# Tutorial (JKQTPDatastore): 1-Dimensional Group Statistics with JKQTPDatastore             {#JKQTPlotterBasicJKQTPDatastoreStatisticsGroupedStat}

[JKQTPlotterBasicJKQTPDatastore]: @ref JKQTPlotterBasicJKQTPDatastore "Basic Usage of JKQTPDatastore"
[JKQTPlotterBasicJKQTPDatastoreIterators]: @ref JKQTPlotterBasicJKQTPDatastoreIterators "Iterator-Based usage of JKQTPDatastore"
[JKQTPlotterBasicJKQTPDatastoreStatistics]: @ref JKQTPlotterBasicJKQTPDatastoreStatistics "Advanced 1-Dimensional Statistics with JKQTPDatastore"
[JKQTPlotterBasicJKQTPDatastoreRegression]: @ref JKQTPlotterBasicJKQTPDatastoreRegression "Regression Analysis (with the Statistics Library)"
[JKQTPlotterBasicJKQTPDatastoreStatisticsGroupedStat]: @ref JKQTPlotterBasicJKQTPDatastoreStatisticsGroupedStat "1-Dimensional Group Statistics with JKQTPDatastore"
[JKQTPlotterBasicJKQTPDatastoreStatistics2D]: @ref JKQTPlotterBasicJKQTPDatastoreStatistics2D "Advanced 2-Dimensional Statistics with JKQTPDatastore"
[statisticslibrary]: @ref jkqtptools_math_statistics "JKQTPlotter Statistics Library"

This tutorial project (see `./examples/datastore_groupedstat/`) explains several advanced functions of JKQTPDatastore in combination with the [[statisticslibrary]] conatined in JKQTPlotter.

***Note*** that there are additional tutorial explaining other aspects of data mangement in JKQTPDatastore:
  - [JKQTPlotterBasicJKQTPDatastore]
  - [JKQTPlotterBasicJKQTPDatastoreIterators]
  - [JKQTPlotterBasicJKQTPDatastoreStatistics]
  - [JKQTPlotterBasicJKQTPDatastoreRegression]
  - [JKQTPlotterBasicJKQTPDatastoreStatisticsGroupedStat]
  - [JKQTPlotterBasicJKQTPDatastoreStatistics2D]
  
[TOC]

The source code of the main application can be found in [`datastore_groupedstat.cpp`](https://github.com/jkriege2/JKQtPlotter/tree/master/examples/datastore_groupedstat/datastore_groupedstat.cpp). 
This tutorial cites only parts of this code to demonstrate different ways of working with data for the graphs.

# Barcharts & Boxplots from categorized data

## Generating a Dataset for Grouped Barcharts

To demonstrate the grouped statistics, we first have to generate a dataset. The datapoints consist of pairs `<group,value>`, where the groups are encoded by the numbers 1,2,3 and in each group, several measurements are taken:
```.cpp
    size_t colBarRawGroup=datastore1->addColumn("barchart, rawdata, group");
    size_t colBarRawValue=datastore1->addColumn("barchart, rawdata, value");

    //      data for group 1
    datastore1->appendToColumns(colBarRawGroup, colBarRawValue, 1, 1.1);
    datastore1->appendToColumns(colBarRawGroup, colBarRawValue, 1, 1.5);
    datastore1->appendToColumns(colBarRawGroup, colBarRawValue, 1, 0.8);
    // ...

    //      data for group 2
    datastore1->appendToColumns(colBarRawGroup, colBarRawValue, 2, 2.2);
    // ...
    
    //      data for group 3
    datastore1->appendToColumns(colBarRawGroup, colBarRawValue, 3, 4.1);
    // ...
    
```

Note that the data does not have to be sorted. You can add the dataset in any order!

