Design of Experiments > Accuracy and Precision

In any experiment, it is impossible to achieve perfect measurements (even the best atomic clock isn’t flawless: it loses a second every 300 billion years)[1]. The degree to which your measurement deviates from the true value is called **accuracy**.

Another concept closely related to accuracy is **precision**, which describes the *quality *of your measurements.

## Accuracy

**Accuracy is how close you are to the true value or theoretical value.** For example, let’s say you know your true height is exactly 5’9″.

- You measure yourself with a yardstick and get 5’0″. Your measurement is not accurate.
- You measure yourself again with a laser yardstick and get 5’9″. Your measurement is accurate.

**Note**: The true value is sometimes called the *theoretical value*.

## Precision

**Precision is how close two or more measurements are to each other**. If you consistently measure your height as 5’0″ with a yardstick, your measurements are precise.

## Accuracy of Analysis and Precision Together

If you are precise, that doesn’t necessarily mean you are accurate. However, if you are consistently accurate, you are also precise.

### “More” Precise

If you want to tell which set of data is more precise, find the range (the difference between the highest and lowest scores). For example, let’s say you had the following two sets of data:

- Sample A: 32.56, 32.55, 32.48, 32.49, 32.48.
- Sample B: 15.38, 15.37, 15.36, 15.33, 15.32.

Subtract the lowest data point from the highest:

- Sample A: 32.56 – 32.48 = .08.
- Sample B: 15.38 – 15.32 = .06.

**Sample B has the lowest range (.06) and so is the more precise.**

## More Examples

While accuracy is “how close to the mark,” precision is “how close measurements are together.” If you measure once and get the true value, you’re accurate. If you consistently measure the true value over repeated measurements, you are precise.

**Accurate and precise:**If a weather thermometer reads 75^{o}F outside and it really is 75^{o}F, the thermometer is accurate. If the thermometer consistently registers the exact temperature for several days in a row, the thermometer is also precise.**Precise, but not accurate**: A refrigerator thermometer is read ten times and registers degrees Celsius as: 39.1, 39.4, 39.1, 39.2, 39.1, 39.2, 39.1, 39.1, 39.4, and 39.1. However, the real temperature inside the refrigerator is 37 degrees C. The thermometer isn’t accurate (it’s almost two degrees off the true value), but as the numbers are all close to 39.2, it*is*precise.

## Why accuracy in statistics is important

Accuracy in statistics is important because it helps us draw good conclusions from data. Inaccurate data leads to incorrect conclusions, which could result in poor decisions with adverse consequences. While it might not be important if you aren’t accurate when measuring your own weight, mismeasurement of weight in a clinical setting could result in serious consequences.

Several factors can have an impact on data accuracy, including:

- Poor data collection methods.
- Applying incorrect statistical methods, such as using a chi-square test on data that isn’t random,.
- Misinterpreting results.

To boost data accuracy, follow these good practices:

- Use the right sampling method for your design, gather data from representative samples if possible (although sometimes you might be forced to use a less rigid method such as convenience sampling), and be aware of any bias.
- Use suitable tests for the data and adhere to correct assumptions for those tests.
- Understand your data’s limitations. For example, avoid inferring causality from correlation.

## References

[1] Howell, E. (2022). New atomic clock loses only one second every 300 billion years.