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class="menu navigation"><div class="list-h"><a target="_blank" rel="external nofollow noopener noreferrer" href="https://github.com/MHuiG" active-action="action-https:githubcomMHuiG"><i class="fa-brands fa-github color-github fa-fw"></i><p>Github</p></a><a href="/pages/friends/" active-action="action-pagesfriends"><i class="fa-duotone fa-link color-friends fa-fw"></i><p>友链</p></a><a href="/pages/about/" active-action="action-pagesabout"><i class="fa-duotone fa-user-tie color-about fa-fw"></i><p>关于</p></a><a href="https://www.travellings.cn/go-by-clouds.html" target="_blank" active-action="action-https:wwwtravellingscngo-by-cloudshtml" rel="external nofollow noopener noreferrer"><i class="fa-duotone fa-subway color-travellings fa-fw"></i><p>Travelling</p></a></div></div></div></div><div id="scroll-down" style="display:none"><i class="fa fa-chevron-down scroll-down-effects"></i></div></div></div><div id="safearea"><div class="body-wrapper"><div id="l_main" class><article itemscope itemtype="http://schema.org/Article" class="article post white-box reveal md shadow floatable blur article-type-post" id="post" itemprop="blogPost"><link itemprop="mainEntityOfPage" href="https://blog.mhuig.top/p/2f345bb/"><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="MHuiG"></span><span hidden itemprop="post" itemscope itemtype="http://schema.org/Post"><meta itemprop="name" content="MHuiG"><meta itemprop="description" content="MHuiG&#39;s Blog (MHuiG的博客) MHuiG&#39;s Neverland（MHuiG的梦幻岛） —— MHuiG(@MHuiG) 随便写写画画的地方 - 技术博客"></span><span hidden><meta itemprop="image" content="/lib/favicon/android-chrome-192x192.png"></span><div class="article-meta" id="top"><h1 class="title" itemprop="name headline"> 辛普森悖论 | 你还相信数据吗</h1><div class="new-meta-box"><div class="new-meta-item author" itemprop="author" itemscope itemtype="http://schema.org/Person"> <a itemprop="url" class="author" target="_blank" href="https://mhuig.top/" rel="nofollow noopener"><img itemprop="image" src="/lib/avatar/avatar-16.webp?v=2199236952" class="lazyload" data-srcset="/lib/avatar/avatar-16.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw=="><p itemprop="name">MHuiG</p></a></div><div class="new-meta-item wordcount"><a class="notlink"><i class="fa-duotone fa-keyboard fa-fw" aria-hidden="true"></i><p>字数：1.3k 字</p></a></div><div class="new-meta-item readtime"><a class="notlink"><i class="fa-duotone fa-hourglass-half fa-fw" aria-hidden="true"></i><p>时长：4 分钟</p></a></div></div></div><div id="layoutHelper-page-plugins"></div><div id="post-body" itemprop="articleBody"><blockquote><p>数据是一个有力的武器，它既能被用来澄清现实，也能被用来混淆是非</p></blockquote><p>你知不知道，数据也会说谎？</p><div class="story post-story"><h2 id="一个栗子"><a href="#一个栗子" class="headerlink" title="一个栗子"></a>一个栗子</h2><p>假设您患有肾结石并去看医生。医生告诉你有两种治疗方法，治疗 A（开放手术 open surgery）和治疗 B（体外冲击波碎石术 ESWL）。</p><p>你问哪种治疗效果更好，医生说：“一项研究发现治疗 A 的成功概率高于治疗 B。”</p><p>你说：“我会接受治疗 A，谢谢！”</p><p>这时医生打断你，“但同样的研究还研究了哪种治疗效果更好，这取决于患者是大肾结石还是小肾结石。”</p><p>你说：“好吧，我有大肾结石还是小肾结石？”</p><p>你说话的时候，医生又打断了你，说：“其实没关系。你看，他们发现治疗 B 比治疗 A 成功的概率更高，不管你的肾结石是大还是小。”</p><p>你可能想知道你是否没看错。听起来不可能。但这是真的：在<a target="_blank" rel="external nofollow noopener noreferrer" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1339981/">一项实际研究</a>中，发现治疗 B 比治疗 A 对大肾结石和小肾结石起作用的概率更高，尽管事实上治疗 A 的总体 概率高于治疗 B。