{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Statistics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many specialized packages for dealing with data analysis and statistical programming. One very important code that you will see in MATH1024, Introduction to Probability and Statistics, is [R](http://www.r-project.org/). A Python package for performing similar analysis of large data sets is [pandas](http://pandas.pydata.org/). However, simple statistical tasks on simple data sets can be tackled using `numpy` and `scipy`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Getting data in" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A data file containing the monthly rainfall for Southampton, taken from the [Met Office data](http://www.metoffice.gov.uk/pub/data/weather/uk/climate/stationdata/southamptondata.txt) can be [downloaded from this link](https://github.com/IanHawke/maths-with-python/blob/master/southampton_precip.txt). We will save that file locally, and then look at the data.\n", "\n", "The first few lines of the file are:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "#Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec\r\n", "1855 85.6 54.3 61.3 10.1 60.0 43.9 101.0 47.9 88.4 187.5 28.2 55.4\r\n", "1856 93.5 50.6 36.3 127.3 55.7 40.3 16.5 64.7 67.6 74.5 38.7 87.1\r\n", "1857 72.3 10.6 54.4 60.7 19.0 38.2 43.7 66.3 93.6 191.4 57.1 25.0\r\n", "1858 27.0 33.1 22.9 94.1 65.7 14.1 69.6 55.5 75.2 66.2 50.1 116.6\r\n", "1859 59.6 78.3 49.7 92.4 36.8 45.7 66.6 58.3 135.3 119.8 125.1 127.1\r\n", "1860 129.2 29.3 59.3 47.6 88.7 205.0 84.7 115.0 99.2 53.2 80.2 127.7\r\n", "1861 20.7 60.2 76.4 10.2 41.3 100.8 103.5 22.2 78.0 27.7 164.3 53.2\r\n", "1862 104.0 20.1 124.2 57.5 123.9 53.8 52.8 36.3 29.7 171.8 22.4 72.7\r\n", "1863 129.4 32.4 38.7 20.5 55.2 94.6 26.4 63.9 98.7 115.3 60.7 64.4\r\n" ] } ], "source": [ "!head southampton_precip.txt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use `numpy` to load this data into a variable, where we can manipulate it. This is not ideal: it will lose the information in the header, and that the first column corresponds to years. However, it is simple to use." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = numpy.loadtxt('southampton_precip.txt')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 1855. , 85.6, 54.3, ..., 187.5, 28.2, 55.4],\n", " [ 1856. , 93.5, 50.6, ..., 74.5, 38.7, 87.1],\n", " [ 1857. , 72.3, 10.6, ..., 191.4, 57.1, 25. ],\n", " ..., \n", " [ 1997. , 16.4, 112.2, ..., 64.5, 151.4, 100.5],\n", " [ 1998. , 118.5, 9.5, ..., 135.1, 59. , 87.3],\n", " [ 1999. , 129.4, 28.8, ..., 66.8, 49.6, 138.8]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the first column - the year - has been converted to a floating point number, which is not helpful. However, we can now split the data using standard `numpy` operations:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "years = data[:, 0]\n", "rainfall = data[:, 1:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now plot, for example, the rainfall in January for all years:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "nbconvert": { "hide_code": true } }, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import rcParams\n", "rcParams['figure.figsize']=(12,9)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from matplotlib import pyplot" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9ssL7kkvUuaCLsTPteDPjvRab68dfBvBCAIellL8O4GkAtkYdFRlo2uB4cwEd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\nb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pyplot.plot(years, rainfall[:,0])\n", "pyplot.xlabel('Year')\n", "pyplot.ylabel('Rainfall in January');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic statistical functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`numpy` contains a number of basic statistical functions, such as `min`, `max` and `mean`. These will act on entire arrays to give the \"all time\" minimum, maximum, and average rainfall:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Minimum rainfall: 0.0\n", "Maximum rainfall: 280.7\n", "Mean rainfall: 67.03591954022988\n" ] } ], "source": [ "print(\"Minimum rainfall: {}\".format(rainfall.min()))\n", "print(\"Maximum rainfall: {}\".format(rainfall.max()))\n", "print(\"Mean rainfall: {}\".format(rainfall.mean()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of more interest would be either\n", "\n", "1. the mean (min/max) rainfall in a given month for all years, or\n", "2. the mean (min/max) rainfall in a given year for all months.