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@ -34,7 +34,7 @@
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"metadata": {},
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"source": [
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"### 假设校验的基本思想\n",
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"<img src=\"assets/20201114091803.png\" width=\"70%\">"
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"<img src=\"assets/20201114091803.png\" width=\"50%\">"
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]
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},
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@ -130,7 +130,7 @@
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"metadata": {},
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"source": [
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"### 左侧检验与右侧检验\n",
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"<img src=\"assets/20201114095426.png\" width=\"100%\">"
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"<img src=\"assets/20201114095426.png\" width=\"70%\">"
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]
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},
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@ -147,7 +147,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<img src=\"assets/20201114100216.png\" width=\"70%\">"
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"<img src=\"assets/20201114100216.png\" width=\"30%\">"
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]
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@ -202,7 +202,7 @@
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"source": [
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"### 总体均值检验\n",
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"什么时候用Z检验，什么时候用T检验\n",
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"<img src=\"assets/20201114101438.png\" width=\"70%\">\n",
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"<img src=\"assets/20201114101438.png\" width=\"50%\">\n",
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"一般是用T检验"
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]
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},
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@ -320,10 +320,10 @@
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"source": [
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"这里是双侧，即二分之一α，1-α/2=0.975，查表\n",
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"<br>网上搜索：统计分布临界值\n",
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"<img src=\"assets/20201115111943.png\" width=\"70%\">\n",
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"<img src=\"assets/20201115111943.png\" width=\"50%\">\n",
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"<br><br>\n",
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"1.9+0.6=1.96，统计量为10.4比1.96大，意味着面积肯定小于1.96临界值（α/2）的面积\n",
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"<img src=\"assets/20201115112520.png\" width=\"70%\">\n",
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"<img src=\"assets/20201115112520.png\" width=\"50%\">\n",
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"根据双侧检验，若p值 < α/2，拒绝H0"
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]
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},
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@ -366,7 +366,7 @@
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"<br>-2.83在-1.96左侧，也就是p值的面积小于α/2，在α = 0.05的水平上拒绝H0\n",
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"<br>结论：\n",
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"<br>有证据表明新机床加工的零件的椭圆度与以前有显著差异\n",
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"<img src=\"assets/20201115151902.png\" width=\"50%\">"
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"<img src=\"assets/20201115151902.png\" width=\"30%\">"
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]
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},
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{
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@ -394,7 +394,7 @@
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"<br>2.4在1.645右侧，也就是p值的面积小于α，在α = 0.05的水平上拒绝H0\n",
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"<br>结论：\n",
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"<br>有证据表明新生产的灯泡的使用寿命有显著提高\n",
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"<img src=\"assets/20201115152913.png\" width=\"50%\">"
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"<img src=\"assets/20201115152913.png\" width=\"30%\">"
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]
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},
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{
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@ -464,7 +464,7 @@
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"metadata": {},
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"source": [
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"网上搜索：t分布临界值表\n",
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"<img src=\"assets/20201116212408.png\" width=\"70%\">"
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"<img src=\"assets/20201116212408.png\" width=\"50%\">"
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]
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},
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{
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@ -514,7 +514,7 @@
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"**实例1：**\n",
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"<br>\n",
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"有12名接种卡介苗的儿童，8周虐用两批不同的结核菌素，一批是标准结核菌素，一批是新制结核菌素，分别注射在儿童的前臂，两种结核菌素的皮肤浸润反应平均直径(mm)如表所示，问两种结核菌素的反应性有无差别。\n",
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"<img src=\"assets/20201116215635.png\" width=\"70%\">"
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"<img src=\"assets/20201116215635.png\" width=\"50%\">"
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]
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},
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{
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@ -593,7 +593,7 @@
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"**实例2：**\n",
