# 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, not yet published
to package repo.  (Coming soon.)

Both graphs is computed by the app in the `examples` folder using this `elm-stat` 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 `CsvData`, for extracting Csv data from a text string and for extracting 2-D data from Csv. 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 CsvData 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 csv using `CsvData.get`.  This function is
`\str ->  Just <| Csv.parse <| filter str`, where `Csv` is from
`zgohr/elm-csv`.  The function `CsvData.intelligentGet`
does additional checking and manipulation, e.g., it
tries to return the text header that many data files have.

```
> maybeCsv = CsvData.get rawdata
    Just { headers = ["year","value"], records = [["1880","-0.12"]
          ,["1881","-0.07"],["1882","-0.08"],["1883","-0.15"]] }
    : Maybe Csv.Csv
```

For this example, we extract the value by hand:

```
> csv = { headers = ["year","value"], records = [["1880","-0.12"],
         ["1881","-0.07"],["1882","-0.08"],["1883","-0.15"]] }
    : { headers : List String, records : List (List String) }
```

With the csv data in hand, we convert it to a list of points.  In the
case at hand, we extract columns 0 and 1.  The `getPointList` function
allows one to work with multi-column data.

```
> data  = CsvData.getPointList 0 1 csv
    [{ x = 1880, y = -0.12 },{ x = 1881, y = -0.07 },{ x = 1882, y = -0.08 }
    ,{ x = 1883, y = -0.15 }]
    : Data
```

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

```
> Stat.mean .y data
  Just -0.105 : Maybe Float
> Stat.stdev .y data
  Just 0.0013666 : 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 = 18.7099, leftDataPoint = { x = 1880, y = -0.12 }
  , leftRegressionPoint = { x = 1880, y = -0.09 }
  , m = -0.009999, n = 4, r2 = 0.12195
  , rightDataPoint = { x = 1883, y = -0.15 }
  , rightRegressionPoint = { x = 1883, y = -0.1200 }
  , xMax = 1883, xMean = 1881.5, xMin = 1880, xStdev = 1.29099
  , yMean = -0.105, yStdev = 0.036968 }
```

## 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
```