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Sample size planning for multiple correlation: reply to Shieh (2013).

Douglas Bonett¹, Thomas Wright

¹University of California.

|July 30, 2014

Summary

This summary is machine-generated.

The Bonett-Wright sample size formula accurately estimates squared multiple correlation. A new 2-step formula for absolute precision is also accurate, making complex methods unnecessary for regression analysis.

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Area of Science:

Statistics
Psychometrics

Background:

The Bonett-Wright formula (2011) offers accurate sample size planning for squared multiple correlation (R²) estimation.
Shieh (2013) inaccurately assessed the Bonett-Wright formula's precision.

Purpose of the Study:

Evaluate the Bonett-Wright formula under broader conditions, addressing Shieh's critique.
Introduce and assess a new 2-step sample size formula for absolute precision in R² estimation.

Main Methods:

The Bonett-Wright formula's accuracy was tested under Shieh's proposed conditions.
A novel 2-step formula was developed and evaluated for absolute precision.

Main Results:

Both the Bonett-Wright formula (for relative precision) and the new 2-step formula (for absolute precision) demonstrated high accuracy.
The formulas provide reliable sample size estimations for squared multiple correlation.

Conclusions:

Simple sample size formulas are crucial for accurate multiple regression design.
Computationally intensive methods are unnecessary when simple, accurate formulas are available.