《英国医学会杂志》（BMJ）自2008年9月开始至2015年由两位流行病与统计学专家不间断地出了300多期statistical question系列。在这个系列中，两位学者每次出一道统计学选择题，进行选择并解释。现在医学论文与统计分析公众号的郑老师精选300道Statistical Question，请有兴趣的朋友们进行回答。我在其中进行英文版的学习，加强统计学实践知识和提高英语阅读能力。
医学四大期刊：lancet,nature,BMJ, NEJM
journal：[`dʒɝnl]n.（专业性）日志，日报，杂志；分类账。
【结构分析】journal=journ（日，天）+al（形容词后缀）→每日的→日志，日报，杂志。法语词根journ-（天，日）来自古法语，由jo-和形容词后缀-urn组成。
目录：
2021年7月计划0篇，7月实际4篇。
Question01-11: distribution
Question02-12: error
Question03- 07：the study design
Question04-15: probability
2021年8月计划5篇；8月实际6篇。
Question05-16:measure of spread
Question 06-14:study design
Question 07-18：normally distributed
Question 08-20: normal distribution
Question 09-04: sample size
Question 10-21：statistical test
Question01-11: distribution
The average number of suicides reported each month in one county last year was 3.2. To compare numbers of suicides between months, calculating P values or confidence intervals, which probability distribution would be most appropriate to use?
Binomial
Normal
Poisson
Weibull
Answer：The Poisson distribution describes the occurrence of rare events happening at random in a large population, which fits the bill here. It is also necessary to check that there are not linkages between the suicides, or clustering, as this will affect the interpretation of the expected probabilities. the Poisson distribution is helpful for ‘back of the envelope’ calculations ，because when the number of events is reasonably large, the standard deviation of the distribution is the same number as the square root of the mean. (Technically the binomial distribution could be used but it requires long calculations of large numbers.)
suicide：[`suɪsaɪd] v.自杀n.自杀；自杀者。
【结构分析】suicide=sui（自己）+cid（切割，杀）+e→自杀；拉丁词根cid-/cis-（切，杀）；
Bill:=case
Linkages:链结，
Clustering:聚类，
Interpret： v. 解释；口译。 【结构分析】interpret=inter（之间）+pret（交换）→在中间交换（信息）→解释，口译。
back of the envelope’ calculations：信封背后的计算。
Deviation：[`divɪ`eʃən]n.偏差；误差；背离。
【结构分析】deviation=de（离开）+vi（道路）+ation（动名词后缀）→偏离。拉丁词根vi-/via-（行走，道路）来自拉丁语名词via（道路）。它和拉丁词根vehi-/vect-（交通，运输）以及日耳曼单词way（道路）最终都源自原始印欧语词根*wegh-（交通，运输）。
需要去检查自杀之间与聚类的关联性，因为它会影响对预期概率的解释。
这个分布的标准偏差和均值的平方根相同。(从技术上来讲，二项分布可以被使用，但需要对大量数据进行长时间计算)
2021年7月1日星期四
Question02-12: error（202107121周一）
In a trial of a herbal treatment for symptoms of menopause /the power calculation described in the protocol /required 400 patients to be randomised. Unfortunately, recruitment was slow and the trial had to be stopped after 200 patients as funding was running out. Which if any of the following statements is true?
a) The possibility of a type one error is increased and the possibility of a type two error is unaltered.
b) The possibility of a type two error is increased and the possibility of a type one error is unaltered.
c) The possibility of both a type one error and a type two error is increased.
d) The possibility of both types of error is unaltered.
Answer
A type one error occurs when a study indicates/ an effect or an association that does not exist, the so called “false positive result.” The rate of false positive results (we are prepared to accept as the price for scientific enquiry) is chosen /by the investigator or the reader and is referred /to as the level for statistical significance. Often this is set at 5% or one in 20. This kind of error has nothing to do with sample size.
A type two error occurs when a study fails to detect an effect or an association that does exist. For any given investigation, smaller studies have less ability to pick up an association or effect than do larger studies.
Small studies can be misleading in another way. As small studies are “imprecise” and have wide confidence intervals, it is only the ones with abnormally large effects that manage to achieve “statistical significance.” If the only studies conducted on, say, a new surgical technique are small, then by relying only on the “statistically significant” ones we are likely to overestimate the promise of the new treatment. So even though we might rely on the “significant” study to show that something is going on, it would be prudent to consider all the “non-significant” studies as well in estimating the likely size of the effect.
Herbal treatment:traditonal chinese medicine treatment。
menopause :=meno+pause(暂停、停止);the time during which a woman gradually stops menstruating, usually at around the age of 50.
Indicate:in(在里面)+dic（指示）+ate（V的后缀）=在里面指示=表明，指出，告知。
Detect=de（反义）+tect（遮盖）→打开遮盖→察觉，发现，探测。
precise：precise：[prɪ`saɪs] adj.精确的；明确的。 【结构分析】precise=pre（在前面）+cis（切割）+e→预先切割好的→精准匹配好的→精确的，明确的。Im(不)。
The rate of false positive results （we are prepared to accept ）as the price for scientific enquiry is chosen /by the investigator or the reader and is referred /to as the level for statistical significance.
