Which Measure Should be Used for Testing in a Paired Design: Simple Difference, Percent Change, or Symmetrized Percent Change?

Abstract

We aimed to determine the most proper change measure among simple difference, percent, or symmetrized percent changes in simple paired designs. For this purpose, we devised a computer simulation program. Since distributions of percent and symmetrized percent change values are skewed and bimodal, paired t-test did not give good results according to Type I error and the test power. To be to able use percent change or symmetrized percent change as change measure, either the distribution of test statistics should be transformed to a known theoretical distribution by transformation methods or a new test statistic for these values should be developed.

Keywords:

• Change measures
• Paired designs
• Percent change
• Simple difference
• Symmetrized percent change

Mathematics Subject Classification:

• 62-xx (Statistics)
• 62-07 (Data analysis)

Notes

ρ correlation coefficient between before and after measurements; σ₁ and σ₂ standard deviations; μ₁ and μ₂ means of before and after measurements in population.

ρ correlation coefficient between before and after measurements; σ₁ and σ₂ standard deviations; μ₁ and μ₂ means of before and after measurements in population.

ρ correlation coefficient between before and after measurements; σ₁ and σ₂ standard deviations; μ₁ and μ₂ means of before and after measurements in population.

ρ correlation coefficient between before and after measurements; σ₁ and σ₂ standard deviations; μ₁ and μ₂ means of before and after measurements in population.

ρ correlation coefficient between before and after measurements; σ₁ and σ₂ standard deviations; μ₁ and μ₂ means of before and after measurements in population.