Vitruvian_Man_Experiment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Vitruvian Man\n",
    "\n",
    "When Leonardo da Vinci drew the now-famous image of a human male circumscribed by a circle and a square, he was conveying the ideal of human body proportions. He wrote, in mirror script, accompanying the drawing: \n",
    "\n",
    "\"For the human body is so designed by nature that the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part of the whole height; the open hand from the wrist to the tip of the middle finger is just the same; the head from the chin to the crown is an eighth, and with the neck and shoulder from the top of the breast to the lowest roots of the hair is a sixth; from the middle of the breast to the summit of the crown is a fourth. If we take the height of the face itself, the distance from the bottom of the chin to the under side of the nostrils is one third of it; the nose from the under side of the nostrils to a line between the eyebrows is the same; from there to the lowest roots of the hair is also a third, comprising the forehead. The length of the foot is one sixth of the height of the body; of the forearm, one fourth; and the breadth of the breast is also one fourth. The other members, too, have their own symmetrical proportions, and it was by employing them that the famous painters and sculptors of antiquity attained to great and endless renown.\n",
    "\n",
    "Similarly, in the members of a temple there ought to be the greatest harmony in the symmetrical relations of the different parts to the general magnitude of the whole. Then again, in the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centred at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.\"\n",
    "\n",
    "#### Scientific Question: \n",
    "Now, we ask: Is it the case that man (or woman) is as tall as he (she) is wide? Is the length of the body, measured from the top of the head to the bottom of the feet, indeed equal to the width of the body from outstretched finger to outstretched finger? \n",
    "\n",
    "#### Hypothesis: \n",
    "Null hypothesis: The length and width of human bodies is, on the whole, equal. \n",
    "\n",
    "#### Methods: \n",
    "All participants were socially pressured to participate and no signed consent was acquired. (What is the Declaration of Helsinki, anyway?) See next block for demographics. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9 \"adults\" (6 females, mean age 28.44, +/- 2.70 std) participated in this study.\n"
     ]
    }
   ],
   "source": [
    "% participant_data = {'subjID',age,height,width,female?}\n",
    "\n",
    "participant_data = {...\n",
    "'V1',27,166.5,169,1;\n",
    "'A1',26,169,172.5,1;\n",
    "'V2',31,161.5,155.5,1;\n",
    "'M1',25,160,155,1;\n",
    "'C1',26,185,181,1;\n",
    "'D1',30,184,192.5,0;\n",
    "'F1',33,172,175,0;\n",
    "'D2',28,172,173,0;\n",
    "'S1',30,177,171,1};\n",
    "N = length(participant_data);\n",
    "Nfemales = sum(cell2mat(participant_data(:,5)));\n",
    "Mage = mean(cell2mat(participant_data(:,2))); STDage = std(cell2mat(participant_data(:,2)));\n",
    "heights = cell2mat(participant_data(:,3));\n",
    "widths = cell2mat(participant_data(:,4));\n",
    "format long g\n",
    "fprintf('%d \"adults\" (%d females, mean age %.2f, +/- %.2f std) participated in this study.',N,Nfemales,Mage,STDage);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Correlate Heights and Widths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The correlation between height and width is r = 0.907489, with a p-value of 0.000724!\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Plot\n",
    "hxw_fig = scatter(heights,widths,'markeredgecolor', [127/255, 49/255, 158/255]);\n",
    "set(gca, 'FontName', 'Georgia')\n",
    "xlabel('Height (cm)')\n",
    "xlim([150 200])\n",
    "xticks([150:5:200])\n",
    "ylabel('Width (cm)')\n",
    "ylim([150 200])\n",
    "title('Comparison of Human Height to Human Width','FontWeight','bold')\n",
    "\n",
    "%% Regression line & correlation coefficient\n",
    "reg_line = lsline;\n",
    "[r,p] = corrcoef(heights,widths);\n",
    "r = r(1,2);\n",
    "p = p(1,2);\n",
    "\n",
    "fprintf('The correlation between height and width is r = %f, with a p-value of %f!',r,p);\n",
