Guidelines for selecting variability measure in limited-size ANOVA experiments.

Area of Science:

• Applied Sciences
• Statistical Modeling
• Data Visualization

Background:

• Accurate graphical representation of variability is crucial in applied sciences.
• Choosing between pooled and individual standard deviations (SDs) is challenging in ANOVA with low replicates (n).

Purpose of the Study:

• Provide practical guidelines for selecting pooled versus individual SDs in tables and figures for low-replicate experiments.
• Aid researchers in making informed decisions about variability representation.

Main Methods:

• Extensive Monte Carlo simulations (over 2,000 scenarios) to analyze SD estimate behavior.
• Comparison of pooled and individual SD performance using Mean Absolute Deviation (MAD).
• Evaluation of Levene's and Fmax (Hartley's) tests for guiding SD selection.

Main Results:

• Pooled SDs are more accurate under homogeneity or low heterogeneity, especially for n ≤ 4.
• Individual SDs are preferable for moderate to high variance heterogeneity and n ≥ 5.
• Levene's test generally outperforms Fmax test in selecting the appropriate variability measure.

Conclusions:

• Guidelines are proposed for selecting pooled or individual SDs based on variance heterogeneity and replication number.
• These findings are directly applicable to experimental settings in applied sciences with limited replicates and treatments.
• Proper selection of variability measures enhances the accuracy of scientific communication.