这是研究数据：</p><table><thead><tr><th align="center"></th><th align="center">治疗 A 有帮助</th><th align="center">治疗 B 有帮助</th></tr></thead><tbody><tr><td align="center">大肾结石</td><td align="center"> 69% (55 / 80)</td><td align="center">73% (192 / 263)</td></tr><tr><td align="center"> 小肾结石</td><td align="center"> 87% (234 / 270)</td><td align="center">93% (81 / 87)</td></tr><tr><td align="center"> 所有患者</td><td align="center"> 83% (289 / 350)</td><td align="center">78% (273 / 350)</td></tr></tbody></table><p>表中的第一项显示，80 名大肾结石患者接受了 A 治疗，治疗帮助了其中 55 人，成功率为 69%。这不如治疗 B 好，它帮助了 263 名大肾结石患者中的 192 人，成功率为 73%。以类似的方式，第二行显示治疗 B 比治疗 A 对患有小肾结石的人更有效。</p><p>但是当你把每一列的数字加起来时，你会发现治疗 A 确实比治疗 B 整体效果更好。</p><p>值得花时间检查所有数字加起来检验一下，并说服自己我没有欺骗你.</p><p>刚刚展示的这种现象被称为辛普森悖论。如果你和包括我在内的大多数人一样，那么辛普森悖论在你第一次见到它时就会令人震惊。因为它违反了我们对世界推理的本能方式。而且，正如我们看到的那样，辛普森悖论不仅是一种怪异的现象，而且它经常在具有重要决策后果的地方出现。</p></div><div class="story post-story"><h2 id="表达式"><a href="#表达式" class="headerlink" title="表达式"></a>表达式</h2><p>我们抽离出符号表达：</p><table><thead><tr><th align="center"></th><th align="center">统计对象 1</th><th align="center"> 统计对象 2</th></tr></thead><tbody><tr><td align="center"> 分项指标 1</td><td align="center"><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-1.091ex" xmlns="http://www.w3.org/2000/svg" width="2.499ex" height="2.878ex" role="img" focusable="false" viewBox="0 -789.7 1104.4 1271.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mfrac"><g data-mml-node="msub" transform="translate(240.2,477.2) scale(0.707)"><g data-mml-node="mi"><path data-c="1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389 373 390 377 395T388 406 404 418Q438 442 450 442 454 442 457 439T460 434Q460 425 391 149 320-135 320-139 320-147 365-148H390Q396-156 396-157T393-175Q389-188 383-194H370Q339-192 262-192 234-192 211-192T174-192 157-193Q143-193 143-185 143-182 145-170 149-154 152-151T172-148Q220-148 230-141 238-136 258-53T279 32Q279 33 272 29 224-10 172-10 117-10 75 30T33 157ZM352 326Q329 405 277 405 242 405 210 374T160 293Q131 214 119 129 119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109 352 326Z"/></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 54 315 52T339 48 401 46H427V0H416Q395 3 257 3 121 3 100 0H88V46H114Q136 46 152 46T177 47 193 50 201 52 207 57 213 61V578Z"/></g></g><g data-mml-node="msub" transform="translate(220,-345) scale(0.707)"><g 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152-151T172-148Q220-148 230-141 238-136 258-53T279 32Q279 33 272 29 224-10 172-10 117-10 75 30T33 157ZM352 326Q329 405 277 405 242 405 210 374T160 293Q131 214 119 129 119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109 352 326Z"/></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315 301 241Q265 210 201 149L142 93 218 92Q375 92 385 97 392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19 31Q50 38 56 46T86 81Q115 113 136 137 145 147 170 174T204 211 233 244 261 278 284 308 305 340 320 369 333 401 340 431 343 464Q343 527 309 573T212 619Q179 619 154 602T119 569 109 550Q109 549 114 549 132 549 151 535T170 489Q170 464 154 447T109 429Z"/></g></g><g data-mml-node="msub" transform="translate(220,-345) scale(0.707)"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317 40 348 55 381 75 411 101 433 134 442Q209 442 230 378L240 387Q302 442 358 442 423 442 460 395T497 281Q497 173 421 82T249-10Q227-10 210-4 199 1 187 11T168 28L161 36Q160 35 139-51T118-138Q118-144 126-145T163-148H188Q194-155 194-157T191-175Q188-187 185-190T172-194Q170-194 161-194T127-193 65-192Q-5-192-24-194H-32Q-39-187-39-183-37-156-26-148H-6Q28-147 33-136 36-130 94 103T155 350Q156 355 156 364 156 405 131 405 109 405 94 377T71 316 59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26 282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405 339 405 328 402T306 393 286 380 269 365 254 350 243 336 235 326L232 322Q232 321 229 308T218 264 204 212Q178 106 178 