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@Gilles86
Last active June 27, 2022 15:29
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{
"cells": [
{
"cell_type": "code",
"execution_count": 58,
"id": "8ca5ee9b",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.stats as ss\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"id": "734853b6",
"metadata": {},
"source": [
"Subjects are sampling from two distributions. The first has an average of `0`, the 2nd has a changing average o `x`. Their sds are .25"
]
},
{
"cell_type": "code",
"execution_count": 114,
"id": "dc57aab5",
"metadata": {},
"outputs": [],
"source": [
"n_samples = 1000\n",
"sd1 = .25\n",
"sd2 = .25\n",
"dist1 = ss.norm(0, sd1)\n",
"\n",
"df = []\n",
"\n",
"for x in np.linspace(-2, 2, 15):\n",
"\n",
" dist2 = ss.norm(x, sd2)\n",
" \n",
" diff = dist2.rvs(n_samples) - dist1.rvs(n_samples)\n",
" \n",
" df.append(pd.DataFrame({'log(frac)':[x]*n_samples, 'chose_2':diff > 0.0}))\n",
" \n",
"df =pd.concat(df)"
]
},
{
"cell_type": "markdown",
"id": "006f8bc7",
"metadata": {},
"source": [
"## log x-ticks"
]
},
{
"cell_type": "code",
"execution_count": 115,
"id": "bf9a708b",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/gdehol/miniconda3/lib/python3.8/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
" warnings.warn(\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sns.lineplot('log(frac)', 'chose_2', data=df)\n",
"\n",
"plt.xticks(np.linspace(-2, 2, 5))\n",
"\n",
"plt.xlabel('log(option 2/option 1)')\n",
"sns.despine()"
]
},
{
"cell_type": "markdown",
"id": "f6120d6b",
"metadata": {},
"source": [
"## Natural x-ticks"
]
},
{
"cell_type": "code",
"execution_count": 116,
"id": "7d44049a",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/gdehol/miniconda3/lib/python3.8/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
" warnings.warn(\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sns.lineplot('log(frac)', 'chose_2', data=df)\n",
"\n",
"plt.xticks(np.linspace(-2, 2, 5), np.round(np.exp(np.linspace(-2, 2, 5)), 2))\n",
