ISO TC209 WG1, Nov. 11, 2005.Page 1 ISO TC209 WG1 N Statistical Issues - reissue.ppt ISO Statistical Issues Mark Varney, Statistician ISO TC209 WG1 Nov. 11, 2005

ISO TC209 WG1, Nov. 11, 2005.Page 2 Table C.1 – Student’s t Table C.1 is correct –Confidence limit is 1-sided May wish to add an additional significant digit Add reference since different from GUM table –GUM table is 2-sided

ISO TC209 WG1, Nov. 11, 2005.Page 3 95% Upper Confidence Limit(UCL) Current requirement: For m = 2 to 9 locations 1.All location means must meet limit -- AND % UCL based on location means must meet limit

ISO TC209 WG1, Nov. 11, 2005.Page 4 95% Upper Confidence Limit(UCL) 1.For 5-9 locations, requirement for locations to be within limits provides 95% confidence mean is in limit. Calculation of 95% UCL is superfluous.

ISO TC209 WG1, Nov. 11, 2005.Page 5 95% Upper Confidence Limit(UCL) 2. “False alarm” rate of failing 95% UCL requirement when room is OK is high for 2-3 locations Example: Suppose limit calculated per section 3.2 is 1000 Room average=700, std dev=100, normal distribution m: # locations Probability of failing UCL requirement 250% 37%

ISO TC209 WG1, Nov. 11, 2005.Page 6 95% Upper Confidence Limit(UCL) 3.Intent of ISO appears to be that entire room - all locations - should be in limits 95% UCL for mean only relates to the overall room mean being within limits 4.95% UCL calculation is sensitive to outliers 5.Particulate is seldom normally distributed UCL calculation assumes normal distribution Not a critical assumption, though; method is robust

ISO TC209 WG1, Nov. 11, 2005.Page 7 Recommendation: Eliminate 95% UCL 1.For m=5-9, already have 95% confidence - For 4 locations, confidence is almost 95% (93.8%) 2.False alarm rate is too high for m= % UCL relates to room mean; meaningful? 4.Sensitivity to outliers 5.Normality assumption often not met

ISO TC209 WG1, Nov. 11, 2005.Page 8 Possible Statistical Approaches Goal: Show that limits are met throughout room Suggested strategy –Sample enough locations to show with X% confidence that at least Y% of locations meet limit Statistical Approach: tolerance limits –Nonparametric –Parametric (smaller N L, but assume normality)

ISO TC209 WG1, Nov. 11, 2005.Page 9 Suggested Statistical Approach Select # locations to provide 90% confidence that at least 90% of locations meet limit

ISO TC209 WG1, Nov. 11, 2005.Page 10 Suggested Statistical Approach Tighter confidence/verification by room class