102Z"/></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315 301 241Q265 210 201 149L142 93 218 92Q375 92 385 97 392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19 31Q50 38 56 46T86 81Q115 113 136 137 145 147 170 174T204 211 233 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y="220"/></g></g></g></g></svg><svg data-labels="true" preserveAspectRatio="xMaxYMid" viewBox="1278 -1319.5 1 2139"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:2" transform="translate(0,810.5)"><text data-id-align="true"/><g data-idbox="true" transform="translate(0,-750)"><g data-mml-node="mtext"><path data-c="28" d="M94 250Q94 319 104 381T127 488 164 576 202 643 244 695 277 729 302 750H315 319Q333 750 333 741 333 738 316 720T275 667 226 581 184 443 167 250 184 58 225-81 274-167 316-220 333-241Q333-250 318-250H315 302L274-226Q180-141 137-14T94 250Z"/><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315 301 241Q265 210 201 149L142 93 218 92Q375 92 385 97 392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19 31Q50 38 56 46T86 81Q115 113 136 137 145 147 170 174T204 211 233 244 261 278 284 308 305 340 320 369 333 401 340 431 343 464Q343 527 309 573T212 619Q179 619 154 602T119 569 109 550Q109 549 114 549 132 549 151 535T170 489Q170 464 154 447T109 429Z" transform="translate(389,0)"/><path data-c="29" d="M60 749 64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12 224-76 186-143 145-194 113-227 90-246Q87-249 86-250H74Q66-250 63-250T58-247 55-238Q56-237 66-225 221-64 221 250T66 725Q56 737 55 738 55 746 60 749Z" transform="translate(889,0)"/></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p>以上就是辛普森悖论比较通俗易懂的表达式了。</p></div><div class="story post-story"><h2 id="我们忽略了什么"><a href="#我们忽略了什么" class="headerlink" title="我们忽略了什么"></a>我们忽略了什么</h2><p>从数据生成过程（因果模型）来看分析.</p><p>事实证明，小肾结石被认为是不严重的病例，治疗 B（体外冲击波碎石术 ESWL）比治疗 A（开放手术 open surgery）更加激进。</p><p>对于小肾结石，医生更有可能推荐保守疗法 A，因为病情不太严重，患者最有可能首先成功恢复。</p><p>对于严重的大肾结石，医生往往选择更激进的疗法 B。即使疗法 B 在这些病例中表现更好，由于是更严重的病例，疗法 B 的总体恢复率低于疗法 A.</p><p>在这个现实世界的例子中，肾结石的大小（病例的严重性）是一个混合变量，它会同时影响自变量（疗法）和因变量（恢复率）.</p><p><mjx-container class="MathJax" jax="SVG" display="true" width="full" style="min-width:33.359ex"><svg style="vertical-align:-.566ex;min-width:33.359ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.262ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -750)"><g data-mml-node="math"><g data-mml-node="mtable" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 750) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="5294.3 -750 1 1000"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr"><g data-mml-node="mtd"><g data-mml-node="mi"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">疗</text></g><g data-mml-node="mi" transform="translate(1000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">法</text></g><g data-mml-node="mo" transform="translate(2277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 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style="vertical-align:-.566ex;min-width:41.317ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.262ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -750)"><g data-mml-node="math"><g data-mml-node="mtable" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 750) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="7053.1 -750 1 1000"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr"><g data-mml-node="mtd"><g data-mml-node="mi"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">恢</text></g><g data-mml-node="mi" transform="translate(1000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">复</text></g><g