\n", "\n", "So the mean rainfall in the first year, 1855, would be" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean rainfall in 1855: 68.63333333333334\n" ] } ], "source": [ "print (\"Mean rainfall in 1855: {}\".format(rainfall[0, :].mean()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Whilst the mean rainfall in January, averaging over all years, would be" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean rainfall in January: 81.86482758620689\n" ] } ], "source": [ "print (\"Mean rainfall in January: {}\".format(rainfall[:, 0].mean()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we wanted to plot the mean rainfall per year, across all years, this would be tedious - there are 145 years of data in the file. Even computing the mean rainfall in each month, across all years, would be bad with 12 months. We could write a loop. However, `numpy` allows us to apply a function along an axis of the array, which does this is one operation:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mean_rainfall_in_month = rainfall.mean(axis=0)\n", "mean_rainfall_per_year = rainfall.mean(axis=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `axis` argument gives the direction we want to *keep* - that we do not apply the operation to. For this data set, each row contains a year and each column a month. To find the mean in a given month we want to keep the row information (`axis` 0) and take the mean over the column. To find the mean in a given year we want to keep the column information (`axis` 1) and take the mean over the row.\n", "\n", "We can now plot how the mean varies with each year." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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eTZrYbPLdQLWOd7S48rzzlPDudtN/J6/jPT+vfse18DY53gcPtkd4NylqEvI7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pyplot.plot(years, mean_rainfall_per_year)\n", "pyplot.xlabel('Year')\n", "pyplot.ylabel('Mean rainfall');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also compute the standard deviation:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "std_rainfall_per_year = rainfall.std(axis=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then add confidence intervals to the plot:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vXm3fUJFPH8NqWDCA77ZbPz+MHXNMcmW5zQC+fr2tVErSJZe0M4YighVwY/w+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\nCrgx5gmSJniet94Ys72k50s6V9LPJL1J0qclvVHST1sb5JD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KDQC9QdAG0FVz587VXFch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\nkAIOAAAD/R9usvW/dsUDVAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pyplot.errorbar(years, mean_rainfall_per_year, yerr = std_rainfall_per_year)\n", "pyplot.xlabel('Year')\n", "pyplot.ylabel('Mean rainfall');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This isn't particularly pretty or clear: a nicer example would use better packages, but a quick fix uses an alternative `matplotlib` approach:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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F+55yijfLAY9HUHQYhrnQG4tV4DgOLGsXvR7PEYtESgkpMbXaKSUFOCGrgAKcAAAGg0UL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pyplot.plot(years, mean_rainfall_per_year)\n", "pyplot.fill_between(years, mean_rainfall_per_year - std_rainfall_per_year, \n", " mean_rainfall_per_year + std_rainfall_per_year,\n", " alpha=0.25, color=None)\n", "pyplot.xlabel('Year')\n", "pyplot.ylabel('Mean rainfall');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Categorical data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the means by month, it would be better to give them names rather than numbers. We will also summarize the available information using a boxplot:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rL9r88CSXz59fnuQR8+cPS/L81trHWmvXJLk6yQNXWT9g3KzTC8CYbWKO9O1a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\nMPUfzB6cPA9V+wHAuo1xRJo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']\n", "pyplot.boxplot(rainfall, labels=months)\n", "pyplot.xlabel('Month')\n", "pyplot.ylabel('Mean rainfall');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Much better ways of working with categorical data are available through more specialized packages." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can go beyond the basic statistical functions in `numpy` and look at other standard tasks. For example, we can look for simple trends in our data with a *linear regression*. There is a function to compute the linear regression in `scipy` we can use. We will use this to see if there is a trend in the mean yearly rainfall:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WUZMsCu9K3W4J8QOFd86wc7yjnLnSHDWJ+0BHx5sA1VFcadfDW1PJMZq0GB1V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TcAvP/9Mpd++cv5V65MSzDjXZWoiQ/hrVTzyjmFN+kajONdhPCeMUMmmMnJ5m10vFuJW7kyagEd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\nBZx6aru3g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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import stats\n", "\n", "slope, intercept, r_value, p_value, std_err = stats.linregress(years, mean_rainfall_per_year)\n", "\n", "pyplot.plot(years, mean_rainfall_per_year, 'b-', label='Data')\n", "pyplot.plot(years, intercept + slope*years, 'k-', label='Linear Regression')\n", "pyplot.xlabel('Year')\n", "pyplot.ylabel('Mean rainfall')\n", "pyplot.legend();" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The change in rainfall (the slope) is -0.028739338949246847.\n", "However, the error estimate is 0.021587122926201515.\n", "The correlation coefficient between rainfall and year is -0.11064686384415015.\n", "The probability that the slope is zero is 0.18520267346715713.\n" ] } ], "source": [ "print(\"The change in rainfall (the slope) is {}.\".format(slope))\n", "print(\"However, the error estimate is {}.