From 582043dbb5d032adc9b3dfe7476edb1a3905fded Mon Sep 17 00:00:00 2001 From: benjas <909336740@qq.com> Date: Tue, 17 Nov 2020 23:03:04 +0800 Subject: [PATCH] =?UTF-8?q?Add=20=E5=8D=A1=E6=96=B9=E6=A3=80=E9=AA=8C?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../假设检验-checkpoint.ipynb | 121 ++++++++++++++++-- .../assets/20201117223133.png | Bin 0 -> 100920 bytes .../assets/20201117224924.png | Bin 0 -> 24322 bytes .../assets/20201117225550.png | Bin 0 -> 45499 bytes .../assets/20201117225642.png | Bin 0 -> 41201 bytes .../假设检验章节/假设检验.ipynb | 95 ++++++++++++++ 6 files changed, 203 insertions(+), 13 deletions(-) create mode 100644 notebook_必备数学基础/假设检验章节/assets/20201117223133.png create mode 100644 notebook_必备数学基础/假设检验章节/assets/20201117224924.png create mode 100644 notebook_必备数学基础/假设检验章节/assets/20201117225550.png create mode 100644 notebook_必备数学基础/假设检验章节/assets/20201117225642.png diff --git a/notebook_必备数学基础/假设检验章节/.ipynb_checkpoints/假设检验-checkpoint.ipynb b/notebook_必备数学基础/假设检验章节/.ipynb_checkpoints/假设检验-checkpoint.ipynb index 452b588..4a27fa2 100644 --- a/notebook_必备数学基础/假设检验章节/.ipynb_checkpoints/假设检验-checkpoint.ipynb +++ b/notebook_必备数学基础/假设检验章节/.ipynb_checkpoints/假设检验-checkpoint.ipynb @@ -34,7 +34,7 @@ "metadata": {}, "source": [ "### 假设校验的基本思想\n", - "" + "" ] }, { @@ -130,7 +130,7 @@ "metadata": {}, "source": [ "### 左侧检验与右侧检验\n", - "" + "" ] }, { @@ -147,7 +147,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "" + "" ] }, { @@ -202,7 +202,7 @@ "source": [ "### 总体均值检验\n", "什么时候用Z检验,什么时候用T检验\n", - "\n", + "\n", "一般是用T检验" ] }, @@ -320,10 +320,10 @@ "source": [ "这里是双侧,即二分之一α,1-α/2=0.975,查表\n", "
网上搜索:统计分布临界值\n", - "\n", + "\n", "

\n", "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", - "\n", + "\n", "根据双侧检验,若p值 < α/2,拒绝H0" ] }, @@ -366,7 +366,7 @@ "
-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", "
结论:\n", "
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", - "" + "" ] }, { @@ -394,7 +394,7 @@ "
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", "
结论:\n", "
有证据表明新生产的灯泡的使用寿命有显著提高\n", - "" + "" ] }, { @@ -464,7 +464,7 @@ "metadata": {}, "source": [ "网上搜索:t分布临界值表\n", - "" + "" ] }, { @@ -514,7 +514,7 @@ "**实例1:**\n", "
\n", "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", - "" + "" ] }, { @@ -593,7 +593,7 @@ "**实例2:**\n", "
\n", "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", - "" + "" ] }, { @@ -641,9 +641,104 @@ "
  • 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", "
  • 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", - "\n", + "\n", "
  • 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", - " " + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 卡方检验(Chi-square test)\n", + "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", + "\n", + "### 基本思想\n", + "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" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**实例1:**\n", + "
