Credence (statistics): Difference between revisions
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Expanded the example to show how credence converts to gambling odds. |
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If a bag contains 4 red marbles and 1 blue marble, and a person withdraws one marble at random, then they should believe with 80% credence that the random marble will be red. In this example, the [[probability]] of drawing a red marble is 80%. |
If a bag contains 4 red marbles and 1 blue marble, and a person withdraws one marble at random, then they should believe with 80% credence that the random marble will be red. In this example, the [[probability]] of drawing a red marble is 80%. |
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Credence values can be based entirely on subjective feelings.<ref name="Critch" /><ref name="Strevens" /> For example, if Alice is fairly certain that she saw Bob at the grocery store on Monday, then she might say, "I believe with 90% credence that Bob was at the grocery store on Monday." If the prize for being correct is $100, then Alice will wager $89 that her memory is accurate, but she would not be willing to wager $91 or more. |
Credence values can be based entirely on subjective feelings.<ref name="Critch" /><ref name="Strevens" /> For example, if Alice is fairly certain that she saw Bob at the grocery store on Monday, then she might say, "I believe with 90% credence that Bob was at the grocery store on Monday." If the prize for being correct is $100, then Alice will wager $89 that her memory is accurate, but she would not be willing to wager $91 or more. Given that Alice is 90% credent, that can be expressed as gambling odds in the following ways: |
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* 90% credence |
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* 1 / 9 fractional odds (1 to 9) |
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* 1.11 decimal odds |
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* -900 moneyline odds |
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* The return on a $100 wager is $11.11 (plus the $100 initial wager). |
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==References== |
==References== |
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Revision as of 17:04, 25 December 2014
Credence is a statistical term that expresses how much a person believes that a proposition is true.[1] As an example, a reasonable person will believe with 50% credence that a fair coin will land on heads the next time it is flipped. If the prize for correctly predicting the coin flip is $100, then a reasonable person will wager $49 on heads, but they will not wager $51 on heads.
Credence is a measure of belief strength, expressed as a percentage. Credence values range from 0% to 100%. Credence is deeply related to odds, and a person's level of credence is directly related to the odds at which they will place a bet. Credence is especially important in Bayesian statistics. If a scientific article reports a 95% confidence interval for a particular value that is being measured, then a reader should believe with 95% credence that the true value falls within that 95% confidence interval (assuming the reader trusts the authors and the experimental methods).[2]
If a bag contains 4 red marbles and 1 blue marble, and a person withdraws one marble at random, then they should believe with 80% credence that the random marble will be red. In this example, the probability of drawing a red marble is 80%.
Credence values can be based entirely on subjective feelings.[1][2] For example, if Alice is fairly certain that she saw Bob at the grocery store on Monday, then she might say, "I believe with 90% credence that Bob was at the grocery store on Monday." If the prize for being correct is $100, then Alice will wager $89 that her memory is accurate, but she would not be willing to wager $91 or more. Given that Alice is 90% credent, that can be expressed as gambling odds in the following ways:
- 90% credence
- 1 / 9 fractional odds (1 to 9)
- 1.11 decimal odds
- -900 moneyline odds
- The return on a $100 wager is $11.11 (plus the $100 initial wager).
References
- ^ a b Critch, Andrew. "Credence – a measure of belief strength". Retrieved 18 December 2014.
- ^ a b Strevens, Michael. "Notes on Bayesian Confirmation Theory" (PDF). New York University. Retrieved 18 December 2014.