Template:ConfidenceInterval: Difference between revisions
From HorizonXI Wiki
(Created page with "<includeonly><onlyinclude><!-- standard case: return an estimation of the 95% confidence interval -->{{#ifexpr: {{{1}}} > 3 and {{{1}}} < ({{{2}}} - 3) | +/- {{#expr: 100*(1.96 * (sqrt (({{{1}}} / {{{2}}}) * (1-({{{1}}} / {{{2}}})) / {{{2}}} ))) round {{{digits|2}}}}}<!-- -->|<!-- if less than three success registered, use "rule of 3" for the upper bound -->{{#ifexpr: {{{1}}} <= 3 and {{{1}}} >= 0 | + {{#expr: 100* 3/{{{2}}} round {{{digits|2}}}}}<!-- -->|<!-- if nearly...") |
m (added trivial case of zero sample to return nothing at all) |
||
| (4 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
<includeonly><onlyinclude><!-- | <includeonly><onlyinclude><!-- | ||
If no sample at all, return nothing | |||
-->{{#ifeq:{{{2}}}|0||<!-- | |||
standard case: return an estimation of the 95% confidence interval | standard case: return an estimation of the 95% confidence interval | ||
-->{{#ifexpr: {{{1}}} > 3 and {{{1}}} < ({{{2}}} - 3) | +/- {{#expr: 100*(1.96 * (sqrt (({{{1}}} / {{{2}}}) * (1-({{{1}}} / {{{2}}})) / {{{2}}} ))) round {{{digits| | -->{{#ifexpr: {{{1}}} > 3 and {{{1}}} < ({{{2}}} - 3) |+/-{{#expr: 100*(1.96 * (sqrt (({{{1}}} / {{{2}}}) * (1-({{{1}}} / {{{2}}})) / {{{2}}} ))) round {{{digits|1}}}}}<!-- | ||
-->|<!-- | -->|<!-- | ||
if less than three success registered, use "rule of 3" for the upper bound | if less than three success registered, use "rule of 3" for the upper bound | ||
-->{{#ifexpr: {{{1}}} <= 3 and {{{1}}} >= 0 | + {{#expr: 100* 3/{{{2}}} round {{{digits| | -->{{#ifexpr: {{{1}}} <= 3 and {{{1}}} >= 0 |+/-{{#expr: 100* 3/{{{2}}} round {{{digits|1}}}}}<!-- | ||
-->|<!-- | -->|<!-- | ||
if nearly all draws end in successes, use "rule of 3" for the lower bound | if nearly all draws end in successes, use "rule of 3" for the lower bound | ||
-->{{#ifexpr: {{{1}}} >= ({{{2}}} - 3) and {{{1}}} <= {{{2}}} | - {{#expr: 100* 3/{{{2}}} round {{{digits| | -->{{#ifexpr: {{{1}}} >= ({{{2}}} - 3) and {{{1}}} <= {{{2}}} |+/-{{#expr: 100* 3/{{{2}}} round {{{digits|1}}}}}<!-- | ||
-->|<!-- | -->|<!-- | ||
-->}}<!-- | -->}}<!-- | ||
-->}}<!-- | -->}}<!-- | ||
-->}}<!-- | -->}}<!-- | ||
--></onlyinclude></includeonly> | -->}}</onlyinclude></includeonly> | ||
==Usage== | ==Usage== | ||
Calculates the 95% confidence interval for inputs k successes on n total number of draws. Returns a percentage value without % sign with | Calculates the 95% confidence interval for inputs k successes on n total number of draws. Returns a percentage value without % sign with one decimal (if more or less digits are desired, use the digits argument). | ||
<pre>{{ConfidenceInterval|k|n}}</pre> | <pre>{{ConfidenceInterval|k|n}}</pre> | ||
*50 success on 100 draws represents a success rate of ({{#expr: 100*(50/100)}} {{ConfidenceInterval|50|100}})% | *50 success on 100 draws represents a success rate of ({{#expr: 100*(50/100)}}{{ConfidenceInterval|50|100}})% | ||
*250 success on 500 draws represents a success rate of ({{#expr: 100*(250/500)}} {{ConfidenceInterval|250|500}})% | *250 success on 500 draws represents a success rate of ({{#expr: 100*(250/500)}}{{ConfidenceInterval|250|500}})% | ||
*50 success on 500 draws represents a success rate of ({{#expr: 100*(50/500)}} {{ConfidenceInterval|50|500|digits=5}})% (displaying up to 5 digits with the digits argument here). | *50 success on 500 draws represents a success rate of ({{#expr: 100*(50/500)}}{{ConfidenceInterval|50|500|digits=5}})% (displaying up to 5 digits with the digits argument here). | ||
