Talk:Accuracy and precision
From AWF-Wiki
(Difference between revisions)
| Line 5: | Line 5: | ||
::*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. The standard error of the mean is the standard deviation of the estimated means. So the question how precise a sample based estimate is, can be answered by looking at the distribution of estimates (here we are interested in the distribution of all possible sample outcomes that stays unknown. Therefore we estimate the standard error based on the sample at hand). But this distribution gives us no insight in the accuracy of an estimate (means: accuracy cannot be measured by the standard error!). 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) | ::*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. The standard error of the mean is the standard deviation of the estimated means. So the question how precise a sample based estimate is, can be answered by looking at the distribution of estimates (here we are interested in the distribution of all possible sample outcomes that stays unknown. Therefore we estimate the standard error based on the sample at hand). But this distribution gives us no insight in the accuracy of an estimate (means: accuracy cannot be measured by the standard error!). 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) | ||
| + | |||
:::*Thank you Lutz! Still, the ''standard error of the mean'' can give us an estimation for an interval, in which the unknown true mean may lie, right? - Yet, it won't give us any information about the bias... [[User:Lburgr|- Levent]] 11:47, 15 January 2011 (CET) | :::*Thank you Lutz! Still, the ''standard error of the mean'' can give us an estimation for an interval, in which the unknown true mean may lie, right? - Yet, it won't give us any information about the bias... [[User:Lburgr|- Levent]] 11:47, 15 January 2011 (CET) | ||
| + | |||
::::*Correct! It's even more, because there is a defined confidence interval around the estimated mean. That means we expect the true population parameter to lie in this interval with a defined and known probability. The point is that the true population parameter stays known. Therefore we are not able to estimate the "true" bias of an estimate. We have to trust that the applied sampling design, plot design and estimators allow unbiased estimates (unbiasedness is therefore a characteristic of an estimator and not of the estimate). [[User:Fehrmann|Fehrmann]] 09:39, 7 July 2011 (CEST) | ::::*Correct! It's even more, because there is a defined confidence interval around the estimated mean. That means we expect the true population parameter to lie in this interval with a defined and known probability. The point is that the true population parameter stays known. Therefore we are not able to estimate the "true" bias of an estimate. We have to trust that the applied sampling design, plot design and estimators allow unbiased estimates (unbiasedness is therefore a characteristic of an estimator and not of the estimate). [[User:Fehrmann|Fehrmann]] 09:39, 7 July 2011 (CEST) | ||
Latest revision as of 14:15, 19 September 2011
[edit] 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. The standard error of the mean is the standard deviation of the estimated means. So the question how precise a sample based estimate is, can be answered by looking at the distribution of estimates (here we are interested in the distribution of all possible sample outcomes that stays unknown. Therefore we estimate the standard error based on the sample at hand). But this distribution gives us no insight in the accuracy of an estimate (means: accuracy cannot be measured by the standard error!). 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)
- Thank you Lutz! Still, the standard error of the mean can give us an estimation for an interval, in which the unknown true mean may lie, right? - Yet, it won't give us any information about the bias... - Levent 11:47, 15 January 2011 (CET)
- Correct! It's even more, because there is a defined confidence interval around the estimated mean. That means we expect the true population parameter to lie in this interval with a defined and known probability. The point is that the true population parameter stays known. Therefore we are not able to estimate the "true" bias of an estimate. We have to trust that the applied sampling design, plot design and estimators allow unbiased estimates (unbiasedness is therefore a characteristic of an estimator and not of the estimate). Fehrmann 09:39, 7 July 2011 (CEST)
