Estimating upper confidence bounds for positive ratios of normal random variables

Abstract

Positive ratios of normal random variables are required for meaningful advertising claims. Positive ratios less than 1 for supporting superiority claims on attributes deemed important to minimize (e.g., our soap cleans effectively and is only 1/3 as harsh as the leading competitor) require estimating (1 − α) upper confidence bounds (UCBs) to protect against unwarranted deflated estimates. Here, we extend the ratio and multiplicative methods to estimate the UCB. Results show that the UCBs estimated by the ratio method are superior to those estimated by the multiplicative method and that the ratio method maintains inverse relation between the ratios X/Y and Y/X.

Keywords:

• Benefits
• Claims
• Confidence bounds
• Detractors
• Multiplicative statements
• Positive ratio
• Ratio of normal random variables
• Ratio statements