长难句翻译1：我们正准备接受假阳性结果作为科学要求价格接近于，通过研究者或者读者和统计学意义水平的参考。
正确翻译：我们准备接受的假阳性结果率作为科学调查的价格是由研究者或读者选择的，并被称为统计显着性水平。
主要错误点：chosen是选择，而不是接近，接近是close。
长难句翻译2：小研究能力小于大研究。
it is only the ones with abnormally large effects that manage to achieve “statistical significance.”
长难句翻译3：它仅仅是在正常大影响下成功的实现统计学意义。
正确翻译：因此只有具有异常大影响的研究才能实现“统计意义”
主要错误点：ab前缀是相反的意思，改变了原来单词意思。
If the only studies conducted on, say, a new surgical technique are small, then by relying only on the “statistically significant” ones we are likely to overestimate the promise of the new treatment。
长难句翻译4：如果只有研究被执行，说，一个新的外科手术技术是小的，然后仅仅依靠 “统计学意义”，我们很可能过度估计新治疗的效果。
正确翻译：比如对一种新的外科手术技术进行的研究样本量很小，那么仅依靠“具有统计学意义”的研究，我们可能会高估新疗法的前景。
主要错误点：promise，有前景的，promise=pro（在前面，提前）+mis（放出）+e→提前放出的东西→许诺，希望
So even though we might rely on the “significant” study to show that something is going on ，it would be prudent to consider all the “non-significant” studies as well in estimating the likely size of the effect.
长难句翻译5：因此即使我们可能依靠有“统计意义”的研究去展示某些事正在发生，它可能什么去思考所有“无意义”研究和估计可能的影响的大小。
正确翻译：因此，即使我们可能依靠“统计学意义”研究来表明正在发生某些事情，但在估计影响的可能大小时也应预先考虑所有“没有统计学意义”研究。
主要错误点：size本意是大小，不只有样本量的含义。prudent：[`prʊdnt]adj.谨慎的；精明的；节俭的。
【结构分析】prudent=pr(o)（提前）+ud（=vid，看）+ent（形容词后缀）→有远见的，未雨绸缪的→谨慎的，精明的，节俭的。
2021年7月12日星期一
Question03- 07：the study design（20210716周五）
A group of investigators decided to test the hypothesis that using post menopausal hormones increases the risk of breast cancer. They identified 500 women with newly diagnosed breast cancer, and 500 women of the same age, from the same neighbourhoods as the first group of women, who did not have breast cancer. Then they asked all women about their past use of postmenopausal hormones.
What answer best describes the study design used here?
a) A retrospective cohort study
b) An incidence study
c) A case crossover study
d) A case-control study
Answer
d—
Case-control studies gather participants together on the basis of whether they are cases with disease or controls free from disease. The question is then asked “What have these people done in the past that may have led to disease?”
Retrospective cohorts by contrast follow up a group of people who have already been gathered together for some reason in the past (perhaps they attended the same school or were born in the same maternity unit). The question is then asked “What has happened to these people now?” Cohort studies may of course measure incidence.
A case crossover study is a special example of a case-control study/ where all people are cases /though the timing and degree of exposure to risk factors may vary.
hypothesis：[haɪ`pɑθəsɪs]n.假设。
【结构分析】hypothesis=hypo（在下面）+thes（摆放）+sis（名词后缀）→摆放在下面，作为论证基础的东西→假设
an idea or explanation of something that is based on a few known facts but that has not yet been proved to be true or correct. [Oxford definition]
hormones：
breast:either of the two round soft parts at the front of a woman’s body that produce milk when she has had a baby. [Oxford definition]
2021年7月16日（星期五）
Question04-15: probability（20210720周二）
Mike has only two children, and they are called Pat and Alex, which could equally be boys’ or girls’ names. In fact, Pat is a girl.What is the probability that Alex is a boy?
a) 50%
b)Slightly less than 50%
c)Slightly more than 50%
d)Between 60% and 70%
e)Between 40% and 30%
Answer
Although this could be about the relative popularity of ambiguous names for boys and girls or about subtle imbalances in the sex ratio, it is not meant to be. The clue to the correct answer is in thinking about what we do not know about the family and what we do know already, and applying this to the expected probabilities of girls and boys.
We do not know if Pat was born first or second. We do know that there are only two children and that Pat is a girl. I am assuming that in the population, 50% of children are girls.
The birth order and relative frequency of two child families are: boy, boy (25%), girl, girl (25%), boy, girl (25%) girl, boy (25%). We know Mike’s family does not have two boys, since Pat is a girl, so we are only left with three choices for families with at least one girl. Two of these pairs have a boy and one does not. Hence the probability that Alex is a boy is two thirds or 66.7%.
If we had been told that Pat was born first then the probability that Alex is a boy drops to 50%.
This is initially surprising but illustrates that applying what we know already makes a difference to the meaning of a simple statistic such as “fifty percent of children are girls.” The formal study of conditional probabilities such as these is covered by Bayesian statistics.
