{ "metadata": { "name": "principles_statistics" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Principles of statistics in Statistical Parametric Mapping" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook is a basic introduction to the statistics of statistical parametric mapping (SPM). The page is designed for\n", "readers who have had very little formal statistical background, and\n", "I have tried to keep formulae to a minimum. \n", "\n", "For a more technical treatment of the statistical background, see the [chapter on the general linear model](http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2/pdfs/Ch7.pdf)\n", "in the book [Human Brain Function (2nd edition)](http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2)" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Getting the data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to run this tutorial, you'll need to \n", "[download](http://imaging.mrc-cbu.cam.ac.uk/downloads/Tutscans/egscans.tar.gz) \n", "and unpack a set of data files.\n", "\n", "The following two commands will download and unpack them on linux:\n", "\n", " wget http://imaging.mrc-cbu.cam.ac.uk/downloads/Tutscans/egscans.tar.gz\n", " tar xzf egscans.tar.gz\n", "\n", "The `fetch_scans()` function below will do all the downloading\n", "in a cross-platform manner, using python-only tools. You should run it even if you downloaded the files\n", "manually, as it will compute the necessary paths for the rest of the script (it won't re-download files\n", "already present)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import os\n", "import tarfile\n", "import urllib\n", "\n", "def fetch_scans():\n", " # Names of the files in the data bundle\n", " scans_dir = 'egscans'\n", " files = [os.path.join(scans_dir, 'snn03055dy%i.img' % i) for i in range(1,13)]\n", " \n", " # The remote url and filename for local storage\n", " data_url = 'http://imaging.mrc-cbu.cam.ac.uk/downloads/Tutscans/egscans.tar.gz'\n", " tarball = 'egscans.tar.gz'\n", "\n", " # First, check that we don't already have the files, whose names are:\n", " if all(map(os.path.isfile, files)):\n", " print 'All files already present, nothing to download.'\n", " return files\n", " \n", " # If we don't have them, make the storage directory, fetch (if needed)\n", " # and unpack skipping the .mat files that are in the tarball.\n", " if not os.path.isdir(scans_dir):\n", " os.mkdir(scans_dir)\n", "\n", " if not os.path.isfile(tarball):\n", " print \"Fetching remote tarball, this may take some time depending on your network...\"\n", " urllib.urlretrieve(data_url, tarball)\n", "\n", " print \"Unpacking scans, omitting .mat files\"\n", " tf = tarfile.open(tarball, 'r:gz')\n", " image_files = [ f for f in tf.getmembers() if not f.name.endswith('.mat')]\n", " tf.extractall(scans_dir, image_files)\n", " print \"All files unpacked into\", scans_dir, ', done!'\n", " return files\n", "\n", "files = fetch_scans()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "All files already present, nothing to download." ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Starting the analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now make actual images out of these files" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import nibabel as nib\n", "images = map(nib.load, files)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": true, "input": [ "# grand mean for data\n", "GM = 50" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we load the affine transformation from the first image (it's the same for all) and extract the conversion\n", "parameters from voxels to MNI space (in mm)." ] }, { "cell_type": "code", "collapsed": true, "input": [ "# transformation from voxel no to mm\n", "M = images[0].get_affine()\n", "# mm to voxel no\n", "iM = np.linalg.inv(M)\n", "# coordinates of voxel of interest in mm (MNI space)\n", "posmm = [-20.0, -42, 34]\n", "# coordinates in voxel space (in homogenous coordinates)\n", "posvox = np.dot(iM, posmm + [1])\n", "# We grab the spatial part of the output. Since we want to use it as an \n", "# index, we need to make it a tuple\n", "posvox = tuple(posvox[:3].astype(int))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to define a small utility function commonly used in SPM, we'll call it `global_mean`." ] }, { "cell_type": "code", "collapsed": true, "input": [ "def global_mean(img):\n", " \"\"\"Compute a \"sorted global mean\" of an image.