for small and medium effect sizes), indicating a small effect. Whereas in Example 10.5, the effect size of 0.834 indicates a large effect because it exceeds Cohen's standard of 0.8 for a large effect size.
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