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"<br>\n",
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"25例糖尿病患者随机分成两组，甲组单纯用药物治疗，乙组采用药物治疗合并饮食疗法，二个月后测空腹血糖(mmoL)如表所示，问两种疗法治疗后患者血糖值是否相同?\n",
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"<img src=\"assets/20201116221815.png\" width=\"70%\">"
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"<img src=\"assets/20201116221815.png\" width=\"50%\">"
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]
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},
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{
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@ -641,9 +641,104 @@
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" <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",
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" <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",
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"\n",
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"<img src=\"assets/20201117073547.png\" width=\"70%\">\n",
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"<img src=\"assets/20201117073547.png\" width=\"30%\">\n",
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" <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",
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" <img src=\"assets/20201117075130.png\" width=\"70%\">"
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" <img src=\"assets/20201117075130.png\" width=\"30%\">"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 卡方检验（Chi-square test）\n",
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"用于检验两个(或多个)率或构成比之间差别是否有统计学意义，配对卡方检验检验配对计数资料的差异是否有统计学意义。\n",
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"\n",
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"### 基本思想\n",
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"检验实际频数(A)和理论频数(T的差别是否由抽样误差所引起的。也就是由样本率(或样本构成比)来推断总体率或构成比"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**实例1：**\n",
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"<br>\n",
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"两种药物治疗青溃疡有效率的比较\n",
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"<img src=\"assets/20201117223133.png\" width=\"30%\">\n",
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"理论频数与实际频数的差别：\n",
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"$$\n",
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"X^2 = \\sum \\frac{(A_{RC}-T_{RC})^2}{T_{RC}}\n",
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"$$\n",
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"ARC是位于R行C列交叉处的实际频数，TRC是位于R行C列交叉处的理论频数。(ARC-TRC)反映实际频数与理论频数的差距，除以TRC为的是考虑相对差距。所以，x^2值反映了实际频数与理论频数的吻合程度，X^2值大，说明实际频数与理论频数的差距大。Ⅹ^2值的大小除了与实际频数和理论频数的差的大小关外，还与它们的行、列数有关。即自由度的大小。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 理论频数根据假设来计算\n",
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"无效假设是A药组与B药组的总体有效率相等，均等于合计的阳性率(110/165)。那么理论上，A药组的85例中阳性人数应为85(110/165)=56.67，阴性人数为85(55/165)=28.33；同理，B药组的80例中阳性人数应为80(110/165)=53.33，阴性人数为80(55/165)=26.67。\n",
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"<img src=\"assets/20201117224924.png\" width=\"30%\">"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"基本公式: \n",
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"$$\n",
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"X^2 = \\sum \\frac{(A-T)^2}{T}\n",
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"$$\n",
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"$$\n",
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"= \\frac{[a-\\frac{(a+b)(a+c)}{a+b+c+d}]^2}{\\frac{(a+b)(a+c)}{a+b+c+d}}\n",
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"+ \\frac{[b-\\frac{(a+b)(b+d)}{a+b+c+d}]^2}{\\frac{(a+b)(b+d)}{a+b+c+d}}\n",
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"+...\n",
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"+ \\frac{[d-\\frac{(c+d)(b+d)}{a+b+c+d}]^2}{\\frac{(c+d)(b+d)}{a+b+c+d}}\n",
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"$$\n",
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"$$\n",
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"= \\frac{(ad-bc)^2 * n}{(a+b)(c+d)(a+c)(b+d)}\n",
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"$$\n",
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"$$\n",
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"v = 1\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"若检验假设H0:π1=π2成立，四个格子的实际频数A与理论频数T相差不应该很大，即统计量x2不应该很大。如果x2值很大，即相对应的P值很小，若P≤α，则反过来推断A与T相差太大，超出了抽样误差允许的范围，从而怀疑H0的正确性，继而拒绝Ho，接受其对立假设H1,即π1≠π2。"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**实例2**\n",
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"<br>\n",
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"某药品检验所随机抽取574名成年人，研究抗生素的耐药性。问两种人群的耐药率是否一致?\n",
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"\n",
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"<img src=\"assets/20201117225550.png\" width=\"30%\">\n",
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"<img src=\"assets/20201117225642.png\" width=\"30%\">"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"(1) 建立假设并确定检验水准\n",
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"<ul>\n",
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" <li>H0:两种人群对该抗生素的耐药率相同,即π1=m2;(两总体率相等)\n",
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" <li>H1:两种人群对该抗生素的耐药率不同,即π1≠m2:(两总体不相等)\n",
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" <li>α=0.05\n",
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"</ul>\n",
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"(2) 计算检验统计量\n",
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"$$\n",
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"X^2 = \\frac{(180-17410)^2}{17410}+\\frac{(215-22090)^2}{22090}+...\n",
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"+\\frac{(106-10010)^2}{10010} = 23.12\n",
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"$$\n",
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"(3) 得出结果\n",
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"査表确定P值,P>0.05,得出结论。按0.05水准，不拒绝H0，可以认为两组人群对该抗生素的耐药率的差异无统计学意义。"
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]
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},
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{
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benjas
4 years ago
