Talk:Accuracy and precision
From AWF-Wiki
(Difference between revisions)
(→One statistical question) |
|||
| Line 1: | Line 1: | ||
==One statistical question== | ==One statistical question== | ||
* Just to get my own statistical knowledge straight: Is '''precision''' quantified by the ''variance'' or the ''standard deviation'' while '''accuracy''' can be measured as the ''standard error of the mean''? <br> <u> Estimators </u>as i recall them - just for some TeX training:<br> Variance <math> s^2 = \sum_{i=1}^n (x_i-\bar{x})^2/(n-1)</math> <br> Standard deviation <math> s= \sqrt{s^2} </math> <br> Standard error of the mean (for large populations) <math> \hat{s} = \sqrt{s^2/n} </math><br> Help me out here! [[User:Lburgr|- Levent]] 12:08, 14 January 2011 (CET) | * Just to get my own statistical knowledge straight: Is '''precision''' quantified by the ''variance'' or the ''standard deviation'' while '''accuracy''' can be measured as the ''standard error of the mean''? <br> <u> Estimators </u>as i recall them - just for some TeX training:<br> Variance <math> s^2 = \sum_{i=1}^n (x_i-\bar{x})^2/(n-1)</math> <br> Standard deviation <math> s= \sqrt{s^2} </math> <br> Standard error of the mean (for large populations) <math> \hat{s} = \sqrt{s^2/n} </math><br> Help me out here! [[User:Lburgr|- Levent]] 12:08, 14 January 2011 (CET) | ||
| + | |||
| + | ::You are right with the first statement: precision is something that is related to the width of the distribution (or the confidence interval) around an estimated mean. So the question how precise a sample based estimate is, can be answered by looking at the distribution of estimates. But this distribution gives us no insight in the accuracy of an estimate. An estimated mean can be very precise (all single estimates are very close together and the confidence interval in which we expect the true mean with a certain probability is very narrow) but still not accurate. Imagine your measurement device is not calibrated and all measurements are systematically too small. This error is known as bias or systematic error and can not be compensated by a higher sample size. You can likewise imagine an biased estimator (formula) that is not appropriate to approximate the true value. In practice the share of this measurement error on the total error is often unknown.[[User:Fehrmann|Fehrmann]] 14:56, 14 January 2011 (CET) | ||
Revision as of 15:56, 14 January 2011
One statistical question
- Just to get my own statistical knowledge straight: Is precision quantified by the variance or the standard deviation while accuracy can be measured as the standard error of the mean?
Estimators as i recall them - just for some TeX training:
Variance \( s^2 = \sum_{i=1}^n (x_i-\bar{x})^2/(n-1)\)
Standard deviation \( s= \sqrt{s^2} \)
Standard error of the mean (for large populations) \( \hat{s} = \sqrt{s^2/n} \)
Help me out here! - Levent 12:08, 14 January 2011 (CET)
- You are right with the first statement: precision is something that is related to the width of the distribution (or the confidence interval) around an estimated mean. So the question how precise a sample based estimate is, can be answered by looking at the distribution of estimates. But this distribution gives us no insight in the accuracy of an estimate. An estimated mean can be very precise (all single estimates are very close together and the confidence interval in which we expect the true mean with a certain probability is very narrow) but still not accurate. Imagine your measurement device is not calibrated and all measurements are systematically too small. This error is known as bias or systematic error and can not be compensated by a higher sample size. You can likewise imagine an biased estimator (formula) that is not appropriate to approximate the true value. In practice the share of this measurement error on the total error is often unknown.Fehrmann 14:56, 14 January 2011 (CET)
