1.2 KiB
(Chapter 6, STAT 1040)
Bias v. Chance Error
Bias
Bias affects all measurements the same way, making them all too large or too small. Bias is detected by comparing to an external standard.
Chance error
Chance errors change from measurement to measurement but average out over time. There is no way to remove all chance errors from a measuring process. An example of chance error would be starting a stopwatch then attempting to stop it at exactly 5 seconds, then repeating. The times will vary, but each measurement will vary in a different way.
- Chance error is how much an individual measurement varies from the exact value. It can be positive or negative.
- The standard deviation of repeated measurements gives us the expected size of a chance error
IndividualMeasurement = ExactValue + ChanceError Outliers
Histograms of repeated measurements tend to follow the normal curve.
According to the empirical rule, 99.7% of such measurements should be +-3σ of the exact value. Measurements that are not within 3σ are considered outliers.
Removing outliers reduces σ.
Terminology
| Term | Definition |
|---|---|
| Best Guess | Average/Mean |
| Off by how much/Give or take | standard deviation |