# 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 Csv file. The second example uses the new API in the `RawData` module.

Both graphs is computed by the app in the `examples` folder using this library. See
the [Demo App](https://jxxcarlson.github.io/app/dataviewer.html) to try the app out on line.

## The API

There are two modules, `Stat`, for computing statistics of 2-D data, and `RawData`, for `RawData` from a text string and for extracting 2-D data from the resulting `RawData` value. 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(..)
```

Here is an extract of the data in `data/temperature-anomalies.csv`:

```
> rawdata = "year,value\n1880,-0.12\n1881,-0.07\n1882,-0.08\n1883,-0.15\n"
"year,value\n1880,-0.12\n1881,-0.07\n1882,-0.08\n1883,-0.15\n"
    : String
```

Next, transform it to a RawData value using `RawData.get`.  This function automatically detects the type 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"], ...
```

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 D.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. Here is what the data looks like:

```
Global Land and Ocean Temperature Anomalies, January-December
Units: Degrees Celsius
Base Period: 1901-2000
Year,Value
1880,-0.12
1881,-0.07
...
2015,0.91
2016,0.95
```

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