Precision versus Accuracy

1. Precision versus Accuracy • Precision is the variation of X around <X> • expressed as standard deviation or variance • Accuracy is the closeness of <X> to the “true” value of X • Precision and accuracy are often mixed in the literature

2. Precision versus Accuracy Precise, not accurate Accurate, not precise Precise and accurate Not accurate and not precise

3. Precision and true variance Precisionunderestimates true variance Precision equals true variance Precisionoverestimates true variance

4. Normal distributions and Z-scores X - average Z = -------- sigma Remember this function has two halves. E.g. 68+16+16=100.

5. Normal distributions andRMS Z-scores X - average Z = --------------- sigma 2 ΣZ RMS-Z = -------- n RMS Z-score~0.5 RMS Z-score=1.0 (reference) RMS Z-score~2

6. Z-scores and RMS Z-scores • Local geometry RMS Z-scores: • Too tight restraining  0 < RMS Z-score < 1 • Proper Gaussian distribution  RMS Z-score 1 • Too loose restraining  1 > RMS Z-score • Structure Z-scores (normally...): • Z-scores > 0 are “better” than average • Z-scores < 0 are “worse” than average • However: AZ-score of -1 is equally likely as a Z-score of +1!! lBoth not good!