    \n", + "两种药物治疗青溃疡有效率的比较\n", + "\n", + "理论频数与实际频数的差别:\n", + "$$\n", + "X^2 = \\sum \\frac{(A_{RC}-T_{RC})^2}{T_{RC}}\n", + "$$\n", + "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。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 理论频数根据假设来计算\n", + "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", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "基本公式: \n", + "$$\n", + "X^2 = \\sum \\frac{(A-T)^2}{T}\n", + "$$\n", + "$$\n", + "= \\frac{[a-\\frac{(a+b)(a+c)}{a+b+c+d}]^2}{\\frac{(a+b)(a+c)}{a+b+c+d}}\n", + "+ \\frac{[b-\\frac{(a+b)(b+d)}{a+b+c+d}]^2}{\\frac{(a+b)(b+d)}{a+b+c+d}}\n", + "+...\n", + "+ \\frac{[d-\\frac{(c+d)(b+d)}{a+b+c+d}]^2}{\\frac{(c+d)(b+d)}{a+b+c+d}}\n", + "$$\n", + "$$\n", + "= \\frac{(ad-bc)^2 * n}{(a+b)(c+d)(a+c)(b+d)}\n", + "$$\n", + "$$\n", + "v = 1\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**实例2**\n", + "
    \n", + "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", + "\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(1) 建立假设并确定检验水准\n", + "\n", + "(2) 计算检验统计量\n", + "$$\n", + "X^2 = \\frac{(180-17410)^2}{17410}+\\frac{(215-22090)^2}{22090}+...\n", + "+\\frac{(106-10010)^2}{10010} = 23.12\n", + "$$\n", + "(3) 得出结果\n", + "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。" ] }, { diff --git a/notebook_必备数学基础/假设检验章节/assets/20201117223133.png b/notebook_必备数学基础/假设检验章节/assets/20201117223133.png new file mode 100644 index 0000000000000000000000000000000000000000..b4101b93517c8f322837ef9cf5c2fbcab5a9ab1e GIT binary patch literal 100920 zcmV*SKwZCyP)Px#1ZP1_K>z@;j|==^1poj532;bRa{vGmbN~PnbOGLGA9w%&|D{PpK~#8N>|F(b z71j6N?hasK7g)Mex*J3#L`0BMLKILGrIio_R8$nO5orYlX(gq*yK}qiy|?lG&v)m| z@_0NX1k~Su4}3c_ch0SI?>*<-J9p;U<>chx-wI3mt9zt-y_bi79=6C9UmpIqaW7;m zULNiZw#XJ=9{wII<*Jh%|5yh6uaI>`^C*wSx5J%qKfHPP--O-=^uDuk<3?=Rvc=|j&O;uyZk2xVC;P_V 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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" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**实例1:**\n", + "
    \n", + "两种药物治疗青溃疡有效率的比较\n", + "\n", + "理论频数与实际频数的差别:\n", + "$$\n", + "X^2 = \\sum \\frac{(A_{RC}-T_{RC})^2}{T_{RC}}\n", + "$$\n", + "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。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 理论频数根据假设来计算\n", + "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", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "基本公式: \n", + "$$\n", + "X^2 = \\sum \\frac{(A-T)^2}{T}\n", + "$$\n", + "$$\n", + "= \\frac{[a-\\frac{(a+b)(a+c)}{a+b+c+d}]^2}{\\frac{(a+b)(a+c)}{a+b+c+d}}\n", + "+ \\frac{[b-\\frac{(a+b)(b+d)}{a+b+c+d}]^2}{\\frac{(a+b)(b+d)}{a+b+c+d}}\n", + "+...\n", + "+ \\frac{[d-\\frac{(c+d)(b+d)}{a+b+c+d}]^2}{\\frac{(c+d)(b+d)}{a+b+c+d}}\n", + "$$\n", + "$$\n", + "= \\frac{(ad-bc)^2 * n}{(a+b)(c+d)(a+c)(b+d)}\n", + "$$\n", + "$$\n", + "v = 1\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**实例2**\n", + "
    \n", + "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", + "\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(1) 建立假设并确定检验水准\n", + "
      \n", + "
    • 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", + "
    • 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", + "
    • α=0.05\n", + "
    \n", + "(2) 计算检验统计量\n", + "$$\n", + "X^2 = \\frac{(180-17410)^2}{17410}+\\frac{(215-22090)^2}{22090}+...\n", + "+\\frac{(106-10010)^2}{10010} = 23.12\n", + "$$\n", + "(3) 得出结果\n", + "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。" + ] + }, { "cell_type": "code", "execution_count": null,