Mr. Keller
Chemistry Teacher

## Precision vs. Accuracy

Precision--Precision is a measure of the repeatability of a set of measurements. When a set of measurements of the same quantity are all close together then the data are precise. If a set of measurements vary widely then they are imprecise.

Different measuring tools provide a different amount of precision just based on their design. The more lines that are marked on a ruler, the more precise measurements made with the ruler can be. With more lines it is possible to make a measurement with more certain digits before reaching the point where an estimate for the value of the last digit must be made.

A common metaphor for precision is the placement of darts on a dart-board. A dart player has good precision if he or she can throw the darts and place them all very close to one another on the board.

Precision is usually measured using a plus-or-minus amount and a percent error. If these two measures are large then there is poor precision in the measurements. This means that, although the repeated measurements should give nearly the same result, they do not. Random variation in measurement accounts for small changes which can't be eliminated. No matter how careful you are, measurements are always a little higher than average or a little lower than average. This effect is small if measurements are made carefully. It cannot account for a percent error greater than perhaps 2 - 3%.

Poor precision is may be due to more than just random error. For example, in measuring volume by displacement of water there may be bubbles included with the sample. If this is so then the amount of volume taken up by bubbles will probably not be proportional to the volume measured and will vary by some large amount from trial to trial. Poor precision must be commented on and explained in the Analysis section of a lab report.

Accuracy --Accuracy is a measure of the truth of an experimental result. It must be measured against a known and trusted standard.

In the dart-board metaphor accuracy has to do with whether the darts hit the part of the board the player aimed for. If the player is aiming for the bull’s-eye and can reliably hit it then the throws are accurate and precise. If the player aims for the bull’s-eye but can’t hit it then the throws are inaccurate.

Accuracy is a measure of how close to the truth a result is. To judge accuracy you must compare your result to a known standard. A result is the average of a group of measurements of the same thing. You can only judge accuracy if someone else has measured something to create the standard and you have reason to believe that their result is true. For example, there are scientific reference books that have been put together from decades of painstaking research. These results are checked and re-checked and are taken as standards of comparison. An untrustworthy source might be a page on the Web or a classmate. Answers from these sources may or may not be true but we have no way to judge.

You can use a percent difference to measure just how accurate a result is. The difference between your experimental result and the true result from the trusted reference is divided by the true result from the trusted reference. This quotient is multiplied by 100% to get the degree to which your result differs from the true result. Here is a formula:

```              (Your result) - (True measurement)
------------------------------------------------- x 100%
(True measurement)
```

If the percent difference is positive then your result is bigger than the true measurement by the percentage you calculated. If the percent difference is negative then your result is smaller than the true measurement.

To sum up:

1. Precision measures how close measurements are to each other.
2. Accuracy measures how close a result is to the truth.
Image source: http://climatica.org.uk/climate-science-information/uncertainty Last updated: Sep 18, 2015
Lab Report Writing Information