Add t检验应用条件

notebook_必备数学基础/假设检验章节/.ipynb_checkpoints/假设检验-checkpoint.ipynb

@@ -603,8 +603,9 @@
     "建立检验假设，确定检验水准\n",
     "<br>H0：μ1=μ2；H1：μ1≠μ2；α=0.05\n",
     "<br>计算检验统计量\n",
+    "<br>由原数据算得:\n",
     "$$\n",
-    "由原数据算得: n_1=12, \\sum X_1=182.5,\\sum X_1^2=2953.43,n_2=13,\\sum X_2=141.0,\n",
+    "n_1=12, \\sum X_1=182.5,\\sum X_1^2=2953.43,n_2=13,\\sum X_2=141.0,\n",
     "\\sum X_2^2=1743.16, \\overline{X}_1=\\sum X_1/n_1=182.5/12=15.21, \n",
     "\\overline{X}_2/n_2=14.16/13=10.85\n",
     "$$\n",
@@ -618,6 +619,33 @@
     "$$"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## T检验应用条件\n",
+    "<ul>\n",
+    "    <li>两组计量资料小样本比较。\n",
+    "    <li>样本对总体有较好代表性，对比组间有较好组间均衡性一一随机抽样和随机分组\n",
+    "    <li>样本来自正态分布总体，配对t检验要求差值服从正态分布，大样本时，用z检验，且正态性要求可以放宽\n",
+    "    <li>两独立样本均数t检验要求方差齐性一一两组总体方差相等或两样本方差间无显著性正态性"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 正态性检验和两总体方差的齐性检验\n",
+    "正态性检验\n",
+    "<ul>\n",
+    "    <li>图示法:常用的图示法包括P-P图法和QQ图法。图中数据呈直线关系可认为呈正态分布，不呈直线关系可认为呈偏态分布\n",
+    "    <li>偏度检验:主要计算偏度系数,H0O:G1=0,总体分布对称H1:G1#0,总体分布不对称\n",
+    "\n",
+    "<img src=\"assets/20201117073547.png\" width=\"70%\">\n",
+    "    <li>峰值检验，主要计算峰度系数，H0: G2=0，总体分布为正态峰，H1：G2≠0，总体分布不是正态峰\n",
+    "    <img src=\"assets/20201117075130.png\" width=\"70%\">"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,

notebook_必备数学基础/假设检验章节/假设检验.ipynb

@@ -603,8 +603,9 @@
     "建立检验假设，确定检验水准\n",
     "<br>H0：μ1=μ2；H1：μ1≠μ2；α=0.05\n",
     "<br>计算检验统计量\n",
+    "<br>由原数据算得:\n",
     "$$\n",
-    "由原数据算得: n_1=12, \\sum X_1=182.5,\\sum X_1^2=2953.43,n_2=13,\\sum X_2=141.0,\n",
+    "n_1=12, \\sum X_1=182.5,\\sum X_1^2=2953.43,n_2=13,\\sum X_2=141.0,\n",
     "\\sum X_2^2=1743.16, \\overline{X}_1=\\sum X_1/n_1=182.5/12=15.21, \n",
     "\\overline{X}_2/n_2=14.16/13=10.85\n",
     "$$\n",
@@ -618,6 +619,33 @@
     "$$"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## T检验应用条件\n",
+    "<ul>\n",
+    "    <li>两组计量资料小样本比较。\n",
+    "    <li>样本对总体有较好代表性，对比组间有较好组间均衡性一一随机抽样和随机分组\n",
+    "    <li>样本来自正态分布总体，配对t检验要求差值服从正态分布，大样本时，用z检验，且正态性要求可以放宽\n",
+    "    <li>两独立样本均数t检验要求方差齐性一一两组总体方差相等或两样本方差间无显著性正态性"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 正态性检验和两总体方差的齐性检验\n",
+    "正态性检验\n",
+    "<ul>\n",
+    "    <li>图示法:常用的图示法包括P-P图法和QQ图法。图中数据呈直线关系可认为呈正态分布，不呈直线关系可认为呈偏态分布\n",
+    "    <li>偏度检验:主要计算偏度系数,H0O:G1=0,总体分布对称H1:G1#0,总体分布不对称\n",
+    "\n",
+    "<img src=\"assets/20201117073547.png\" width=\"70%\">\n",
+    "    <li>峰值检验，主要计算峰度系数，H0: G2=0，总体分布为正态峰，H1：G2≠0，总体分布不是正态峰\n",
+    "    <img src=\"assets/20201117075130.png\" width=\"70%\">"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,