"plt.xlabel('option 2/option 1')\n",
"\n",
"sns.despine()"
]
},
{
"cell_type": "markdown",
"id": "67c3f048",
"metadata": {},
"source": [
"## Weber fraction = difference at 2 standard deviations"
]
},
{
"cell_type": "code",
"execution_count": 117,
"id": "4dd46199",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9772498680518208"
]
},
"execution_count": 117,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Standard deviation of the difference of two normal distribtions is the sqrt of their summed squares\n",
"sd_diff = np.sqrt(sd1**2 + sd2**2)\n",
"\n",
"# At that point, roughly ~97.7% of probability mass is smaller\n",
"ss.norm().cdf(2)"
]
},
{
"cell_type": "code",
"execution_count": 136,
"id": "8191e5a6",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/gdehol/miniconda3/lib/python3.8/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
" warnings.warn(\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"So the weber fraction is 1.03\n"
]
},
{
"data": {
"image/png": 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uziPhoKJIw5HI9qfkIdJHhKJxLr74d7x7+akcOLqcYDRORaGPfJ9G0JXtT8lDpI9Ysa6R1599HP/IPThgbA3BaJzBOmUlPUTJQ6QPcM5x930PEgm2Mvmw4yjI9WAGZX4NRyI9Q8lDpA9oCce49+478JQO5IQjZxAIx6kuzsfn0UdYeob2PJE+4MNPl/Dpe69Ttceh7DW8gnA8ziANRyI9SBeHi/RysXiCJiui9vS/Mn3v8ZgZXo2gKz1MRx4ivVxTMMobn9fhGTiab+6zM63hGDWlBeRoBF3pQUoeIr3cE8+9yM1//C8G+kKMGlBINJ5gQImGI5GepeQh0ouFonFuuflmVn/wL6btOpxYwlHg81Cs4Uikhyl5iPRiK76s5/Xnn6Rw3P4cutswWsMxhpRrBF3peUoeIr2Uc47b77mXaDjIHtOOpqooj3giQaWGI5FeQMlDpJdqDce4/5478VbUctzMgwlF45QU5OLP1Skr6XnaC0V6qdUNAXIHjqZi8GT2HTWAtkiM8YOKezosEUDJQ6RXiiccKxtD8I3TmTmignxfDm1RKCvUKSvpHXTaSqQXqm8NMevJZ2kNRTlobDWBSJwBRXnkeTWCrvQOnSYPM/OY2Q/M7A9mNmWjst9kLjSR7PWPp57hhgtPw7N8LrvXlhGKxakp1XAk0nt05cjjb8CBQB1wlZn9pV3ZsRmJSiSLhWNx7rr9NnLyizji8MMByDENRyK9S1eSxyTn3MnOuSuAyUCRmT1sZnmALjYX6WZLv1jLay/MpnCnA5m+61DawjEGlebj1Qi60ot0ZW/8qofOORdzzp0DvA+8ABRlKC6RrHXbXfcQi4TZcf9vMaKqkGgiwcBinbKS3qUryWOumc1ov8A5dzFwKzAiE0GJZKu2cIynn3wC34ARHHnwfsTiCbw5ORTn68JI6V063SOdc6dsZvlNwE0bXpvZoc6557oxNpGss64lzJRzL6PutflMHVtNayTG0HK/RtCVXqc7T6L+bzfWJZJ1EgnH