25 lines
1.2 KiB
Markdown
25 lines
1.2 KiB
Markdown
(Chapter 6, STAT 1040)
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# Bias v. Chance Error
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## Bias
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Bias *affects all measurements the same way, making them all too large or too small*. Bias is detected by comparing to an external standard.
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## Chance error
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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.
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- Chance error is how much an individual measurement varies from the exact value. It can be positive or negative.
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- The standard deviation of repeated measurements gives us the expected size of a chance error
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$$ IndividualMeasurement = ExactValue + ChanceError $$
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# Outliers
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Histograms of repeated measurements tend to follow the normal curve.
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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*.
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Removing outliers reduces σ.
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# Terminology
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| Term | Definition |
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| -- | -- |
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| Best Guess | Average/Mean |
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| Off by how much/Give or take | standard deviation |
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