Post History
#4: Question reopened
by
Monica Cellio
·
2021-07-06T03:09:40Z (over 3 years ago)
#3: Question closed
by
Monica Cellio
·
2021-06-06T23:55:36Z (over 3 years ago)
#2: Post edited
by
Mithrandir24601
·
2021-06-02T08:18:26Z (over 3 years ago)
fixed latex formatting
- To complete the table below most comfortably for teenagers,
- 1. what are the simplest stories?
- 2. what natural numbers $\le 99$ contrast the base rate fallacy the most? Please don't repeat a number.
- I'm trying to improve on [this question](https://matheducators.stackexchange.com/q/16977/15364) that uses two-digits just $\le 20$, because
- 3. the Bayes table can be further contrasted using small with bigger ($\ge 20$) natural numbers. I don't know why Joseph O'Rourke stopped at 20, when he's using two digits anyways.
- 4. Two-digit natural numbers don't fit the common story of letting D be a disease and $H_0$ be a negative (diagnostic) test result. You need natural numbers in the thousands to contrast the huge number of false positives with the teeny number of true positives. What $H_0, D$ are more intuitive? Green denotes true positive and negative, red false positive and negative.
- $\begin{array}{r|cc|c}
\text{Number of occurrences}&D &\lnot D &\text{Total}\\ \hline- H_a &\color{green}{\Pr(D)\Pr(+|D)}&\color{red}{\Pr(D^C)\Pr(+|D^C)}&\text{add the 2 left entries}\\
H_0 &\color{red}{\Pr(D)\Pr(-|D)}&\color{green}{\Pr(D^C)\Pr(-|D^C)}&\text{add the 2 left entries}\\ \hline- \text{Total}&\text{add the 2 above entries}&\text{add the 2 above entries}&\text{two digit natural number}
- \end{array}$
- To complete the table below most comfortably for teenagers,
- 1. what are the simplest stories?
- 2. what natural numbers $\le 99$ contrast the base rate fallacy the most? Please don't repeat a number.
- I'm trying to improve on [this question](https://matheducators.stackexchange.com/q/16977/15364) that uses two-digits just $\le 20$, because
- 3. the Bayes table can be further contrasted using small with bigger ($\ge 20$) natural numbers. I don't know why Joseph O'Rourke stopped at 20, when he's using two digits anyways.
- 4. Two-digit natural numbers don't fit the common story of letting D be a disease and $H_0$ be a negative (diagnostic) test result. You need natural numbers in the thousands to contrast the huge number of false positives with the teeny number of true positives. What $H_0, D$ are more intuitive? Green denotes true positive and negative, red false positive and negative.
- $\begin{array}{r|cc|c}
- \text{Number of occurrences}&D &\lnot D &\text{Total}\\\ \\hline
- H_a &\color{green}{\Pr(D)\Pr(+|D)}&\color{red}{\Pr(D^C)\Pr(+|D^C)}&\text{add the 2 left entries}\\
- H_0 &\color{red}{\Pr(D)\Pr(-|D)}&\color{green}{\Pr(D^C)\Pr(-|D^C)}&\text{add the 2 left entries}\\\ \\hline
- \text{Total}&\text{add the 2 above entries}&\text{add the 2 above entries}&\text{two digit natural number}
- \end{array}$
#1: Initial revision
by
DNB
·
2021-06-02T07:36:40Z (over 3 years ago)
What story and two-digit Natural Numbers best fit Bayes' Theorem chart?
To complete the table below most comfortably for teenagers,
1. what are the simplest stories?
2. what natural numbers $\le 99$ contrast the base rate fallacy the most? Please don't repeat a number.
I'm trying to improve on [this question](https://matheducators.stackexchange.com/q/16977/15364) that uses two-digits just $\le 20$, because
3. the Bayes table can be further contrasted using small with bigger ($\ge 20$) natural numbers. I don't know why Joseph O'Rourke stopped at 20, when he's using two digits anyways.
4. Two-digit natural numbers don't fit the common story of letting D be a disease and $H_0$ be a negative (diagnostic) test result. You need natural numbers in the thousands to contrast the huge number of false positives with the teeny number of true positives. What $H_0, D$ are more intuitive? Green denotes true positive and negative, red false positive and negative.
$\begin{array}{r|cc|c}
\text{Number of occurrences}&D &\lnot D &\text{Total}\\ \hline
H_a &\color{green}{\Pr(D)\Pr(+|D)}&\color{red}{\Pr(D^C)\Pr(+|D^C)}&\text{add the 2 left entries}\\
H_0 &\color{red}{\Pr(D)\Pr(-|D)}&\color{green}{\Pr(D^C)\Pr(-|D^C)}&\text{add the 2 left entries}\\ \hline
\text{Total}&\text{add the 2 above entries}&\text{add the 2 above entries}&\text{two digit natural number}
\end{array}$