\".format(std_err))\n", "print(\"The correlation coefficient between rainfall and year\"\n", " \" is {}.\".format(r_value))\n", "print(\"The probability that the slope is zero is {}.\".format(p_value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks like there's a good chance that the slight decrease in mean rainfall with time is a real effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Random numbers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Random processes and random variables may be at the heart of probability and statistics, but computers cannot generate anything \"truly\" random. Instead they can generate *pseudo-random* numbers using random number generators (RNGs). Constructing a random number generator is a *hard problem* and wherever possible you should use a well-tested RNG rather than attempting to write your own.\n", "\n", "Python has many ways of generating random numbers. Perhaps the most useful are given by the [`numpy.random`](http://docs.scipy.org/doc/numpy/reference/routines.random.html) module, which can generate a `numpy` array filled with random numbers from various distributions. For example:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/ih3/anaconda/lib/python3.4/site-packages/matplotlib/figure.py:397: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n", " \"matplotlib is currently using a non-GUI backend, \"\n" ] }, { "data": { "image/png": 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kX57kgqo6L8mVSW7p7uckuTXJVUlSVc9NckmSc5NckOSaqqpN6j8AAMC2sa4p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\npaW9qapjvgHsJCcsugMAwO6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy import random\n", "\n", "uniform = random.rand(10000)\n", "normal = random.randn(10000)\n", "\n", "fig = pyplot.figure()\n", "ax1 = fig.add_subplot(1,2,1)\n", "ax2 = fig.add_subplot(1,2,2)\n", "ax1.hist(uniform, 20)\n", "ax1.set_title('Uniform data')\n", "ax2.hist(normal, 20)\n", "ax2.set_title('Normal data')\n", "fig.tight_layout()\n", "fig.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Whilst the standard distributions are given by the convenience functions above, the [full documentation of `numpy.random`](http://docs.scipy.org/doc/numpy/reference/routines.random.html) shows many other distributions available. For example, we can draw $10,000$ samples from the [Beta distribution](http://docs.scipy.org/doc/numpy/reference/generated/numpy.random.beta.html#numpy.random.beta) using the parameters $\\alpha = 1/2 = \\beta$ as" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beta_samples = random.beta(0.5, 0.5, 10000)\n", "\n", "pyplot.hist(beta_samples, 20)\n", "pyplot.title('Beta data')\n", "pyplot.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can do this $5,000$ times and compute the mean of each set of samples:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_trials = 5000\n", "beta_means = numpy.zeros((n_trials,))\n", "\n", "for trial in range(n_trials):\n", " beta_samples = random.beta(0.5, 0.5, 10000)\n", " beta_means[trial] = numpy.mean(beta_samples)\n", " \n", "pyplot.hist(beta_means, 20)\n", "pyplot.title('Mean of Beta trials')\n", "pyplot.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see the *Central Limit Theorem* in action: the distribution of the means appears to be normal, despite the distribution of any individual trial coming from the Beta distribution, which looks very different." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise: Anscombe's quartet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Four separate datasets are given:\n", "\n", "| x | y | x | y | x | y | x | y |\n", "|------|-------|------|------|------|-------|------|-------|\n", "| 10.0 | 8.04 | 10.0 | 9.14 | 10.0 | 7.46 | 8.0 | 6.58 |\n", "| 8.0 | 6.95 | 8.0 | 8.14 | 8.0 | 6.77 | 8.0 | 5.76 |\n", "| 13.0 | 7.58 | 13.0 | 8.74 | 13.0 | 12.74 | 8.0 | 7.71 |\n", "| 9.0 | 8.81 | 9.0 | 8.77 | 9.0 | 7.11 | 8.0 | 8.84 |\n", "| 11.0 | 8.33 | 11.0 | 9.26 | 11.0 | 7.81 | 8.0 | 8.47 |\n", "| 14.0 | 9.96 | 14.0 | 8.10 | 14.0 | 8.84 | 8.0 | 7.04 |\n", "| 6.0 | 7.24 | 6.0 | 6.13 | 6.0 | 6.08 | 8.0 | 5.25 |\n", "| 4.0 | 4.26 | 4.0 | 3.10 | 4.0 | 5.39 | 19.0 | 12.50 |\n", "| 12.0 | 10.84 | 12.0 | 9.13 | 12.0 | 8.15 | 8.0 | 5.56 |\n", "| 7.0 | 4.82 | 7.0 | 7.26 | 7.0 | 6.42 | 8.0 | 7.91 |\n", "| 5.0 | 5.68 | 5.0 | 4.74 | 5.0 | 5.73 | 8.0 | 6.89 |" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1\n", "\n", "Using standard `numpy` operations, show that each dataset has the same mean and standard deviation, to two decimal places." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2\n", "\n", "Using the standard `scipy` function, compute the linear regression of each data set and show that the slope and correlation coefficient match to two decimal places." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3\n", "\n", "Plot each dataset. Add the best fit line. Then look at the description of [Anscombe's quartet](https://en.wikipedia.org/wiki/Anscombe%27s_quartet), and consider in what order the operations in this exercise *should* have been done." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" }, "nbconvert": { "title": "Statistics" } }, "nbformat": 4, "nbformat_minor": 0 }