Lesson plan
Probable error
In statistics, probable error defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside. Thus for a symmetric distribution it is equivalent to half the interquartile range, or the median absolute deviation. One such use of the term probable error in this sense is as the name for the scale parameter of the Cauchy distribution, which does not have a standard deviation. The probable error can also be expressed as a multiple of the standard deviation σ, which requires that at least the second statistical moment of the distribution should exist, whereas the other definition does not. For a normal distribution this is \gamma = 0.6745 \times \sigma ( ).
Article summary
In statistics, probable error defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside. Thus for a symmetric distribution it is equivalent to half the interquartile range, or the median absolute deviation. One such use of the term probable error in this sense is as the name for the scale parameter of the Cauchy distribution, which does not have a standard deviation. The probable error can also be expressed as a multiple of the standard deviation σ, which requires that at least the second statistical moment of the distribution should exist, whereas the other definition does not. For a normal distribution this is \gamma = 0.6745 \times \sigma ( ).
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.