8voAby1rZu9dx1NemEs84agq1gi60vt0Z/LQVyORbVDXEuD0ow5h6VvPcfC4asKxOH6fhyKNoCu9UHcmD9eNdYlknVn/eIKlH88jr8DP5JEVtIZj1Jb7ezoskQ7p2j+RXiASS3DPnbfjKSxj+vTDyPcl7ySv0Ai60kt1Z/JY2o11iWSVRcu/4PV/Pod/p6lM23kwgUiM0gLfV0lEpLfpcvIwM7+Z/dbM/p56PcbMvrmh3Dmnu81FttLNt91JIh5j6OTD2WVIKYFInCFlBT0dlshmpXPkcSsQBr6Rer0SuKTbIxLJMoFIjMrhYymdfByHHzAJADMo8+uUlfRe6SSPUc65PwFRAOdcEF1hJbLN1reEaSkfQ9nUM5Mj6IbjVBfnketVl6T0XulcAxgxswJSV1WZ2SiSRyIispUSCcd9D/2DFxYnGD1wGEMr/NS1hakp1aRP0rul89XmImA2MNTM7gbmAP+VkahEssTaxlYuvvB85j9+EwePrSaecHhzjBKNoCu9XJePPJxzz5nZu8A+JE9XXeCcW5+xyESywD2zHqGtuZFBMw/hgB0H0JoaQdej4Uikl0vnaqspQMg59yRQBvzKzIZnKjCR/i4UjXP/PXfgK6livwMOorTARyyRoLpEI+hK75fOaavrgYCZ7Q5cCCwD7shIVCJZ4MNPl/L2Ky9SsPPBTNuphmg8QZ43h2INRyJ9QDrJI+acc8BRwFXOuSsB9eqJbIVEwjHn5VfJ8XgZMGE6e49IDkcypKwAM52ykt4vna84LWb2S+BUYH8z8wDq1RPZCs2hKOMnT2PYj+9m5l47kOvNoSWsEXSl70jnyOMEkpfmnuWc+xIYAlyekahE+rml65p5c0k9CV8BM3apIRSNU5TnxZ+rU1bSN3Q5eaQSxt1AaWpYkpBzTn0eImkKReP85sKfcu2FpzN+UDHDKvy0RWIajkT6lHSutvoO8BbwbeA7wJtmdnymAhPpr1asbWDOk48Q95czc9cakl2JUF6o4Uik70jnGPnXwN7OubUAZjYAeB54MBOBifRHzjnuvv9BQoE2Rkw4jCmjqghG41QU5moEXelT0unzyNmQOFLq0txeJOs1B2M8cv/deMsG8s3p08j15hCMxhmsU1bSx6Rz5DHbzJ4B7k29PgF4qvtDEum/3p7/CfPefpXSKSczc9fBxBMOT45RpuFIpI9JZ3iSC83sOGAKyeFJbnTOPZKxyET6mXAsTshTwMgjL2DEnlMYWuGnMRhhcGkBXo8O4qVvSeu6QOfcQ8BDGYpFpF+ra4mwrClBYtwhHLPfjgDE4gkGlWo4Eul70rna6lgz+8zMmsys2cxazKw5k8GJ9BfOOWb/6xVu/fvfKPTE2HdUFYFIjHJ/LoUajkT6oHSOlf8EHOmcK3XOlTjnip1zJZkKTKQ/aQ7GuPPmG3n3keuZuuMAcr05BCJxhlb4ezo0ka2STvJY45xbmLFIRPqxRavW8upzT1A47gC+OWEksXgCn8c01az0WZ0eL5vZsamnc83sfuAftJtB0Dn3cGZCE+kfwrE49973ANFwiEkHH01tuZ+GQIQRlX7N2yF9VldOtn4r9dMBAWB6uzIHKHmIbEFdS4RH7r8Lb0UtJxxxMM45Es5p3g7p0zpNHs65MwHM7HaSswc2pl6XA3/OaHQifZxzjs9W19EcilM14TCmjK6iLRKnUneUSx+XzmUeu21IHADOuQYz27P7QxLpP5pDMepDUHz8Hzly98H4PDk0BaOMG6SpcKRvS2t4ktTRBgBmVkGa94mIZJsv6lt5/r1FJBzM2Dk5W2C+L4dS3VEufVw6yePPwGtm9gczuxh4jeTluyLSgUgsweNPzeb6HxxKbXg5Q8oLaA5FGVrhJ0cd5dLHpTM8yR1mNhc4mOTwJMc65xZkLDKRPq6uNcz9d9+J+Qr49owDcM7hgAGaLVD6gXSHJ1kAKGGIdMI5x0dLvuCDV5+nfMLh7D9uMK3hGINK8snzqqNc+j6NxiaSAS3hGPfffx+JWJSZx56Iz5NDOJbQ0OvSbyh5iGTA6sYgj8+6F1/1SE45YirhWBx/roeSfF1jIv2D9mSRbhaNJ1jVGGTAUT9njAUYXFZAXVuYsQOLMVNHufQPOvIQ6Wb1rWHmrWyiJbeSk791KAnnMIPKInWUS/+h5CHSjZxzfL6mib/8+gJ8dYuZPLKCllCMmtICcr36uEn/ob1ZpBu1hmM8+viTLH9rNrtUGD5PDtF4nBpN+CT9jJKHSDf6sinEg/fdRU5hGeecfAyhaJzifB/F+bqjXPoXJQ+RbhKNJ5i/aDmL332ZHfaZSW1lMW2RGMM04ZP0Q0oeIt2koS3CbXfcBYk4J59yGvGEw5NjVBRqwifpf5Q8RLrJ8voAK9ocpTvvz9EHTaYlHGVwaQFejz5m0v/oPg+RbtASirKsro3Goftz9lEn4fXkEE84BqmjXPopfSUS6QZrmkM8Muc1ErEo03ceRCASo6zAR2Gevp9J/6TkIbKNYvEEi1c3cN9F34fXbmZQST7BaJyh6iiXfkzJQ2Qb1bdFuPuBh4mHWjn62OOJxRN4c4wyvzrKpf9S8hDZRssbAjzzyL34SgdwyjFH0BKOMbTcj0cTPkk/puQhsg1awzHemb+ItQvfZuIhR5Pr85JwjuoSdZRL/6bkIbIN1jSFuHfWg4Dj3O9/j7ZInMrCXApyNeGT9G+6FERkK8XiCVY0BGja4RAO/uVO7LHLONa3hhk3qLinQxPJOB15iGyl+rYI7y5roCEQ5cQZBxCNJ8j35VBaoHGspP9T8hDZSisbg1z/p98TfPVO9h5RQXMoytAKPznqKJcsoOQhshXawjE+WrqWxS//g2pfkBwDB1RpwifJEkoeIlthTXOIO+97ABcJctaZZ9IajjGwOJ98nzrKJTsoeYikKRZPsLy+jdeffpDCAUOYNnUq4ViCIWUFPR2ayHaj5CGSpsZglGff+JDWpfM45MjvEIkn8Od6KCnQxYuSPZQ8RNK0oj7A3GUNVO41kx98L3nKaliFHzN1lEv2UPIQSUMgEmPRmhY+C/g5+5eXMbh2KGZQqY5yyTJKHiJpWNMc4tF/vkVk9SccMn4gLaEYNaUF5Hr1UZLsoj1epIviCceyujaeuusG1s26iNJciMbj1GjCJ8lCSh4iXVTfFublj5bTuOAV9p1+JM7jozg/+RDJNkoeIl0QjSf4dE0rD82ahYuF+f5ZZ9EWSXaUi2QjJQ+RLli6vo1VjQE+fulxqmpHsfPuE/DkGBWFmvBJspOSh0gnmgJRltcHePH9xUTrVnD8SafQFokxuLQAr0cfIclOuqtJZAti8QQff9lMgc/Da19EOfryJzhj+hiCCccgdZRLFtPXJpEtWNEQIBiN88z81TQEInxrwgjw5VNa4KMwT9+9JHspeYhsRksoytL1AZoCUa674W803H4eVYl6gtE4Q9VRLllOyUOkA4mE45M1LfhyjEvvnUPdnJsYN3oHamqH480xyv3qKJfspuNukQ6sagrSEozxxPsreO/OS/D7C7j0iutpiyYYXuHHowmfJMspeYhsJBCJsXhdG2ubw9xy9f8R+fIz/ueG2xkwcBD1gQjVJeooF9FpK5F2nHN8tqaVeDzBFc8uJL7qI4447iSmH3EUbZE4lYW5FORqwicRHXmItLO2OUx9IMJD737B6tYo1975CGMH+oknHMFojJ2HlPR0iCK9go48RFJC0Tifrmlhybo27rv97xw6Ip89RlRRUOCnPhBmTHUxJRrHSgRQ8hD5yufrWglEYlxyza3UP3cDvkUvANAUjDCgOI/ack0zK7KBkocIsL4lxJfNIW565l2WPXoFo3bane+f91NC0Thmxo4DizVToEg7Sh6S9SKxBJ+saWXeikaeuOa35CSi/OW6m8jxeGkJRdllcCl5XnWSi7Sn5CFZb2ldK3WtYS6/8lpCS9/jv/77j4wcNYb6QJjR1UWU+tXPIbIxXW0lWa0pEGV5XYA7Xl9G/ph9Of2CIk447SyaQ1EqC/OoLdcwJCIdUfKQrBWLJ1j4ZTNvLFrD20vWc84hu3Pk7jMJx+I45xg7qJgc3Uku0iElD8laKxoCrKgP8NfLLsF9+TGHnv0cCedoDsXYc2gZ+T71c4hsjvo8JCu1hKJ8vraN/7vtYepff4gpe0+goKCAhkCEkVV+yjVDoMgWKXlI1tkwYu5T7yzinTsuYcCQ4fzmD5fSHIxS5s9leEVhT4co0uvptJVknVVNQRauaubGy35Noq2BK+65H29uAZFojHHq5xDpEh15SFYJRGJ8vLqZG5+bR3TNYs768YXsvPsEmkIRdqopUT+HSBfpyEOyxoYRc5+Yt5oVAQ//d/fTTBlbQ31bhBGVhVQW5fV0iCJ9ho48JGusaQrxxqJ13Pn365i6QwkH7jyUYMxRUuBleKX6OUTSoeQhWSEUjTN/VRP/86fLqX/hJkaHPiEaTxBLJNipplQzA4qkSclDssLn61q57qE5LH/2VvY+aCbfOvo4GgLJfg5N7iSSPiUP6ffWt4R4+oNlPHHlrygsKePPV15LQzDK8Ao/VcWaUlZka6jDXPq1SCzBu8sb+dMlfyBat5y/3P4gXn8JBV5j5ICing5PpM9S8pB+bWldK7e9tpTcXafzvSm7s++BB9MSirL70Ar1c4hsAyUP6bcaAxFmvfk5ry5az6nT9+HEvYeyvi3MLoNL8edq1xfZFvoESb8Uiyd4ffF6/vSL8ynIy+P4c2fREIhQW15AdYn6OUS2lTrMpV9aXt/Gr/50Dc0LX+WIg/YlEncU5nrZoUr9HCLdQclD+pVYPMGK+gBXPvIKHzxwBSN33Zsfnn8B4XiC8YNL8Hq0y4t0B522kn4hkXCsbw2zaF0ry9e1cOMf/gOPx8O1f7uZlnCcnQeXUpin3V2ku+jTJH1eYyDCojWttIRjrG0Oc9U/XiHasJqfX3w5/oqBDCzNZ2Cp+jlEupOSh/RZbeEYS9a38mVziA8WfcEtt95Gc+03KC4bwOX3vci+Ow0FYLTu5xDpdkoe0ueEonFW1AdYsr6Nfzz3Eg/dfSvr3n8BF4twzAU1/PyMw8j15NAYjLL3yAr1c4hkgJKH9BmxeIJVjUHmf9HEcx+u5Mafn0bgi0/w5Oaz74xj+fGPfsROu+6Gc471bWHGDyqhSP0cIhmhT5b0ehs6w2e98Db3P/4sa2v2JRRLMGjUzux34nc558zTKCktIxSNs74thGEMq/AzSP0cIhmj5CG92vrmAJfecBd33XoTaz9+G/PmctJfn+KE/cYz8vxbiMYTtIZj1LWFKcr3stOgEsoKc8nzaqRckUxS8pBeqTkY5ZKbHuSq315AuGkd3pIBTDnhPH563g8ZNbyW1nCM9a1h8n05jKj0U1WcpyFHRLYjfdqk13DO8eQzz/PCZw283lrJipVR8qpHcOx5/82PTjsej9dHOBanJRylpjSfAcX5lOR7MdMAhyLbm5KH9LjGxkauu/Fmrrj6Otat/JyCMfsw+exL+fmx32DiTw8nFI8TwyjL9zK2rJjSAp9GxBXpYRlPHmY2A7gS8AA3Oecu26jcUuWHAwHgDOfcu1va1swqgPuBEcBS4DvOuYZMt0W2XiKRoLm5mYaGBhobG9ltt93weDz87Be/4Zor/kw0HCK3ZiwTTvk155z5XcYNqcQBPl8OOwwoVD+GSC+T0eRhZh7gWuBQYCXwtpk95pxb0G61mcCY1GMycD0wuZNtfwHMcc5dZma/SL3+eSbbIhAMBmlsbKS+vp4hw4bjcnL5YP5HvDBnDuvrG75KDI2NDZz+H5dgRWXMvv9WZt9+NaFACzj3VV2H/PExYrnFzHuvnvxxBzL9qJM5+fCp1JTmk+/LYUhZgfoxRHqxTH8yJwGLnHOfA5jZfcBRQPvkcRRwh3POAW+YWZmZ1ZA8qtjctkcBU1Pb3w78kwwlj98//hF//fEJxEJtX1tetfMURh9+NgBv/vl7uET8a+UD95zGyENOJRGL8tZfz96k3sGTj2DYAd8mGmxh7tXnb1I+7IDjGbLPtwg1reO9v/3nJuUjpn2Xmr2mE1i3gg9u/fW/C1J/oEcdfg7Vu+5P88pP+PD2iwCX/OcSgGPc8f9J1fh9qF/0HvPvuji5nUvgAFyCXU//AxWj92Td/Jf56J4/kojHcfHoV//NoFP/TN7