data-mml-node="mi" transform="translate(2000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">率</text></g><g data-mml-node="mo" transform="translate(3277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347 722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153 722 140 707 133H70Q56 140 56 153Z"/></g><g data-mml-node="mi" transform="translate(4333.6,0)"><path data-c="1D453" d="M118-162Q120-162 124-164T135-167 147-168Q160-168 171-155T187-126Q197-99 221 27T267 267 289 382V385H242Q195 385 192 387 188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432 298 434 307 482T319 540Q356 705 465 705 502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603 443 622 454 636T478 657L487 662Q471 668 457 668 445 668 434 658T419 630Q412 601 403 552T387 469 380 433Q380 431 435 431 480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282-47 255-132 212-173 175-205 139-205 107-205 81-186T55-132Q55-95 76-78T118-61Q162-61 162-103 162-122 151-136T127-157L118-162Z"/></g><g 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transform="scale(1,-1)" font-size="884px" font-family="serif">病</text></g><g data-mml-node="mi" transform="translate(8717.2,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">例</text></g><g data-mml-node="mi" transform="translate(9717.2,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">的</text></g><g data-mml-node="mi" transform="translate(10717.2,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">严</text></g><g data-mml-node="mi" transform="translate(11717.2,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">重</text></g><g data-mml-node="mi" transform="translate(12717.2,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">性</text></g><g data-mml-node="mo" transform="translate(13717.2,0)"><path data-c="29" d="M60 749 64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12 224-76 186-143 145-194 113-227 90-246Q87-249 86-250H74Q66-250 63-250T58-247 55-238Q56-237 66-225 221-64 221 250T66 725Q56 737 55 738 55 746 60 749Z"/></g></g></g></g></svg><svg data-labels="true" preserveAspectRatio="xMaxYMid" viewBox="1278 -750 1 1000"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:4"><g data-mml-node="mtext"><path data-c="28" d="M94 250Q94 319 104 381T127 488 164 576 202 643 244 695 277 729 302 750H315 319Q333 750 333 741 333 738 316 720T275 667 226 581 184 443 167 250 184 58 225-81 274-167 316-220 333-241Q333-250 318-250H315 302L274-226Q180-141 137-14T94 250Z"/><path data-c="34" d="M462 0Q444 3 333 3 217 3 199 0H190V46H221Q241 46 248 46T265 48 279 53 286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675 336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212 183 211H293Z" transform="translate(389,0)"/><path data-c="29" d="M60 749 64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12 224-76 186-143 145-194 113-227 90-246Q87-249 86-250H74Q66-250 63-250T58-247 55-238Q56-237 66-225 221-64 221 250T66 725Q56 737 55 738 55 746 60 749Z" transform="translate(889,0)"/></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p>为了确定哪种治疗方法确实更好，我们需要通过对两组数据进行分离并比较组内的恢复率而不是按组聚合来控制混合变量。</p><p><mjx-container class="MathJax" jax="SVG" display="true" width="full" style="min-width:35.845ex"><svg style="vertical-align:-.566ex;min-width:35.845ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.262ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -750)"><g data-mml-node="math"><g data-mml-node="mtable" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 750) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="5843.8 -750 1 1000"><g transform="matrix(1 0 0 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data-mml-node="mtd"><g