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Table 3 False alarm rate as a function of skewness in data distribution for IQR, MAD, or FAST-MCD approach with simulation

From: Input data quality control for NDNQI national comparative statistics and quarterly reports: a contrast of three robust scale estimators for multiple outlier detection

Asymmetry in data distribution Potential outlier rate by different methods
Preset skewness Estimated skewness Percentile IQR MAD FAST-MCD
0.000 −0.01(0.077) 0.025(0.005) 0.026(0.007) 0.023(0.007) 0.027(0.008)
1.000 0.983(0.116) 0.025(0.005) 0.035(0.006) 0.036(0.006) 0.078(0.013)
1.414 1.398(0.174) 0.025(0.005) 0.045(0.006) 0.049(0.007) 0.129(0.015)
1.732 1.720(0.221) 0.025(0.005) 0.053(0.007) 0.062(0.007) 0.186(0.014)
2.000 1.959(0.249) 0.025(0.005) 0.060(0.007) 0.073(0.008) 0.227(0.014)
2.236 2.197(0.286) 0.025(0.005) 0.066(0.007) 0.085(0.008) 0.260(0.014)
2.449 2.397(0.318) 0.025(0.005) 0.072(0.007) 0.097(0.009) 0.288(0.014)
2.646 2.581(0.343) 0.025(0.005) 0.077(0.007) 0.108(0.009) 0.313(0.014)
2.828 2.759(0.375) 0.025(0.005) 0.082(0.007) 0.120(0.009) 0.333(0.013)
3.000 2.928(0.409) 0.025(0.005) 0.087(0.007) 0.132(0.009) 0.351(0.013)
3.162 3.076(0.433) 0.025(0.005) 0.092(0.007) 0.144(0.019) 0.367(0.013)
3.317 3.225(0.467) 0.025(0.005) 0.096(0.007) 0.194(0.101) 0.380(0.012)
3.464 3.364(0.502) 0.025(0.005) 0.099(0.007) 0.388(0.167) 0.392(0.011)
  1. Mean rate of potential outliers with standard deviation in parenthesis for 1,000 simulated data sets at each preset skewness level.