This is the fourth instalment of our Think Stats study group; we are working through Allen Downey’s Think Stats, implementing everything in Clojure. This week we made a start on chapter 2 of the book, which introduces us to statistical distributions by way of histograms. This was our first encounter with the incanter.charts namespace, which we use to plot histograms of some values from the National Survey for Family Growth dataset we have worked with in previous sessions.

You can find previous instalments from the study group on our blog:

• Part I: Parsing the Data
• Part II: Cleaning and Augmenting Data
• Part III: Exploring Data

If you’d like to follow along, start by cloning our thinkstats repository from Github:

git clone https://github.com/ray1729/thinkstats.git --recursive

Change into the project directory and fire up Gorilla REPL:

cd thinkstats
lein gorilla

Getting Started

As usual, we start out with a namespace declaration that loads the namespaces we’ll need:

(ns radioactive-darkness
  (:require [incanter.core :as i
               :refer [$ $map $where $rollup $order $fn $group-by $join]]
            [incanter.stats :as s]
            [incanter.charts :as c]
            [incanter-gorilla.render :refer [chart-view]]
            [thinkstats.gorilla]
            [thinkstats.incanter :as ie :refer [$! $not-nil]]
            [thinkstats.family-growth :as f]))

There are two additions since last time: incanter.charts mentioned above, and incanter-gorilla.render that provides a function to display Incanter charts in Gorilla REPL.

We start by generating a vector of random integers to play with:

(def xs (repeatedly 100 #(rand-int 5)))

We can generate a histogram from these data:

(def h (c/histogram xs))

This returns a JFreeChart object that we can display in Gorilla REPL with chart-view:

(chart-view h)

If you’re running from a standard Clojure REPL, you should use the view function from incanter.core instead:

(i/view h)

The first thing we notice about this is that the default number of bins is not optimal for our data; let’s look at the documentation for histogram to see how we might change this.

(require '[clojure.repl :refer [doc]])
(doc c/histogram)

We see that the :nbins option controls the number of bins. We can also set the title and labels for the axes by specifiyng :title, :x-label and :y-label respectively.

(chart-view (c/histogram xs :nbins 5
                            :title "Our first histogram"
                            :x-label "Value"
                            :y-label "Frequency"))

We can save the histogram as a PNG file:

(i/save (c/histogram xs :nbins 5
                            :title "Our first histogram"
                            :x-label "Value"
                            :y-label "Frequency")
            "histogram-1.png")

Birth Weight

Now that we know how to plot histograms, we can start to visualize values from the NSFG data set. We start by loading the data:

(def ds (f/fem-preg-ds))

Plot the pounds part of birth weight (note the use of $! to exclude nil values):

(chart-view (c/histogram ($! :birthwgt-lb ds) :x-label "Birth weight (lb)"))

…and the ounces part of birth weight:

(chart-view (c/histogram ($! :birthwgt-oz ds) :x-label "Birth weight (oz)"))

We can see immediately that these charts are very different, reflecting the different “shapes” of the data. What we see fits well with our intuition: we expect the ounces component of the weight to be distributed fairly evenly, while most newborns are around 7lb or 8lb and babies bigger than 10lb at birth are rarely seen.

Recall that we also computed the total weight in pounds and added :totalwgt-lb to the dataset:

(chart-view (c/histogram ($! :totalwgt-lb ds) :x-label "Total weight (lb)"))

This does not look much different from the :birthwgt-lb histogram, as this value dominates ounces in the computaiton

A Few More Histograms

The shape of a histogram tells us how the data are distributed: it may be approximately flat like the :birthwgt-oz histogram, or bell-shaped like :birthwgt-lb, or an asymetrical bell (with longer tail to the left or to the right) like the following two.

(chart-view (c/histogram ($! :ageatend ds)
                         :x-label "Age"
                         :title "Mother's age at end of pregnancy"))

Let’s try that again, excluding the outliers with an age over 60:

(chart-view (c/histogram (filter #(< % 60) ($! :ageatend ds))
                         :x-label "Age"
                         :title "Mother's age at end of pregnancy"))

Finally, let’s look at pregnancy length for live births:

(chart-view (c/histogram ($! :prglngth ($where {:outcome 1} ds))
                         :x-label "Weeks"
                         :title "Pregnancy length (live births)"))

We have now reached the end of section 2.4 of the book, and will pick up next time with section 2.5.