diff --git a/notebook_必备数学基础/假设检验章节/.ipynb_checkpoints/python卡方检验实例-checkpoint.ipynb b/notebook_必备数学基础/假设检验章节/.ipynb_checkpoints/python卡方检验实例-checkpoint.ipynb
new file mode 100644
index 0000000..2fd6442
--- /dev/null
+++ b/notebook_必备数学基础/假设检验章节/.ipynb_checkpoints/python卡方检验实例-checkpoint.ipynb
@@ -0,0 +1,6 @@
+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/notebook_必备数学基础/假设检验章节/python卡方检验实例.ipynb b/notebook_必备数学基础/假设检验章节/python卡方检验实例.ipynb
new file mode 100644
index 0000000..5f9b7c1
--- /dev/null
+++ b/notebook_必备数学基础/假设检验章节/python卡方检验实例.ipynb
@@ -0,0 +1,548 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 白人和黑人在求职路上会有种族的歧视吗？"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from scipy import stats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>id</th>\n",
+       "      <th>ad</th>\n",
+       "      <th>education</th>\n",
+       "      <th>ofjobs</th>\n",
+       "      <th>yearsexp</th>\n",
+       "      <th>honors</th>\n",
+       "      <th>volunteer</th>\n",
+       "      <th>military</th>\n",
+       "      <th>empholes</th>\n",
+       "      <th>occupspecific</th>\n",
+       "      <th>...</th>\n",
+       "      <th>compreq</th>\n",
+       "      <th>orgreq</th>\n",
+       "      <th>manuf</th>\n",
+       "      <th>transcom</th>\n",
+       "      <th>bankreal</th>\n",
+       "      <th>trade</th>\n",
+       "      <th>busservice</th>\n",
+       "      <th>othservice</th>\n",
+       "      <th>missind</th>\n",
+       "      <th>ownership</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>b</td>\n",
+       "      <td>1</td>\n",
+       "      <td>4</td>\n",
+       "      <td>2</td>\n",
+       "      <td>6</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>17</td>\n",
+       "      <td>...</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td></td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>b</td>\n",
+       "      <td>1</td>\n",
+       "      <td>3</td>\n",
+       "      <td>3</td>\n",
+       "      <td>6</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>316</td>\n",
+       "      <td>...</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td></td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>b</td>\n",
+       "      <td>1</td>\n",
+       "      <td>4</td>\n",
+       "      <td>1</td>\n",
+       "      <td>6</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>19</td>\n",
+       "      <td>...</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td></td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>b</td>\n",
+       "      <td>1</td>\n",
+       "      <td>3</td>\n",
+       "      <td>4</td>\n",
+       "      <td>6</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>313</td>\n",
+       "      <td>...</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td></td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>b</td>\n",
+       "      <td>1</td>\n",
+       "      <td>3</td>\n",
+       "      <td>3</td>\n",
+       "      <td>22</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>313</td>\n",
+       "      <td>...</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>Nonprofit</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>5 rows × 65 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  id ad  education  ofjobs  yearsexp  honors  volunteer  military  empholes  \\\n",
+       "0  b  1          4       2         6       0          0         0         1   \n",
+       "1  b  1          3       3         6       0          1         1         0   \n",
+       "2  b  1          4       1         6       0          0         0         0   \n",
+       "3  b  1          3       4         6       0          1         0         1   \n",
+       "4  b  1          3       3        22       0          0         0         0   \n",
+       "\n",
+       "   occupspecific  ...  compreq  orgreq  manuf  transcom  bankreal trade  \\\n",
+       "0             17  ...      1.0     0.0    1.0       0.0       0.0   0.0   \n",
+       "1            316  ...      1.0     0.0    1.0       0.0       0.0   0.0   \n",
+       "2             19  ...      1.0     0.0    1.0       0.0       0.0   0.0   \n",
+       "3            313  ...      1.0     0.0    1.0       0.0       0.0   0.0   \n",
+       "4            313  ...      1.0     1.0    0.0       0.0       0.0   0.0   \n",
+       "\n",
+       "  busservice othservice  missind  ownership  \n",
+       "0        0.0        0.0      0.0             \n",
+       "1        0.0        0.0      0.0             \n",
+       "2        0.0        0.0      0.0             \n",
+       "3        0.0        0.0      0.0             \n",
+       "4        0.0        1.0      0.0  Nonprofit  \n",
+       "\n",