gsbTOe5a6p68CwHz55OQVkpNfyPJH38NXXkOwroC8cQdS5C8m119MflEx+YUl4E32V5x0+vc5eFw1A4rz1I8h0odkOnkMAVa0e72S5NFFZ+sM6WTbgc651QDOudVmVt3Rf25m5wDnAAwbNmyrGlBTmk/lkBFEQ4GvLR8wcBADS/IAqKzdgUQ89vXy6moGluSRiHmoGDJyk3oHDBjAwJI8orkxqoaO6qC8ioEleYTwd1heXZUsb4sWUTVszEalRnVVBQNL8iioLGfd2D0wM8xSd1qbUTNoIBUleeQPGkjLhAOTZUbqpzG4ZhClJXnkDhtB5MBj8Hi85BeVUFhcQlFxKTvssRcV5ZW4iafgOf1EyspKKPL7yfflUJTvxZ/rocDnIc+3D7me8wDISfVTbLjf2ww8OcaA4nz1Y4j0MebanUro9srNvg0c5pz7fur1qcAk59yP263zJHCpc+6V1Os5wH8BO2xuWzNrdM6VtaujwTlXvqVYJk6c6ObOndu9DRSRjt12W/LnGWf0ZBTSPTr8VpfpQX9WAkPbva4FVnVxnS1tuyZ1aovUz7XdGLOIiHQi08njbWCMmY00s1zgROCxjdZ5DDjNkvYBmlKnpLa07WPA6annpwOPZrgdIiLSTkb7PJxzMTM7H3iG5OW2tzjnPjKzH6bKbwCeInmZ7iKSl+qeuaVtU1VfBjxgZt8DlgPfzmQ7RETk6zJ+HaRz7imSCaL9shvaPXfAeV3dNrW8DpjWvZGKiEhXaaIDERFJm5KHiIikTclDRETSpuQhIiJpy+hNgr2Jma0Dlm3l5lXA+m4Mpy9Qm7NDJtvcW3+fvTWuTNnW9q53zs3YeGHWJI9tYWZznXMTezqO7Ultzg6ZbHNv/X321rgyJVPt1WkrERFJm5KHiIikTcmja27s6QB6gNqcHTLZ5t76++ytcWVKRtqrPg8REUmbjjxERCRtSh4iIpK2rE8eZjbDzD4xs0Wp+dA3Lh9nZq+bWdjMNpkP1sw8ZvaemT2xfSLuXl1o/1FmNs/M3jezuWa2X0/EuS06a2NqnampNn5kZv9KLRubWrbh0WxmP9muwW8lM7vFzNaa2fxO1tvbzOJmdny7ZReY2fzU7+InHWwz1MxeNLOFqXUu6GAdM7OrUr/zeWY2IbU838zeMrMPUtv+vhua26V6N7cvd6U9vVFX9s8tfX47e5875ZzL2gfJod4Xk5y1MBf4ANhpo3Wqgb2BPwL/2UEdPwPuAZ7o6fZkqP1F/LtvbDfg456OOwNtLAMWAMM2vOebqedLYHhPt6mL7T4AmADM7+R38wLJkauPTy3bBZgP+EmOuv08MGaj7WqACannxcCnHfxODweeJjkL3T7Am6nlBhSlnvuAN4F9uqG9nda7uX25K+3p7Y/N7Z9baHOn73Nnj2w/8pgELHLOfe6ciwD3AUe1X8E5t9Y59zYQ3XhjM6sFjgBu2h7BZkBX2t/qUnsbUAj0tSssOm0jcDLwsHNuOSTf8w7qmQYsds5t7SgF25Vz7iWgvpPVfgw8xNdn4hwPvOGcCzjnYsC/gGM2qnu1c+7d1PMWYCEwZKO6jwLucElvAGVmVpN63Zpax5d6bPM+1ZV6N7cvd7E9vV2H++cWPr+dvs+dyfbkMQRY0e71StLbaa4gOd96ohtj2p661H4zO8bMPgaeBM7aTrF1l660cUeg3Mz+aWbvmNlpHdRzInBvhmLc7sxsCMk/FjdsVDQfOMDMKs3MT/IIYujG27erZwSwJ8lv+u1t9veeOtX7Psmk9ZxzbuNtt0pX6u1sX95Ce3q7ze6fm2lzWu9zR7I9eXQ0sXuXvgWZ2TeBtc65d7o3pO2qS+13zj3inBsHHA38IdNBdbOutNEL7EXyKPIw4LdmtuNXFSSnQT4SmJWpIHvAFcDPnXPx9gudcwuB/wWeA2aTPM0X66gCMysieeTyE+dc88bFHWyy4Zt+3Dm3B1ALTDKzXba+GV+LvdN6t7Qvd9KeXquz/bOjNqfzPm9OtiePlXw929YCq7q47RTgSDNbSvJUyMFmdlf3hpdxabU/dSpklJlVZTqwbtSVNq4EZjvn2pxz64GXgN3blc8E3nXOrclopNvXROC+1P57PHCdmR0N4Jy72Tk3wTl3AMlTX59tvLGZ+Uj+ob3bOfdwB/V3+nt3zjUC/wQ2GXRvW3Sl3o335S60pzfr0v65cZu78j5v0fbq0OmND5LfOD8HRvLvztSdN7Pu7+igwzxVNpW+2WHeafuB0fy7w20C8MWG133h0cU2jgfmpNb1kzyk36Vd+X3AmT3dlq1o+wi20GHebr3bSHWYp15Xp34OAz4Gyjda34A7gCu2UOcRfL3D/K3U8gFAWep5AfAy8M1uaGun9W5uX+5Ke3rzY0v755Y+v529z509Mj6HeW/mnIuZ2fnAMySvVrjFOfeRmf0wVX6DmQ0C5gIlQCJ1SdtOrg8d1m5OV9oPHAecZmZRIAic4FJ7XF/QlTY65xaa2WxgHsn+q5ucc/MBUueDDwV+0DMt2Dpmdi/JLzVVZrYSuIhkJ/KG93VLHjKzSpIXiZznnGvYqHwKcCrwYaqPAeBXJP8Ibaj/KZLn0RcBAeDM1Ho1wO1m5iF55uMB51x3XObeYb1d2ZdTl69u0h7n3FPdEFdGdbR/pvH57ex93vL/3Yf+DoiISC+R7X0eIiKyFZQ8REQkbUoeIiKSNiUPERFJm5KHiIikTclDpB0z+0nq8scNr58ys7JuqPdnZrYgNcLpHDMbvlH57NSQIenWe7SZ7dTu9cVmdkg3xFuZGmm21cyu2db6pP/Rpboi7aTuuJ7oknead2e9B5EcWTZgZucCU51zJ6TKCoB/OecmbUW9t5G8QfXBbo63kOQYT7uQvGHy/O6sX/o+HXlIv5b6xj8/9fhJatkIM/vYzG5PHQk8aGZ+M/t/wGDgRTN7MbXu0nZDWGyuroVm9vfUvAjPppLB1zjnXnTOBVIv3yA5XMcGU0kOp4GZTbPk/DAfWnJOjrx2cfyvJeeseMvMRpvZviTHNLrckvM1jDKz2yw1N0cndf3ezN5NlY3rIN4259wrQGib3gDpt5Q8pN8ys71I3tk8meQQGWeb2Z6p4rHAjc653YBm4EfOuatIjr90kHPuoDTqGgNc65zbGWgkeVfvlnyP5NAdG8wEZptZPsmhQk5wzu1KcriUc9ut15w6OrmG5FAarwGPARc65/Zwzi1uF29nda13zk0Argc2meRMpDNKHtKf7Qc8kvoW3Qo8DOyfKlvhnHs19fyu1LpbW9cS59z7qefvkBxTqkNmdgrJQQkvb7d4CvAKyYS2xDn3aWr57SQnddrg3nY/v9FJvJ3VtWHwvy3GK7I5WT22lfR7HQ0LvsHGnX2ddf5tqa5wu+dxkgPzbVpBsiP718CBzrlwatkOJBNZxMy29H9sHOO2xAv/jjmO/g7IVtCRh/RnLwFHp/ozCklOfvRyqmyYmW349n4SyW/+AC0kpyJNp65OpU5x/Q040n19psKZJOdTgOTIpiPMbHTq9akkZ3jb4IR2P1/vJN7O6hLZJkoe0m+55NSitwFvkZwZ7ibn3Hup4oXA6WY2D6ggee4f4Ebg6Q0d5l2sqysuJzmf9KxU5/ZjqeUzSCUP51yIZL/KLDP7kOQIv+1HwM0zszeBC4CfppbdB1yY6hgf1S7ezurqVOrKs78AZ5jZyvaXBIvoUl3JOpacavQJ51y3zGC3DXHkAa865yZ2Yd2lZOASYpGtpXOdIj0k1e/RaeIQ6Y105CEiImlTn4eIiKRNyUNERNKm5CEiImlT8hARkbQpeYiISNr+P9uhdYBMxz2BAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sns.lineplot('log(frac)', 'chose_2', data=df)\n",
"\n",
"x = np.linspace(-2, 2, 15)\n",
"slope = 1./sd_diff\n",
"plt.plot(x, ss.norm().cdf(slope * x), c='k', ls='--')\n",
"\n",
"\n",
"sns.despine()\n",
"\n",
"plt.axhline(ss.norm().cdf(2), c='r', alpha=.5)\n",