*100 success on 100 draws represents a success rate of ({{#expr: 100*(100/100)}} {{ConfidenceInterval|100|100}})% | *100 success on 100 draws represents a success rate of ({{#expr: 100*(100/100)}}{{ConfidenceInterval|100|100}})% | ||
*0 success on 100 draws represents a success rate of ({{#expr: 100*(0/100)}} {{ConfidenceInterval|0|100}})% | *0 success on 100 draws represents a success rate of ({{#expr: 100*(0/100)}}{{ConfidenceInterval|0|100}})% | ||
*4765 success on 4765 draws represents a success rate of ({{#expr: 100*(4765/4765)}} {{ConfidenceInterval|4765|4765}})% | *1 success on 100 draws represents a success rate of ({{#expr: 100*(1/100)}}{{ConfidenceInterval|1|100}})% | ||
*0 success on 365 draws represents a success rate of ({{#expr: 100*(0/365)}} {{ConfidenceInterval|0|365}})% | *2 successes on 100 draws represents a success rate of ({{#expr: 100*(2/100)}}{{ConfidenceInterval|2|100}})% | ||
*100 success on 10 draws represents a success rate of ({{#expr: 100*(100/10)}} {{ConfidenceInterval|100|10}})% (this is a case where the confidence interval makes no sense, thus it is not reported if k > n). | *3 successes on 100 draws represents a success rate of ({{#expr: 100*(3/100)}}{{ConfidenceInterval|3|100}})% | ||
*4 successes on 100 draws represents a success rate of ({{#expr: 100*(4/100)}}{{ConfidenceInterval|4|100}})% | |||
*4765 success on 4765 draws represents a success rate of ({{#expr: 100*(4765/4765)}}{{ConfidenceInterval|4765|4765}})% | |||
*0 success on 365 draws represents a success rate of ({{#expr: 100*(0/365)}}{{ConfidenceInterval|0|365}})% | |||
*100 success on 10 draws represents a success rate of ({{#expr: 100*(100/10)}}{{ConfidenceInterval|100|10}})% (this is a case where the confidence interval makes no sense, thus it is not reported if k > n). | |||
*Trivial case of zero sized sample returns nothing at all: | |||
<pre>{{ConfidenceInterval|0|0}}</pre> | |||
{{ConfidenceInterval|0|0}} | |||
Latest revision as of 20:46, 12 January 2024
Usage
Calculates the 95% confidence interval for inputs k successes on n total number of draws. Returns a percentage value without % sign with one decimal (if more or less digits are desired, use the digits argument).
{{ConfidenceInterval|k|n}}
- 50 success on 100 draws represents a success rate of (50+/-9.8)%
- 250 success on 500 draws represents a success rate of (50+/-4.4)%
- 50 success on 500 draws represents a success rate of (10+/-2.62962)% (displaying up to 5 digits with the digits argument here).
- 100 success on 100 draws represents a success rate of (100+/-3)%
- 0 success on 100 draws represents a success rate of (0+/-3)%
- 1 success on 100 draws represents a success rate of (1+/-3)%
- 2 successes on 100 draws represents a success rate of (2+/-3)%
- 3 successes on 100 draws represents a success rate of (3+/-3)%
- 4 successes on 100 draws represents a success rate of (4+/-3.8)%
- 4765 success on 4765 draws represents a success rate of (100+/-0.1)%
- 0 success on 365 draws represents a success rate of (0+/-0.8)%
- 100 success on 10 draws represents a success rate of (1000)% (this is a case where the confidence interval makes no sense, thus it is not reported if k > n).
- Trivial case of zero sized sample returns nothing at all:
{{ConfidenceInterval|0|0}}