+       "[5 rows x 65 columns]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "data  = pd.io.stata.read_stata('us_job_market_discrimination.dta')\n",
+    "data.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "blacks = data[data.race=='b']  # 黑人\n",
+    "whites = data[data.race=='w']  # 白人"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "count    2435.000000\n",
+       "mean        0.064476\n",
+       "std         0.245649\n",
+       "min         0.000000\n",
+       "25%         0.000000\n",
+       "50%         0.000000\n",
+       "75%         0.000000\n",
+       "max         1.000000\n",
+       "Name: call, dtype: float64"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "blacks.call.describe()  # call为1则是被录取，为0则是不录取"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "count    2435.000000\n",
+       "mean        0.096509\n",
+       "std         0.295346\n",
+       "min         0.000000\n",
+       "25%         0.000000\n",
+       "50%         0.000000\n",
+       "75%         0.000000\n",
+       "max         1.000000\n",
+       "Name: call, dtype: float64"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "whites.call.describe()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "白人的录取均值更高，我们再查看其它的指标，确认是到底是不是因为肤色"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 卡方检验\n",
+    "<ul>\n",
+    "    <li>白人获得职位\n",
+    "    <li>白人被拒绝\n",
+    "    <li>黑人获得职位\n",
+    "    <li>黑人被拒绝\n",
+    "</ul>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 假设检验\n",
+    "<ul>\n",
+    "    <li>H0：种族对求职结果没有显著影响\n",
+    "    <li>H1：种族对求职结果有显著影响"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "blacks_called = len(blacks[blacks['call'] == True])\n",
+    "blacks_not_called = len(blacks[blacks['call'] == False])\n",
+    "whites_called = len(whites[whites['call'] == True])\n",
+    "whites_not_called = len(whites[whites['call'] == False])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "observed = pd.DataFrame({\n",
+    "    'blacks':{'called':blacks_called, 'not_called':blacks_not_called},\n",
+    "    'whites':{'called':whites_called, 'not_called':whites_not_called}\n",
+    "})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>blacks</th>\n",
+       "      <th>whites</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>called</th>\n",
+       "      <td>157</td>\n",
+       "      <td>235</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>not_called</th>\n",
+       "      <td>2278</td>\n",
+       "      <td>2200</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "            blacks  whites\n",
+       "called         157     235\n",
+       "not_called    2278    2200"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "observed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "392\n",
+      "4478\n"
+     ]
+    }
+   ],
+   "source": [
+    "num_called_back = blacks_called +whites_called\n",
+    "num_not_called = blacks_not_called + whites_not_called\n",
+    "\n",
+    "print(num_called_back)\n",
+    "print(num_not_called)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# 得到期望值\n",
+    "rate_of_callbacks = num_called_back / (num_not_called+num_called_back)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.08049281314168377"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rate_of_callbacks"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "391.99999999999994\n",
+      "4478.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "expected_called = len(data) * rate_of_callbacks\n",
+    "expected_not_called = len(data) * (1-rate_of_callbacks)\n",
+    "\n",
+    "print(expected_called)  # 获得的期望人数\n",
+    "print(expected_not_called)  # 没获得的期望人数"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Power_divergenceResult(statistic=16.87905041427022, pvalue=0.0007483959441097264)"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import scipy.stats as stats\n",
+    "observed_frequencies = [blacks_not_called, whites_not_called,\n",
+    "                        whites_called,blacks_called]  # 观测值\n",
+    "expected_frequencies = [expected_not_called/2,expected_not_called/2,\n",
+    "                        expected_called/2,expected_called/2]  # 期望值\n",
+    "\n",
+    "stats.chisquare(f_obs = observed_frequencies,\n",
+    "               f_exp = expected_frequencies)  #算出卡方检验值"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "p值非常非常小, 小于0.05，我们认为在这份数据中，种族歧视是存在的"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/notebook_必备数学基础/假设检验章节/us_job_market_discrimination.dta b/notebook_必备数学基础/假设检验章节/us_job_market_discrimination.dta
new file mode 100644
index 0000000..08c8bc0
Binary files /dev/null and b/notebook_必备数学基础/假设检验章节/us_job_market_discrimination.dta differ