\n", "\n", " This returns the mean of the image voxels that are in the range above \n", " 1/8 of the mean.\"\"\"\n", " \n", " m = img.mean()/8.0\n", " return img[img>m].mean()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "With this utility, we can now get the data for the voxel of interest across all the images, and compute the global mean of each scans:" ] }, { "cell_type": "code", "collapsed": true, "input": [ "nimgs = len(images)\n", "vdata = np.zeros(nimgs)\n", "gdata = np.zeros(nimgs)\n", "for i, V in enumerate(images):\n", " d = V.get_data()\n", " vdata[i] = d[posvox]\n", " gdata[i] = global_mean(d)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can display slices from the scans. Here is slice 30 of the last scan:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "last_image = images[-1]\n", "last_data = last_image.get_data()\n", "imshow(last_data[:, :, 30])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "output_type": "display_data", "png": 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xLHOg4oXtsAZVqkDp734MwAexVOS/LN66xwbVhz/8Ybz++uv4/Oc/j9dffx0f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\n" } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Plot globals" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(gdata, vdata, 'x')\n", "plt.xlabel('TMVV for scan')\n", "plt.ylabel('Voxel value for -20 -42 34')\n", "plt.title('The relationship of overall signal to values for an individual voxel')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "output_type": "display_data", "png": 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GmKHprusNKysrSKVSjdcuX74Mb29vSCQS/P777/e8UCJqdrQkkUharBMbG4v5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\nbJnGvK5evQqJRIKoqCgAgIWFBYyMuC9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AmJmZweXl5Ve3jOif429YRA243W5sbGzg7OwM\nj4+PNbHK14Jms/lDM9JKLJFINHwGorob9u+dsUVEGdPpdGhvb6+bIxqN4uLiAtFoFOFwGNfX13U7\nbxcKBQQCAZyfn8NqtcLj8eD5+VmJV5rUarValEqlz7aE6FuxYBE1sLy8DKPRiMHBQZyentbEvF4v\nAoEADAZDzWkFeC9YLpcLhUIBOzs7dXNXFxW73Y7b21ukUimYTCbs7+9jd3f307WJCO7v7+FwODA6\nOore3l6USiX4fD5EIhEMDw9Dr9cjl8vh5eUFWq0WFosFyWQSx8fH8Hg8X9sUom/EgkWE+iceq9WK\ntbU1Zaz6Mx0dHXA4HHh4eEB3d3dNrv7+frS2tmJiYgI6na7hfJV8Go0G29vbWF9fRy6Xw8rKivJw\nXqN3icrlMhYXF5HP59HW1oZgMIiWlhbMz8/j6ekJ09PTKJfLCAaDmJ2dxdzcHGw2G7q6uuByuf64\nJqKfiM1viYhIFfinCyIiUgUWLCIiUgUWLCIiUgUWLCIiUgUWLCIiUgUWLCIiUoVfYyE6JJ6vlfIA\nAAAASUVORK5CYII=\n" } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "# We can check against the current data in the Cambridge wiki tutorial\n", "from IPython.core.display import Image\n", "Image('http://imaging.mrc-cbu.cam.ac.uk/images/st_globals.gif')" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "" ], "output_type": "pyout", "prompt_number": 9, "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": true, "input": [ "# proportionally scale data\n", "pvdata = vdata / gdata\n", "# scale to global mean of 50\n", "Y = pvdata * GM\n", "# our covariate\n", "ourcov = np.array([5,4,4,2,3,1,6,3,1,6,5,2])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot data \n", "plot(ourcov, Y, 'x')\n", "xlabel('Task difficulty')\n", "ylabel('PS voxel value')\n", "xlim(0, 7)\n", "title('The relationship of task difficulty to voxel value');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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FCxYgLCyszu2z+YgeF3FxwMCBqn0ISiWQmgqMGqW/uMjwPFKfgkKhqHfFQ4YM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\n9H+oxp9e10l9PwAAAABJRU5ErkJggg==\n" } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": true, "input": [ "# guess intercept, slope, estimated points\n", "guessic = 55\n", "guesslope = 0.5\n", "guessPts = guessic + guesslope*ourcov" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "For plotting it will be convenient to