This dataset can be visualized with a simple scatter plot:
```.cpp
    JKQTPXYLineGraph* gScatterForBar;
    plotbarchart->addGraph(gScatterForBar=new JKQTPXYLineGraph(plotbarchart));
    gScatterForBar->setXYColumns(colBarRawGroup, colBarRawValue);
    gScatterForBar->setDrawLine(false);
    gScatterForBar->setSymbolType(JKQTPCross);
    gScatterForBar->setSymbolSize(5);
    gScatterForBar->setSymbolColor(QColorWithAlphaF(QColor("red"), 0.5));
```

The resulting plot looks like this: 

![datastore_groupedstat_barchartrawdata](https://raw.githubusercontent.com/jkriege2/JKQtPlotter/master/screenshots/datastore_groupedstat_barchartrawdata.png)

## Calculating Grouped Statistics for a Barchart 

Now we want to draw a barchart for every group, which indicates the average in each group. This is done using methods from the statistics library.
First we need to group the data using `jkqtpstatGroupData()`, which assembles the data points in each group groupeddataBar
```.cpp
    std::map<double, std::vector<double> > groupeddataBar;
    jkqtpstatGroupData(datastore1->begin(colBarRawGroup), datastore1->end(colBarRawGroup),
                       datastore1->begin(colBarRawValue), datastore1->end(colBarRawValue),
                       groupeddataBar);
```
Now we can calculate the statistics for each group separately: Data is collected in new columns `colBarGroup`, `colBarAverage` and `colBarStdDev`. The statistics is then calculated by simply iterating over `groupeddataBar` and calling functions like `jkqtpstatAverage()` for each group:
```.cpp
    size_t colBarGroup=datastore1->addColumn("barchart, group");
    size_t colBarAverage=datastore1->addColumn("barchart, group-average");
    size_t colBarStdDev=datastore1->addColumn("barchart, group-stddev");

    for (auto it=groupeddataBar.begin(); it!=groupeddataBar.end(); ++it) {
        datastore1->appendToColumn(colBarGroup, it->first);
        datastore1->appendToColumn(colBarAverage, jkqtpstatAverage(it->second.begin(), it->second.end()));
        datastore1->appendToColumn(colBarStdDev, jkqtpstatStdDev(it->second.begin(), it->second.end()));
    }
```

Finally the calculated groups are drawn:
```.cpp
    JKQTPBarVerticalErrorGraph* gBar;
    plotbarchart->addGraph(gBar=new JKQTPBarVerticalErrorGraph(plotbarchart));
    gBar->setXYColumns(colBarGroup, colBarAverage);
    gBar->setYErrorColumn(static_cast<int>(colBarStdDev));
```

The resulting plot looks like this: 

![datastore_groupedstat_barchart](https://raw.githubusercontent.com/jkriege2/JKQtPlotter/master/screenshots/datastore_groupedstat_barchart.png)

In order to safe yo the typing of the code above, shortcuts in the form of adaptors exist:
```.cpp
    jkqtpstatAddYErrorBarGraph(plotbarchart->getPlotter(),
                               datastore1->begin(colBarRawGroup), datastore1->end(colBarRawGroup),
                               datastore1->begin(colBarRawValue), datastore1->end(colBarRawValue));
```
Also other flavors exist that generate different graphs (see the JKQTPlotter documentation):
  - `jkqtpstatAddYErrorLineGraph()` / `jkqtpstatAddXErrorLineGraph()`
  - `jkqtpstatAddYErrorBarGraph()` / `jkqtpstatAddXErrorBarGraph()`
  - `jkqtpstatAddYErrorImpulsesGraph()` / `jkqtpstatAddXErrorImpulsesGraph()`
  - `jkqtpstatAddYErrorParametrizedScatterGraph()` / `jkqtpstatAddXErrorParametrizedScatterGraph()`
  - `jkqtpstatAddYErrorFilledCurveGraph()` / `jkqtpstatAddXErrorFilledCurveGraph()`
  - `jkqtpstatAddYErrorGraph()` / `jkqtpstatAddXErrorGraph()`


