# Elm-stat

![Image](./image/dataviewer.png)

![Image](./image/dataviewer-sealevel.png)

This package is for doing statistics and graphs for n-column data files. The first image above displays an analysis of time series data in a Csv file (temperature anomaly data versus time). The second example is time series data from a 100K space delimited file (sealevel rise data from NASA).

See the online version of the [Demo App](https://jxxcarlson.github.io/app/dataviewer.html).  The code for it is in `./examples` of this repo.

## The API

There are two modules, `Stat`, for computing statistics of 2-D data, and `RawData`, for extracting data from a text string or file. The `Stat` module has functions for computing statistical measures such as the mean and standard deviation of the x or y values, coefficients for the linear regression line, etc.

Let's import both modules to see how they work.

```
> import Stat exposing(..)
> import RawData exposing(..)
> import SampleData
```

Here is some test data:

```
> SampleData.temperature
  """
  Global Land and Ocean Temperature Anomalies
  January-December 1880-2016
  Units: Degrees Celsius
  Base Period: 1901-2000
  Missing: -999
    Year   Value
    1880   -0.12
    1881   -0.07
    1882   -0.08
    1883   -0.15
    ...
```

We transform it to a RawData value using `RawData.get`.  This function automatically detects the type of data in the string: space-delimited, tab-delimited, or comma-delimited (csv).

```
> get SampleData.temperature
  Just {
    columnHeaders = ["Year","Value"]
  , data = [["1880","-0.12"],["1881","-0.07"],["1882","-0.08"], ...
  , metadata = [
      "Global Land and Ocean Temperature Anomalies"
     , "January-December 1880-2016"
     , "Units: Degrees Celsius"
    ]
```

Piping this computation into `getData 0 1`, we extract a list of points:

```
> get SampleData.temperature |> Maybe.andThen (getData 0 1) |> Maybe.map (List.take 2)
  Just [{ x = 1880, y = -0.12 },{ x = 1881, y = -0.07 }, ...]
    : Maybe (List Point)
```


From a `Data = List Point` value, one can compute statistics:

```
> data = get SampleData.temperature |> Maybe.andThen (getData 0 1)  |> Maybe.withDefault []

> Stat.mean .x data
  Just 1948 : Maybe Float
> Stat.mean .y data
  Just 0.04875912408759121 : Maybe Float
```

The `statistics` function computes a package of statistical measures, including left and right endpoints for the regression line for the data.  These can be used to superimpose the regression line on the plot of the data.  This is done in the demo app using `terezka/line-charts`.

```
> Stat.statistics data
  Just { b = -13.276, leftDataPoint = { x = 1880, y = -0.12 }
       , leftRegressionPoint = { x = 1880, y = -0.416 }, m = 0.0068
       , n = 137, r2 = 0.7458, rightDataPoint = { x = 2016, y = 0.95 }
       , rightRegressionPoint = { x = 2016, y = 0.514  }, xMax = 2016
       , xMean = 1948, xMin = 1880, xStdev = 39.693, yMean = 0.0488
       , yStdev = 0.314 }
    : Maybe Statistics
```

## The Demo App

Code for the demo app is in `./examples`.  There is an online version at
[Data explorer](https://jxxcarlson.github.io/app/dataviewer.html).

The data used in the example in the file `data/temperature-anomalies.csv` in this repo. It is a list of global temperature anomalies for the period 1880-2017 from [www.climate.gov](http://www.climate.gov). The annual temperature anomaly is the difference between the global mean temperature and the long-term mean global temperature. For this data set, the long-term mean is computed for the period 1901-2000. 

One can now read data files in any one of three formats: delimited comma, tab, or space(s).