    "if p < .05 && p > .001\n",
    "    pval = 'p < .05';\n",
    "elseif p < .001\n",
    "    pval = 'p < .001';\n",
    "elseif p > .05\n",
    "    pval = 'p > .05';\n",
    "end\n",
    "dim = [0.2 0.5 0.3 0.3];\n",
    "format long g;\n",
    "str = {['r = ' , num2str([round(r*100)/100])],pval};\n",
    "annotation('textbox',dim,'String',str,'FitBoxToText','on','FontAngle','italic','FontName','Georgia');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, clearly we are not exactly as wide as we are tall. If the correlation coefficient were equal to 1, we would still only be able to conclude that a change in height results in a change in width of the same magnitude. This wouldn't quite tell us that those two values would always be identical. \n",
    "\n",
    "However, a correlation of 0.91 is insanely high, and a glance at the graph above tells us that height predicts width with pretty high accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compare Mean Heights and Widths\n",
    "\n",
    "Let's look a bit more closely at our sample's heights and widths:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "avgheight = mean(heights);\n",
    "stdheight = std(heights);\n",
    "semheight = stdheight/sqrt(length(heights));\n",
    "avgwidth = mean(widths);\n",
    "stdwidth = std(widths);\n",
    "semwidth = stdwidth/sqrt(length(widths));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean difference between height and width is 0.277778. This difference did not reach significance!\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% Plot\n",
    "bar([1 2],[avgheight,avgwidth],'facecolor',[127/255, 49/255, 158/255]);\n",
    "hold on\n",
    "errorbar([1 2],[avgheight,avgwidth],[semheight,semwidth],'color','k','LineStyle','none')\n",
    "set(gca, 'FontName', 'Georgia') \n",
    "xticklabels({'Height (cm)','Width (cm)'})\n",
    "ylabel('Centimeters')\n",
    "xlim([0 5])\n",
    "ylim([150 200])\n",
    "dim = [.55 0.6 0.3 0.3];\n",
    "format long g;\n",
    "str = {['M_{H} = ',num2str([round(avgheight*100)/100]),'  Std_{H} = ',num2str([round(stdheight*100)/100])],...\n",
    "['M_{W} = ', num2str([round(avgwidth*100)/100]),'  Std_{W} = ', num2str([round(stdwidth*100)/100])],...\n",
    "'*Error bars denote SEM.'};\n",
    "annotation('textbox',dim,'String',str,'FitBoxToText','on','FontAngle','italic','FontName','Georgia');\n",
    "title('Average Height and Width of the Human Body')\n",
    "\n",
    "%% T-Test\n",
    "[h,p] = ttest(heights,widths);\n",
    "fprintf('The mean difference between height and width is %f. ',avgheight-avgwidth);\n",
    "if h == 0\n",
    "fprintf('This difference did not reach significance!');\n",
    "else\n",
    "fprintf('This difference is significant.');\n",
    "end\n",
    "\n",
    "if .001 < p < .05\n",
    "    pval = 'p < .05';\n",
    "elseif p < .001\n",
    "    pval = 'p < .001';\n",
    "elseif p > .05\n",
    "    pval = 'p > .05';\n",
    "end\n",
    "dim = [.75 0.4 0.3 0.3];\n",
    "format long g;\n",
    "str = {pval};\n",
    "annotation('textbox',dim,'String',str,'FitBoxToText','on','FontAngle','italic','FontName','Georgia');\n",
    "title('Average Height and Width of the Human Body')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conclusions\n",
    "\n",
    "Our correlational analysis of height and width revealed that height and width are tighly correlated in humans (both males and females). While the proportion of height to width is nearly equal, people typically have a slightly shorter wingspan compared with their height. Note that width is also slightly more variable across subjects. \n",
    "\n",
    "After comparing the distribution of heights and widths, we accept the null hypothesis that no differences exist in the means of height and width. Since no sigificant difference exists between height and width, and we may declare that we are indeed Vitruvian Men and Women! "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Matlab",
   "language": "matlab",
   "name": "matlab"
  },
  "language_info": {
   "codemirror_mode": "octave",
   "file_extension": ".m",
   "help_links": [
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "matlab",
   "version": "0.16.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}