data-mml-node="mi"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">大</text></g><g data-mml-node="mi" transform="translate(1000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">肾</text></g><g data-mml-node="mi" transform="translate(2000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">结</text></g><g data-mml-node="mi" transform="translate(3000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">石</text></g><g data-mml-node="mi" transform="translate(4000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">恢</text></g><g data-mml-node="mi" transform="translate(5000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">复</text></g><g data-mml-node="mi" transform="translate(6000,0)"><text data-variant="normal" 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250Q94 319 104 381T127 488 164 576 202 643 244 695 277 729 302 750H315 319Q333 750 333 741 333 738 316 720T275 667 226 581 184 443 167 250 184 58 225-81 274-167 316-220 333-241Q333-250 318-250H315 302L274-226Q180-141 137-14T94 250Z"/></g><g data-mml-node="mi" transform="translate(9067.6,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">疗</text></g><g data-mml-node="mi" transform="translate(10067.6,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">法</text></g><g data-mml-node="mo" transform="translate(11067.6,0)"><path data-c="29" d="M60 749 64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12 224-76 186-143 145-194 113-227 90-246Q87-249 86-250H74Q66-250 63-250T58-247 55-238Q56-237 66-225 221-64 221 250T66 725Q56 737 55 738 55 746 60 749Z"/></g></g></g></g></svg><svg data-labels="true" preserveAspectRatio="xMaxYMid" viewBox="1278 -750 1 1000"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:6"><g data-mml-node="mtext"><path data-c="28" d="M94 250Q94 319 104 381T127 488 164 576 202 643 244 695 277 729 302 750H315 319Q333 750 333 741 333 738 316 720T275 667 226 581 184 443 167 250 184 58 225-81 274-167 316-220 333-241Q333-250 318-250H315 302L274-226Q180-141 137-14T94 250Z"/><path data-c="36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601 351 623 311 626 240 626 194 566 147 500 147 364L148 360Q153 366 156 373 197 433 263 433H267Q313 433 348 414 372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149 440 90 387 34T253-22Q225-22 199-14T143 16 92 75 56 172 42 313ZM257 397Q227 397 205 380T171 335 154 278 148 216Q148 133 160 97T198 39Q222 21 251 21 302 21 329 59 342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z" transform="translate(389,0)"/><path data-c="29" d="M60 749 64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12 224-76 186-143 145-194 113-227 90-246Q87-249 86-250H74Q66-250 63-250T58-247 55-238Q56-237 66-225 221-64 221 250T66 725Q56 737 55 738 55 746 60 749Z" transform="translate(889,0)"/></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p>这样看来激进的治疗 B（体外冲击波碎石术 ESWL）效果更好.</p><p>如果有潜在变量（特别是混合变量）存在，牢记：整体数据未必可靠，要通过科学合理的分组来查看具体细致的数据。</p></div><div class="story post-story"><h2 id="启示"><a href="#启示" class="headerlink" title="启示"></a>启示</h2><ul><li>数据从来都不是完全客观的。我们必须对这些数字持怀疑态度.</li><li> 辛普森悖论的出现是因为人们忽略了研究的因果关系，一旦我们理解了数据生成的机制，我们就可以寻找影响结果的其他因素，而图表不会告诉你这些.</li><li> 充分考察事件的潜在影响因素和维度，系数消除分组数据基数差异造成的影响.</li><li> 要求我们具备科学辩证思维，客观看待关联现象。很多时候，我们选择相信直觉，因为我们的直觉往往很准。但是，在信息不全或者信息非对称的情况下，直觉常常是是值得怀疑的。</li></ul></div></div><div class="footer"><div class="copyright license"><div class="license-title">辛普森悖论 | 你还相信数据吗</div><div class="license-link"><a href="https://blog.mhuig.top/p/2f345bb/">https://blog.mhuig.top/p/2f345bb/</a></div><div class="license-meta"><div 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