"plt.axvline(2./slope, c='r', alpha=.5)\n",
"\n",
"plt.yticks([0.0, np.round(ss.norm.cdf(2.), 3)])\n",
"\n",
"\n",
"print(f'So the weber fraction is {np.round(np.exp(2./slope) - 1., 2)}')\n",
"\n",
"plt.xticks(list(np.linspace(-2, 2, 6))+ [(2./slope)], \n",
" np.round(list(np.exp(np.linspace(-2, 2, 6))) + [np.exp(2./slope)], 2))\n",
"_ = plt.xlabel('option 2/option 1')"
]
},
{
"cell_type": "markdown",
"id": "0ae8bef2",
"metadata": {},
"source": [
"# Weber = distance where 95% of probability mass is behind us (95%correct)"
]
},
{
"cell_type": "code",
"execution_count": 138,
"id": "c6e13a06",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/gdehol/miniconda3/lib/python3.8/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
" warnings.warn(\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"So the weber fraction is 0.79\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sns.lineplot('log(frac)', 'chose_2', data=df)\n",
"\n",
"\n",
"\n",
"\n",
"x = np.linspace(-2, 2, 15)\n",
"\n",
"sd_diff = np.sqrt(sd1**2 + sd2**2)\n",
"slope = 1./sd_diff\n",
"\n",
"plt.plot(x, ss.norm().cdf(slope * x), c='k', ls='--')\n",
"\n",
"\n",
"sns.despine()\n",
"\n",
"plt.axhline(.95, c='r', alpha=.5)\n",
"plt.axvline(ss.norm().ppf(.95)/slope, c='r', alpha=.5)\n",
"\n",
"plt.yticks([0.0, .95])\n",
"\n",
"print(f'So the weber fraction is {np.round(np.exp(ss.norm().ppf(.95)/slope) - 1., 2)}')\n",
"\n",
"plt.xticks(np.linspace(-2, 2, 5), np.round(np.exp(np.linspace(-2, 2, 5)), 2))\n",
"_ = plt.xlabel('option 2/option 1')\n",
"\n",
"plt.xticks(list(np.linspace(-2, 2, 5))+ [ss.norm().ppf(.95)/slope], \n",
" np.round(list(np.exp(np.linspace(-2, 2, 5))) + [np.exp(ss.norm().ppf(.95)/slope)], 2))\n",
"_ = plt.xlabel('option 2/option 1')"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6c0d221a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "b7565f98",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "91a65a84",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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