From 8652c0a7a328774e98fb4a90856b56f38bd19776 Mon Sep 17 00:00:00 2001 From: wizardforcel <562826179@qq.com> Date: Sun, 28 Jan 2018 00:16:51 +0800 Subject: [PATCH] ch16pic --- 16.md | 36 ++++++++++++++++++++++++++++++++++-- img/16-1.png | Bin 0 -> 10623 bytes img/16-10.png | Bin 0 -> 14423 bytes img/16-11.png | Bin 0 -> 13717 bytes img/16-12.png | Bin 0 -> 14975 bytes img/16-13.png | Bin 0 -> 68243 bytes img/16-14.png | Bin 0 -> 19776 bytes img/16-15.png | Bin 0 -> 14842 bytes img/16-2.png | Bin 0 -> 19004 bytes img/16-3.png | Bin 0 -> 23474 bytes img/16-4.png | Bin 0 -> 19004 bytes img/16-5.png | Bin 0 -> 17911 bytes img/16-6.png | Bin 0 -> 19501 bytes img/16-7.png | Bin 0 -> 13613 bytes img/16-8.png | Bin 0 -> 13558 bytes img/16-9.png | Bin 0 -> 17882 bytes 16 files changed, 34 insertions(+), 2 deletions(-) create mode 100644 img/16-1.png create mode 100644 img/16-10.png create mode 100644 img/16-11.png create mode 100644 img/16-12.png create mode 100644 img/16-13.png create mode 100644 img/16-14.png create mode 100644 img/16-15.png create mode 100644 img/16-2.png create mode 100644 img/16-3.png create mode 100644 img/16-4.png create mode 100644 img/16-5.png create mode 100644 img/16-6.png create mode 100644 img/16-7.png create mode 100644 img/16-8.png create mode 100644 img/16-9.png diff --git a/16.md b/16.md index 662d5a0..58e582f 100644 --- a/16.md +++ b/16.md @@ -104,6 +104,8 @@ training_dists = training_counts.select(0).with_columns( training_dists.barh('Uniformity') ``` +![](img/16-1.png) + 这两个分布看起来不一样! 事实上,它们看起来相当不同,我们应该能够基于对这种差异的直截了当的观察来构建一个非常合理的分类器。 一个简单的分类规则是:“如果一致性大于 3,类别就是 1,也就是说这个单元格就有癌症的,否则类别就是 0。 这么粗糙的东西有什么好处吗? 让我们试试看。 对于测试集中的任何个体,我们所要做的就是,查看一致评分是否大于 3。例如,对于前 4 名患者,我们将得到一组四个布尔值: @@ -188,6 +190,8 @@ dists = counts.select(0).with_columns( dists.barh(0) ``` +![](img/16-2.png) + 与“非癌症”类别的分布相比,“癌症”类别的`Mitoses`都集中于最低评分。 所以看起来类别和有丝分裂活动是相关的。 但是,这可能只是由于偶然嘛? @@ -292,12 +296,16 @@ shuffled_dists = shuffled_counts.select(0).with_columns( shuffled_dists.barh(0) ``` +![](img/16-3.png) + 这与原始条形图看起来有点不同,为方便起见,再次展示如下。 ```py dists.barh(0) ``` +![](img/16-4.png) + ### 检验统计量:总变异距离 我们需要一个测试统计量来衡量蓝色和金色分布之间的差异。 回想一下,总变异距离可以用来量化两个类别分布的差异。 @@ -357,6 +365,8 @@ print('Observed TVD:', observed_tvd) Observed TVD: 0.418419465491 ``` +![](img/16-5.png) + 观察到的总变异距离 0.42 根本不接近于假设零假设为真所产生的分布。 数据支持备选假设:有丝分裂评分与类别有关。 ### 两个类别分布的相等性的排列检验 @@ -404,6 +414,8 @@ Observed TVD: 0.638310905047 Empirical P-value: 0.0 ``` +![](img/16-6.png) + 同样,观测距离 0.64 离原假设预测的分布很远。 经验 P 值为 0,所以准确的 P 值将接近于零。 因此,如果类别和有丝分裂评分是不相关的,那么观测的数据是极不可能的。 所以得出的结论是,有丝分裂评分与类别有关,不仅在样本中,而且在总体中。 @@ -458,12 +470,18 @@ weight_smoke.group('Maternal Smoker') ```py nonsmokers = baby.where('Maternal Smoker', are.equal_to(False)) +nonsmokers.hist('Birth Weight', bins=np.arange(40, 181, 5), unit='ounce') ``` +![](img/16-7.png) + ```py -nonsmokers.hist('Birth Weight', bins=np.arange(40, 181, 5), unit='ounce') +smokers = baby.where('Maternal Smoker', are.equal_to(True)) +smokers.hist('Birth Weight', bins=np.arange(40, 181, 5), unit='ounce') ``` +![](img/16-8.png) + 两种分布都大致是钟形,中心在 120 盎司附近。 当然,这些分布并不相同,这就产生了这样一个问题,即差异是否仅仅反映了机会变异,还是反映了总体分布的差异。 这个问题可以通过假设检验来回答。 @@ -540,6 +558,8 @@ Observed statistic: 9.266142572024918 Empirical P-value: 0.0 ``` +![](img/16-9.png) + 原始样本中的观测差异约为 9.27 盎司,与此分布不一致:经验 P 值为 0,这意味着确切的 P 值确实非常小。 因此,测试的结论是,在总体中,不吸烟者和吸烟者的婴儿出生体重的分布是不同的。 @@ -595,6 +615,8 @@ Approximate 95% CI for the difference between means: ``` +![](img/16-10.png) + 不吸烟的母亲的婴儿比吸烟的母亲的婴儿平均重 7.2 盎司到 11.4 盎司。 这比“两个分布不同”更有用。 由于置信区间不包含 0,它也告诉我们这两个分布是不同的。 所以置信区间估计了我们的均值之间的差异,也让我们决定两个基本分布是否相同。 不吸烟的母亲比吸烟的母亲平均年龄稍大。 @@ -606,6 +628,8 @@ Approximate 95% CI for the difference between means: 0.154278698588 to 1.4701157656 ``` +![](img/16-11.png) + 但毫不奇怪,证据并没有指出,他们的平均身高与不吸烟的母亲不同。 零在均值之间差异的置信区间中。 ```py @@ -615,6 +639,8 @@ Approximate 95% CI for the difference between means: -0.390841928035 to 0.204388297872 ``` +![](img/16-12.png) + 总之: 如果你想知道两个基本分布是否相同,则可以使用带有适当检验统计量的排列检验。 当分布是类别时,我们使用总变异距离,而分布是数值时,我们使用均值之间的绝对差。 @@ -684,6 +710,8 @@ bta.group('Group', np.mean) 这是一个展示设定的好方法。每个病人都有一张双面票: +![](img/16-13.png) + 随机化之后,我们可以看到随机选择的一组票的右半部分,以及剩余分组的左半部分。 `observed_outcomes`表收集每个患者潜在结果的信息,每张“票”的未观察的一半留空。 (这只是考虑`bta`表的另一种方式,它载有的信息相同。) @@ -782,6 +810,8 @@ Observed statistic: 0.475 Empirical P-value: 0.00965 ``` +![](img/16-14.png) + 经验 P 值非常小(研究报告 P 值为 0.009,这与我们的计算一致),因此证据倾向于备选假设:潜在实验和控制分布是不同的。 这是实验导致差异的证据,因为随机化确保了没有影响结论的混淆变量。 @@ -847,11 +877,13 @@ Approximate 95% CI for the difference between means: -0.759090909091 to -0.162393162393 ``` +![](img/16-15.png) + 基本分布的均值之间的差异的约 95% 置信区间,范围是约 -80% 到 -20%。换句话说,实验组好转了 20% 到 80% 左右。 注意这个变化很大的估计。那是因为每个组的样本量只有 15 个左右。虽然这些作用于这些数值而没有进一步的假设,但结果并不十分精确。 -# ## 元分析 +### 元分析 虽然 RCT 确实真名了肉毒杆菌毒素 A 实验帮助了患者,但对 31 名患者进行的研究不足以确定治疗的有效性。这不仅仅是因为样本量小。我们在这一部分的结果对于研究中的 31 位患者是有效的,但我们对所有可能患者的总体真正感兴趣。如果 31 名患者是来自较大总体的随机样本,那么我们的置信区间对该总体是有效的。但他们不是随机样本。 diff --git a/img/16-1.png b/img/16-1.png new file mode 100644 index 0000000000000000000000000000000000000000..ddc328ab0a4de5a1f0360c3ed20d2a915ea05a21 GIT binary patch literal 10623 zcma)i2Ut{D)@_;F0JI9)AVE1MNTS`bIxF^fRaIyG#jf|6YHe`c?IU` zQoo&sZ=Sq%dj|iUv=)}c{s#ZK{PyfMd_HR-p=ymnoxgfOUvo z8gbN6w5_RMUD1_4rf^a9SD_!Pto2@Q#(4r;wOX7&sep2wC`=KZOk8XZP{1lE-cjb z7wr2p^7Hen!**&XpV+}aay)W$DAe;Cw6On=zlXpRJ^l@S3Wd6NGUYf5^~Vd$F%;^; zgABORGaei9#S9lkFS*{$?&i{vRPbp+asw+e6e^Gk$Avs%R>0pL z)WXM@&ikpJ%gZ6Nx0Z}Tf^oD(RL4+U*%kW5G*tJlT)gV#e*;{N2Ff1Wrqxw4W=#%>frL4=a?Bp0wli_1pe zXBV-IyUqLfBPv@RCv)QT1-Yfcq9Us)wCzHl^wIu|U~if20(JYsm6VD1xmB1nnV4q< z1Ggm4o;{0}kdTA3nr?ZgW5t6KQnkW=A?=QPr5T;pxI9v>Oy#znaQjh2{HK>^q=L)r zS8|lH)#g^*kIDu177M6ntb8z?snXYCcnRC

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