diff --git a/README.md b/README.md index 5d25abc..5dad07b 100644 --- a/README.md +++ b/README.md @@ -7,7 +7,7 @@ https://github.com/YujiSODE/draw2Sample >See LICENSE or http://opensource.org/licenses/mit-license.php ______ -##Concept +## Concept ![Concept of graphical sampling:draw2Sample_Fig.png](./draw2Sample_Fig.png) __Figure 1. Concept of graphical sampling.__ _f_ (_x_) is a graph drawn on graphical data (_W_ x _H_ px). @@ -19,16 +19,16 @@ and RGBA color value in a pixel is available in order to recognize the shape of the graph. The alpha value is used in this program; a pixel where alpha > 0 is regarded as graph. -##Script +## Script * draw2Sample.js * \[v1.2+\] pValue.js -##How to generating values following a given distribution +## How to generating values following a given distribution 1. __"Sample (_Sp_)":__ ["Rnd"](#output-data) in the result output of "draw2Sample.js" 2. __Generating target values;__ the target values are obtained with bootstrap Method (Efron,1979) via _Sp_. 3. __\(Optional \[v1.2+\]\) Estimating _p_-value;__ _p_-value is estimated with "pValue.js" via _Sp_. -##How to use +## How to use * call "draw2Sample()" in a html file with img/canvas tag. * \(Optional \[v1.2+\]\) call "_pValue()" of "pValue.js", in order to estimate _p_-value; (see [__Estimating _p_-value__](#v12-estimating-p-value) for details of prameters). @@ -43,7 +43,7 @@ The alpha value is used in this program; a pixel where alpha > 0 is regarded as 3. __Sampling__ The sampling from the given graph (2.) is run with __"Run sampling" button__, and the result output is shown in __"Result"__. - ####_Inputs and buttons_ + #### _Inputs and buttons_ * __"Target width":__ the target sampling area, expressed with left side x coordinate (x0) and width (w), shown in red. * __"Sampling interval";__ it sets how many times the given graph (2.) is sampled in a given target area, starting with x0. * __"Range of values":__ the true x-coordinate values in the target sampling area, expressed with left side (v0) and right side (v). @@ -58,14 +58,14 @@ The alpha value is used in this program; a pixel where alpha > 0 is regarded as * __"Email address":__ email address used outputting __"Result"__ as email format. * __"Output as email" button;__ it saves the __"Result"__ as email to given address. - ####_Output data_ + #### _Output data_ * __dataLog:__ csv formatted values expressed as _n_@_y_ for a _n_-th sampling result: _y_ with top left corner as origin. * __*x*@*f(x)*:__ csv formatted values expressed as _x_@_f_ (_x_) for a value of _f_ (_x_) at _x_ with bottom left as origin. * __Rnd:__ csv formatted values estimated as results of a sampling. ______ -##\[v1.2+\] Estimating _p_-value -####__"pValue.js"__ +## \[v1.2+\] Estimating _p_-value +#### __"pValue.js"__ * Probability estimator with given numerical data and bootstrap Method (Efron,1979) on Firefox. `_pValue(data,x,sampleSize,simulation)` `/*` @@ -79,18 +79,18 @@ ______ _p_-value is estimated as probability on v-axis: _P_(`x`) = _P_(_v_ >= `x`). The estimation is based on resampled data with size (`sampleSize`) for n-time (`simulation`) simulations. -####Examples +#### Examples Script 1: `_pValue('1,2');` the result: `{"p":0.504,"x":1.75,"sampleSize":100,"simulation":10}` Script 2: `_pValue('1,2,3');` the result: `{"p":0.323,"x":2.5,"sampleSize":100,"simulation":10}` Script 3: `_pValue('1,2,3',1.1);` the result: `{"p":0.676,"x":1.1,"sampleSize":100,"simulation":10}` Script 4: `_pValue('1,2,3',2,10,1);` the result: `{"p":0.6,"x":2,"sampleSize":10,"simulation":1}` ______ -##Example with the standard normal distribution -###Script used for drawing graph +## Example with the standard normal distribution +### Script used for drawing graph * stdNormDist100pt.js -###Sampling parameters +### Sampling parameters `/*Fri_Sep_09_2016_17:01:16_GMT+0900_(JST),Sampling interval:20,Size: W x H = 400 x 400 px*/` ![Sampling example with the standard normal distribution by script:stdNormDist_scriptOutputAll.jpg](./stdNormDist_scriptOutputAll.jpg) @@ -98,7 +98,7 @@ __Figure 2. Sampling example with the standard normal distribution by script.__ of the standard normal distribution by script and a recognized distribution respectively. Vertical lines show where sampled from blue graph. -###1-sample t-test +### 1-sample t-test The sampled size by "draw2Sample.js": `` 1. `[Resampled size:100;Given mean:0;Simulation:100times;Significance level:0.025]` @@ -108,7 +108,7 @@ The sampled size by "draw2Sample.js": `` 3. `[Resampled size:20;Given mean:0;Simulation:10000times;Significance level:0.025]` Result: `Rejection rate:0.0146` -###_p_-value estimation +### _p_-value estimation The sampled size by "draw2Sample.js": `` _p_-value was estimated as probability on v-axis: _P_(`x`) = _P_(_v_ >= `x`). @@ -118,8 +118,8 @@ _p_-value was estimated as probability on v-axis: _P_(`x`) = _P_(_v_ >= `x`). 4. _P_(1.96): `{"p":0.028,"x":1.96,"sampleSize":100,"simulation":10}` ______ -##Reference +## Reference * Efron, B. 1979. Bootstrap Methods: Another Look at the Jackknife. Ann. Statist. vol. 7, no. 1, p. 1-26. -##\[1.2+\] Library list +## \[1.2+\] Library list * bootstrapEst-2.1/bootstrapMdl.js (Yuji SODE,2016): the MIT License; https://github.com/YujiSODE/bootstrapEst