Final answer:
Correlated or paired designs are more powerful than independent designs because they control extraneous variables, handle inter-subject variability by comparing within subjects or matched individuals thus reducing noise in data, and reduce error variance which increases statistical power to detect treatment effects.
Step-by-step explanation:
Paired (or correlated) designs are considered more powerful than independent designs due to a number of reasons. When analyzing the effectiveness of treatments or interventions on subjects, using matched pairs allows researchers to compare two related samples, such as measurements taken from the same individuals at different times or from matched subjects like married couples. In independent groups, on the other hand, participants are randomly assigned, so the samples are not related, and as such, factors other than the treatment can contribute to any differences seen between groups.
Control of extraneous variables is one reason paired designs can be more powerful. Because the two measurements in a paired design are correlated, any variation due to external factors is likely to affect both measures, which can be controlled for in the analysis, leading to greater precision. Additionally, paired designs have an advantage of effectively dealing with inter-subject variability, as comparisons are made within the same subject or between closely matched subjects, reducing the noise in the data and allowing for clearer detection of effects.
Reduction in error variance also contributes to the increased power of paired designs. By using the same subjects, or matched subjects, researchers are better able to account for individual differences that are unrelated to the experimental manipulation, thus reducing error variance.