# Statistics console

The quick start of Atlas Plot Pro, and the project of its
[tutorial](https://youseful.software/delphi/atlas-plot-pro.html#tutorial). A console program
that runs every function of `TAtlasStats` on small data sets whose answers can
be worked out by hand, then draws a heat map and a box plot into files without
creating a window:

- quantiles, mean and sample standard deviation of 1..10 given in shuffled order;
- box statistics of 1..9 plus 40: quartiles, whiskers at 1.5 IQR, one outlier;
- a four-bin histogram with half-open bins and a closed last bin, `BinOf`, and
  Sturges' rule when the bin count is 0;
- Pearson correlation, an exact quadratic recovered by `PolynomialFit` (also
  outside the data) and the low R squared of a straight line through the same points;
- exponential smoothing with alpha 0.5;
- a fit that `EAtlasPlotError` rejects because two points cannot fix a parabola;
- `TAtlasHeatMap` with an empty (NaN) cell and a fixed 50..100 scale saved as
  `heatmap.png`, and `TAtlasBoxPlot` with two services saved as `boxplot.svg`.

Every result is compared with the expected value; a mismatch raises and the exit
code is 1.

## Build and run

Open `StatisticsConsole.dpr` in Delphi 13; the IDE creates the project file. Add the Atlas Plot Pro `src` folder and the Atlas Plot `src` folder to the project's search path, then build and run for Win32 or Win64. No packages need to be installed. The program needs no input. It checks its own results and stops with an error if any of them differs from the output below.

## Expected output

```
Quantiles of 1..10 in shuffled order
  Q1 3.25  median 5.50  Q3 7.75  mean 5.50  sd 3.0277
  ok: first quartile interpolates between ranks 3 and 4
  ok: median of an even count is the middle pair average
  ok: mean and sample standard deviation
Box statistics of 1..9 and one slow value, 40
  box 3.25..7.75  whiskers 1..9  1 outlier(s)
  ok: quartiles
  ok: whiskers stop at the last value within 1.5 IQR
  ok: 40 is the only outlier
Histogram of 1 2 2 3 3 3 4 4 5 in four bins
  [1, 2): 1
  [2, 3): 2
  [3, 4): 3
  [4, 5]: 3
  ok: bins are half open, the last one closed
  ok: BinOf finds the bin; outside the range is -1
  ok: Bins = 0 applies Sturges' rule: ceil(log2 9) + 1 = 5
Correlation and least-squares fits
  r = 0.80
  ok: Pearson r of a partly ordered pair is 0.8
  quadratic: degree 2, R squared 1.0000, value at 10 = 171.0000
  ok: the parabola is recovered, also outside the data
  straight line: R squared 0.3047
  ok: a line explains less than a third of a parabola
Exponential smoothing of 10 20 20 0 with alpha 0.5
  10.00 15.00 17.50 8.75
  ok: each value moves halfway towards the input
Invalid input raises EAtlasPlotError
  ok: a fit with too few distinct arguments is rejected
Charts rendered without a window
  ok: heatmap.png written
  ok: NaN is an empty cell; 75 is halfway on the 50..100 scale
  ok: boxplot.svg names both categories
  ok: the chart keeps the statistics of each sample
All results verified.
```

Next to the executable you find `heatmap.png` (480 × 300: three node rows, four
hour columns, white-to-black cells with their percentages in contrasting text,
a light grey empty cell for node-b at 06 and a 50..100 colour scale on the
right) and `boxplot.svg` (two boxes; the 60 ms Gateway request is drawn as an
outlier circle).

## What to change first

- Put your own measurements into the arrays and replace the `Expect` calls with
  `Writeln`; every function raises `EAtlasPlotError` on NaN, infinite or empty
  input, so wrap them in `try ... except on EAtlasPlotError` when the data comes
  from outside.
- Change the degree passed to `PolynomialFit` (1 to 6) and compare `RSquared`.
- The heat map stores percentages (91, not 0.91) because `ValueFormat` is a
  `FormatFloat` mask, and `FormatFloat` prints a `%` sign as it is without
  multiplying by 100.
- Change the extensions passed to `SaveToFile`: `.png`, `.bmp`, `.emf` and
  `.svg` are supported.