have the boundaries of our plot region available" ] }, { "cell_type": "code", "collapsed": true, "input": [ "minx = 0\n", "maxx = ourcov.max()+1 # min max x for plots\n", "axs = np.array([minx, maxx, Y.min()*0.98, Y.max()*1.02])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot data with guess intercept and slope\n", "plot(ourcov, Y, 'x')\n", "plot(axs[:2], guessic+guesslope*axs[:2], ':') # guessed line\n", "# plot guessed residuals\n", "for i, c in enumerate(ourcov):\n", " plot([c, c], [Y[i], guessPts[i]], color='r')\n", "plt.axis(axs)\n", "xlabel('Task difficulty')\n", "ylabel('PS voxel value')\n", "xlim(0, 7)\n", "title('A first guess at a linear relationship, and its residuals');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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pKcEvv/yCYcOG4e2331ZZkIQQzZJblIuJRyZy93Ad3G5w/YmeaLx6e/ZSqRRX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\n" } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "# residuals from guess slope\n", "guessRes = Y - guessPts" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we construct the design matrix $X$." ] }, { "cell_type": "code", "collapsed": true, "input": [ "X = np.column_stack([ourcov, ones(nimgs)])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We would like to display it in a useful way" ] }, { "cell_type": "code", "collapsed": true, "input": [ "def scale_design_mtx(X):\n", " \"\"\"utility to scale the design matrix for display\n", "\n", " This scales the columns to their own range so we can see the variations \n", " across the column for all the columns, regardless of the scaling of the \n", " column.\n", " \"\"\"\n", " mi, ma = X.min(axis=0), X.max(axis=0)\n", " col_neq = (ma - mi) > 1.e-8\n", " Xs = np.ones_like(X)\n", " mi = mi[col_neq]\n", " ma = ma[col_neq]\n", " Xs[:,col_neq] = (X[:,col_neq] - mi)/(ma - mi)\n", " return Xs" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": true, "input": [ "def show_design(X, design_title):\n", " \"\"\" Show the design matrix nicely \"\"\"\n", " figure()\n", " plt.gray()\n", " imshow(scale_design_mtx(X), interpolation='nearest')\n", " title(design_title)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "# display using our fancy function\n", "show_design(X, 'Design matrix for the first analysis')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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} ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to know the degrees of freedom. In this simple case, we have two *effects* (the intercept and the slope) and 12 observations, leaving us with 10 degrees of freedom. In general, the number of *effects* we have is given by the number of independent columns in the design matrix $X$ above. This is the *column rank* of $X$. This is given by the numpy function ``numpy.linalg.matrix_rank`` for numpy >= 1.5, but in case you have an earlier version of numpy, a crude calculation of the matrix rank is a couple of lines of code:" ] }, { "cell_type": "code", "collapsed": true, "input": [ "def matrix_rank(X):\n", " U, S, V = np.linalg.svd(X)\n", " # Number of singular values above an arbitrary small threshold\n", " return np.sum(S > 1e-5)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can calculate the degrees of freedom in a more general way:" ] }, { "cell_type": "code", "collapsed": true, "input": [ "df = nimgs - matrix_rank(X)\n", "# mean SoS for guess slope\n", "guessRSS = (guessRes**2).sum() / df" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The analysis giving the least squares fit is very simple: we matrix multiply the pseudoinverse of $X$ (denoted $X^+$) by the data, to get the estimation of the model parameters, the $\\hat\\beta$ 's : $\\hat\\beta = X^+ Y$ " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# the analysis, giving slope and constant\n", "B = dot(pinv(X), Y)\n", "print B" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 0.63928135 54.39383796]" ] } ], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot data with new least squares line\n", "plot(ourcov, Y, 'x')\n", "bound = np.array([minx, maxx])\n", "plot(bound, bound*B[0]+B[1], 