# If “Standard error” and “Confidence intervals” measure precision of measurement, then what are the measurements of accuracy?

In book "Biostatistics for dummies" in page 40 I read:

The standard error (abbreviated SE) is one way to indicate how precise your estimate or measurement of something is.

and

Confidence intervals provide another way to indicate the precision of an estimate or measurement of something.

But there is not written anything how to indicate accuracy of the measurement.

Question: How to indicate the how accurate the measurement of something is? Which methods are used for that?

Not to be confused with Accuracy and Precision of the test: https://en.wikipedia.org/wiki/Accuracy_and_precision#In_binary_classification

• Are you asking about the accuracy of a single parameter or the accuracy of an overall model? – Steven L. Johnson Oct 20 '15 at 22:31
• Accuracy is impacted by systematic errors (or bias) – Aksakal Apr 15 '19 at 18:02
• @Aksakal and precision with random error? – vasili111 Apr 15 '19 at 18:18

Precision can be estimated directly from your data points, but accuracy is related to the experimental design. Suppose I want to find the average height of American males. Given a sample of heights, I can estimate my precision. If my sample is taken from all basketball players, however, my estimate will be biased and inaccurate, and this inaccuracy cannot be identified from the sample itself.

One way of measuring accuracy is by performing calibration of your measurement platform. By using your platform to measure a known quantity, you can reliably test the accuracy of your method. This could help you find measurement bias, e.g., if your tape measure for the height example was missing an inch, you would recognize that all your calibration samples read an inch too short. It wouldn't help fix your experimental design problem, though.

• +1..also, there can be bias in the estimation methodology, independent of the sampling plan...you can get a sense of this using bootstrapping. A good example is the $s=\sqrt{\frac{\sum (x_i-\bar x)^2}{n}}$ (which is biased low, especially for small samples). – user75138 Oct 19 '15 at 13:37

The presicion is driven by the random errors, and accuracy is defined by systematic errors. The precision often can be increased by repeated trials increasing the sample size. Accuracy cannot be fixed by collecting more data of the same measurement because systematic error won't go away.

Systematic error leads to bias of the mean and cannot be determined or fixed within the same experiment. Consider this: the whole point of your experiment is often in detecting the effect, such as deviation from zero. You measure the significance by comparing the deviation to the standard error, but that deviation may itself be a bias (systematic error)! That's why the systematic error is the worst kind of error in physical science.

In physics, for instance, you're supposed to determine the bias (systematic error) outside your experiment, then correct for it in your measurements. Interestingly, in economic forecasting field the biggest problem is the shifts of the mean, which basically an equivalent of systematic error or bias in physical sciences.

You may remember how much embarrassment the systematic error caused to the OPERA guys who "detected" neutrinos moving faster than light! They didn't account for a bunch of sources of systematic errors, and had to rescind the conclusion. After all, neutrino do not breach the speed of light, bummer!