## Calculating Grouped Statistics for a Boxplot 

With the methods above we can also calculate more advanced statistics, like e.g. boxplots:
```.cpp
    size_t colBarMedian=datastore1->addColumn("barchart, group-median");
    size_t colBarMin=datastore1->addColumn("barchart, group-min");
    size_t colBarMax=datastore1->addColumn("barchart, group-max");
    size_t colBarQ25=datastore1->addColumn("barchart, group-Q25");
    size_t colBarQ75=datastore1->addColumn("barchart, group-Q75");
    for (auto it=groupeddataBar.begin(); it!=groupeddataBar.end(); ++it) {
        datastore1->appendToColumn(colBarMedian, jkqtpstatMedian(it->second.begin(), it->second.end()));
        datastore1->appendToColumn(colBarMin, jkqtpstatMinimum(it->second.begin(), it->second.end()));
        datastore1->appendToColumn(colBarMax, jkqtpstatMaximum(it->second.begin(), it->second.end()));
        datastore1->appendToColumn(colBarQ25, jkqtpstatQuantile(it->second.begin(), it->second.end(), 0.25));
        datastore1->appendToColumn(colBarQ75, jkqtpstatQuantile(it->second.begin(), it->second.end(), 0.75));
    }
```
The result can be plotted using JKQTPBoxplotVerticalGraph, which receives a column for each value class of the final plot:
```.cpp
    JKQTPBoxplotVerticalGraph* gBoxplot;
    plotboxplot->addGraph(gBoxplot=new JKQTPBoxplotVerticalGraph(plotboxplot));
    gBoxplot->setPositionColumn(colBarGroup);
    gBoxplot->setMinColumn(colBarMin);
    gBoxplot->setMaxColumn(colBarMax);
    gBoxplot->setMedianColumn(colBarMedian);
    gBoxplot->setPercentile25Column(colBarQ25);
    gBoxplot->setPercentile75Column(colBarQ75);
```

The resulting plot looks like this: 

![datastore_groupedstat_boxplot](https://raw.githubusercontent.com/jkriege2/JKQtPlotter/master/screenshots/datastore_groupedstat_boxplot.png)

In order to safe yo the typing of the code above, shortcuts in the form of adaptors exist:
```.cpp
    jkqtpstatAddHBoxplotsAndOutliers(plotboxplot->getPlotter(),
                                    datastore1->begin(colBarRawGroup), datastore1->end(colBarRawGroup),
                                    datastore1->begin(colBarRawValue), datastore1->end(colBarRawValue));
```
Also other flavors exist that generate different graphs (see the JKQTPlotter documentation):
  - `jkqtpstatAddVBoxplotsAndOutliers()` / `jkqtpstatAddHBoxplotsAndOutliers()`
  - `jkqtpstatVAddBoxplots()` / `jkqtpstatHAddBoxplots()`
  - `jkqtpstatAddBoxplots()`


# (Scatter-)Graphs with X/Y-errors from Categorized Data

## Dataset for XY Scatter Graphs

First we generate a second dataset, which is going to be used for a scaterplot. The datapoints consist of pairs `<x,y>`, that are based on a parabula with random deviations, both in x- and y-direction:
```.cpp
    size_t colScatterRawX=datastore1->addColumn("scatterplot, rawdata, x");
    size_t colScatterRawY=datastore1->addColumn("scatterplot, rawdata, y");
    std::random_device rd; // random number generators:
    std::mt19937 gen{rd()};
    std::normal_distribution<> d1{0,0.5};
    const size_t N=100;
    const double xmax=3.5;
    for (size_t i=0; i<N; i++) {
        const double x=(static_cast<double>(i)-static_cast<double>(N)/2.0)*xmax/(static_cast<double>(N)/2.0);
        const double y=jkqtp_sqr(x)+2.0;
        datastore1->appendToColumns(colScatterRawX, colScatterRawY, x+d1(gen), y+d1(gen));
    }
```

This dataset can be visualized:
```.cpp
    JKQTPXYParametrizedScatterGraph* gScatterRaw;
    plotscattererrors->addGraph(gScatterRaw=new JKQTPXYParametrizedScatterGraph(plotscattererrors));
    gScatterRaw->setXYColumns(colScatterRawX, colScatterRawY);
    gScatterRaw->setDrawLine(false);
    gScatterRaw->setSymbolType(JKQTPCross);
    gScatterRaw->setSymbolSize(5);
```

The resulting plot looks like this: 

![datastore_groupedstat_scatterrawdata](https://raw.githubusercontent.com/jkriege2/JKQtPlotter/master/screenshots/datastore_groupedstat_scatterrawdata.png)