'r')\n", "axis(axs)\n", "xlabel('Task difficulty')\n", "ylabel('PS voxel value')\n", "title('The least squares linear relationship');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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SvU6nQ6/XExMTQ1RUFACzZs2iT58+xMbG4unpySeffGKKQwshhCiAyco4iqLku63X6wkI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\nCCvwfycx6Y3CQpfvAAAAAElFTkSuQmCC\n" } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll need some statistical machinery from scipy" ] }, { "cell_type": "code", "collapsed": true, "input": [ "from scipy.stats import t as tdist, norm as normdist" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now we can compute our stats for this contrast:\n", "The $\\textbf{Residual Sum of Square}$ (RSS) is :\n", "\n", "$$ RSS = \\sum_{i=1}^{12} (Y_i - X_i \\beta)^2$$\n", "\n", "$X_i$ is the $i$th row of the matrix $X$. The $\\textbf{Mean Residual Sum of Square}$ is :\n", "\n", "$$ MRSS = RSS / \\textit{df} $$\n", "\n", "where $\\textit{df}$ are the degrees of freedom, computed as the number of observations (here, 12) minus the rank of the design matrix (ie, the number of independant vectors in X). The $MRSS$ is the noise variance estimation: $\\widehat{\\sigma^2}$.\n", "\n", "The $\\\\textbf{Standard Error}$ (SE) of $c \\\\beta$ is computed with $\\textrm{SE} = \\\\sqrt{\\\\widehat{\\\\sigma^2} c (X^t X)^+ c^t} $ \n", "(why is that so is to be expanded here ...)\n", "The t test is then : $t = \\\\frac{c \\\\beta}{\\\\textrm{SE}} $" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Contrast\n", "C = np.array([1, 0])\n", "# t statistic and significance test\n", "RSS = ((Y - dot(X, B))**2).sum()\n", "MRSS = RSS / df\n", "SE = np.sqrt(MRSS*dot(C, (dot(pinv(dot(X.T, X)), C.T))))\n", "t = dot(C, B)/SE\n", "ltp = tdist(df).cdf(t) # lower tail p\n", "p = 1-ltp # upper tail p \n", "\n", "# print results to window\n", "print 'First TD analysis: t= %2.2f, p= %0.6f' % (t, p)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "First TD analysis: t= 7.95, p= 0.000006" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can package the analysis up into a function:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def t_stat(Y, X, C):\n", " \"\"\" betas, t statistic and significance test given data, design matrix, contrast\n", " \"\"\"\n", " # Calculate the parameters\n", " B = dot(pinv(X), Y)\n", " RSS = ((Y - dot(X, B))**2).sum()\n", " # Recalculate df\n", " df = X.shape[0] - matrix_rank(X)\n", " MRSS = RSS / df\n", " SE = np.sqrt(MRSS*dot(C, (dot(pinv(dot(X.T, X)), C.T))))\n", " t = dot(C, B)/SE\n", " ltp = tdist(df).cdf(t) # lower tail p\n", " p = 1 - ltp # upper tail p\n", " return B, t, p\n", "\n", "# Results are the same\n", "print 'First TD analysis again: B = %s, t= %2.2f, p= %0.6f' % t_stat(Y, X, C)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "First TD analysis again: B = [ 0.63928135 54.39383796], t= 7.95, p= 0.000006" ] } ], "prompt_number": 26 }, { "cell_type": "code", "collapsed": true, "input": [ "# save data for analysis in e.g. SPSS\n", "np.savetxt(\"voxdata.txt\", Y)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "now analysis for added covariate\n", "note that this and all the other analyses here use\n", "exactly the same code as above" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# design matrix, df\n", "X = np.column_stack([ourcov, np.arange(1, nimgs+1), np.ones(nimgs)])\n", "show_design(X, 'Design matrix for added covariate')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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} ], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "# Contrast\n", "C = np.array([1, 0, 0])\n", "# the analysis\n", "B, t, p = t_stat(Y, X, C)\n", "print 'Added covariate analysis: t= %2.2f, p= %0.6f' % (t, p)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Added covariate analysis: t= 7.81, p= 0.000013" ] } ], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditions analysis" ] }, { "cell_type": "code", "collapsed": true, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 29 } ], "metadata": {} } ] }