## Calculating x- and y-Errors from Categorized Data

Now we want to draw a scatterchart of the data, where data-points should be grouped together, in x-intervals of width 0.5. From all the points in each interval, we calculate the in both x- and y-direction the average and standard deviation. First we need to group the data using `jkqtpstatGroupData()`, which assembles the data points in each group groupeddataScatter. For the custom grouping of the datapoints we use the optional functor provided to `jkqtpstatGroupData()`: We use `jkqtpstatGroupingCustomRound1D()` with given parameters 0.25 for the (center) location of the first bin and bin width 0.5. The functor is not built by hand (which would be possible using std::bind), but with the generator function `jkqtpstatMakeGroupingCustomRound1D()`. In addition we use a variant of `jkqtpstatGroupData()`, which outputs a column with the category assigned to every data pair in the input data range:
```.cpp
    std::map<double, std::pair<std::vector<double>,std::vector<double> > > groupeddataScatter;
    size_t colScatterRawGroup=datastore1->addColumn("scatterplot, rawdata, assigned-group");
    jkqtpstatGroupData(datastore1->begin(colScatterRawX), datastore1->end(colScatterRawX),
                       datastore1->begin(colScatterRawY), datastore1->end(colScatterRawY),
                       datastore1->backInserter(colScatterRawGroup),
                       groupeddataScatter,
                       jkqtpstatMakeGroupingCustomRound1D(0.25, 0.5));
```

The column colScatterRawGroup can now be used to color the scatter graph:
```.cpp
    gScatterRaw->setColorColumn(colScatterRawGroup);
```

Now we can calculate the statistics for each group separately: Data is collected in two new columns. Then the statistics is calculated by simply iterating over `groupeddataScatter` and calling functions like `jkqtpstatAverage()` for each group:
```.cpp
    size_t colScatterXAvg=datastore1->addColumn("scatter, x, average");
    size_t colScatterXStd=datastore1->addColumn("scatter, x, stddev");
    size_t colScatterYAvg=datastore1->addColumn("scatter, y, average");
    size_t colScatterYStd=datastore1->addColumn("scatter, y, stddev");

    for (auto it=groupeddataScatter.begin(); it!=groupeddataScatter.end(); ++it) {
        datastore1->appendToColumn(colScatterXAvg, jkqtpstatAverage(it->second.first.begin(), it->second.first.end()));
        datastore1->appendToColumn(colScatterXStd, jkqtpstatStdDev(it->second.first.begin(), it->second.first.end()));
        datastore1->appendToColumn(colScatterYAvg, jkqtpstatAverage(it->second.second.begin(), it->second.second.end()));
        datastore1->appendToColumn(colScatterYStd, jkqtpstatStdDev(it->second.second.begin(), it->second.second.end()));
    }
```

Finally the calculated groups are drawn
```.cpp
    JKQTPXYLineErrorGraph* gScatterErr;
    plotscattererrors->addGraph(gScatterErr=new JKQTPXYLineErrorGraph(plotscattererrors));
    gScatterErr->setXYColumns(colScatterXAvg, colScatterYAvg);
    gScatterErr->setXErrorColumn(static_cast<int>(colScatterXStd));
    gScatterErr->setYErrorColumn(static_cast<int>(colScatterYStd));
    gScatterErr->setSymbolType(JKQTPFilledTriangle);
    gScatterErr->setDrawLine(false);
```

The resulting plot looks like this: 

![datastore_groupedstat_scatter](https://raw.githubusercontent.com/jkriege2/JKQtPlotter/master/screenshots/datastore_groupedstat_scatter.png)


In order to safe yo the typing of the code above, shortcuts in the form of adaptors exist:
```.cpp
    jkqtpstatAddXYErrorLineGraph(plotscattererrors->getPlotter(),
                                 datastore1->begin(colScatterRawX), datastore1->end(colScatterRawX),
                                 datastore1->begin(colScatterRawY), datastore1->end(colScatterRawY),
                                 jkqtpstatMakeGroupingCustomRound1D(0.25, 0.5));
```
Also other flavors exist that generate different graphs (see the JKQTPlotter documentation):
  - `jkqtpstatAddXYErrorLineGraph()`
  - `jkqtpstatAddXYErrorParametrizedScatterGraph()`
  - `jkqtpstatAddXYErrorGraph()`


# Screenshot of the full Program

The output of the full test program [`datastore_groupedstat.cpp`](https://github.com/jkriege2/JKQtPlotter/tree/master/examples/datastore_groupedstat/datastore_groupedstat.cpp) looks like this:

![datastore_groupedstat](https://raw.githubusercontent.com/jkriege2/JKQtPlotter/master/screenshots/datastore_groupedstat.png)