翻译与理解：
Although this could be about the relative popularity of ambiguous names for boys and girls or about subtle imbalances in the sex ratio,it is not meant to be。
我的：虽然这可能是关于男孩和女孩不同名字的相关概率，或者是性别比例的什么不平衡，它并不意味着是；
翻译难点：
ambiguous不认识，根据认识的单次猜测很可能是差异的、不同的。正确的是模棱两可的。
Subtle：不认识，无法猜测。=slight
Imbalances：主要是前缀im的意思不确定。Impossible,否定前缀。我太厉害了，完全正确。
Clue：线索；提示。 【词源解释】来自古英语，本意是“线团”。在古希腊神话中，雅典王子忒修斯作为贡品前往克里特岛，杀死了迷宫里面的人首牛身怪米诺陶洛斯，凭借线团留下的线索逃出迷宫
Google翻译：虽然这可能是与男孩女孩流行相关的模糊名字，或者是性别比例微妙的不平衡，但并不意味着就是。
Question05-16:measure of spread(20210802周一)
Which, if any, of the following are measures of spread?
a) Mode
b) Interquartile range
c) Skewness
d) Variance
Answer
When presenting numerical data it is useful to give an idea of the range of values covered by the data. The maximum and minimum values would define the entire range, but would not describe how typical these values would be. Measures of spread provide a summary of how spread out observations typically are.
The interquartile range is described by the bottom and top values that contain the middle 50% of the observations in the set of data. 25% of observations fallbelow this range and 25% above it.
Variance is the average of the square of all the differences between individual observations and the mean. Taking the square root of this gives the familiar standard deviation.
The mode is the most frequent value in a set of data and does not measure spread.
Skewness is a measure of the lack of symmetry in a set of data and does not measure spread.
Spread:传播，分布。
Mode:众数
Interquartial:四分位数
presenting numerical data：数字数据；
bottom:min；bo掉到了托鹅门的最底部。
fallbelow=fall+be+low
symmetry：[`sɪmətri] n.对称；对称性；匀称；整齐。 【结构分析】symmetry=sym（一起）+metr（尺度）+y（名词后缀）→拥有相同的尺度→对称。 希腊词根metr-/meter-（米，测量，尺度，比例，韵律）来自希腊语名词metron（测量，尺度，比例，韵律）。
symptom：[`sɪmptəm] n.症状；征兆。 【结构分析】symptom=sym（一起）+pto（落下，发生）+m（名词后缀）→一起发生的事情→症状。
Measures of spread provide a summary of how spread out observations typically are.
翻译：分布的测量提供了观察通常是如何（向外分布）分散的（总和）概括。
Variance is the average of the square of all the differences between individual observations and the mean.
方差是单独的观测与均值之差的平方的平均数，
Taking the square root of this gives the familiar standard deviation.
这些平方根给与统一的标准（划分）偏差。
Question 06-14:study design(20210809周一)
A neurologist wanted to study the risk of stroke and transient ischaemic attack in people with a diagnosis of migraine. From her headache clinic she selected cases of migraine and controls without migraine.She collected stroke and transient ischaemic attack outcomes by writing to all subjects and their general practitioners five years later. Which study design best describes what was done?
a) Ecological study
b) Cohort study
c) Clinical trial
d) Case-control study
Answer
The case control design looks at the end of a disease or process. Patients are recruited into the study in two groups. One group, the cases, has already had an outcome and the other group, the controls, has not. The question is then posed as to what these two groups of people did in the past.
Despite the word in this study “cases” of migraine and “controls” without migraine are in fact the beginning of a study looking forward over time to the final outcome of stroke or transient ischaemic attack. This makes the study a cohort study. Migraine is examined as a potential risk factor. In this study migraine is not the outcome but the exposure.
An ecological study might compare hospital stroke admissions data with prescriptions of migraine medication /on a county by county basis throughout the United Kingdom.
A clinical trial is an experiment. The clinical investigator decides what intervention each person will receive and then follows each person over time to observe the effects. As described, the above study does not involve any such intervention.
一个神经科医生想要研究在诊断为偏头痛患者中关于中风和transient ischaemic发作风险。从她的头痛诊所挑选出偏头案例和非偏头痛案例作为对照。5年以后通过写信给所有的受试者和全科医生来收集中风和transient ischaemic发作的结果。这属于哪种研究类型？生态研究，队列研究，临床研究，病例对照研究。
答案分析：这病例对照设计一般在疾病结束或者过程中。病人被安排进入两个组，一个组是病例组，已经有结局；另一个组是对照组，没有结局。然后这个问题被设置：两组人过去做了什么。
（我的理解：病例对照研究，与未患该病的人对照寻找过去是什么导致了患病，观察性研究）
由于在研究中偏头痛“案例”和没有偏头痛的“对照”这些单词是（结束时间对于中风或transient ischaemic发作最终结局）研究的开始， 所以这是一个队列研究。偏头痛被审视为一项潜在危险因素，在这项研究中偏头痛不是结局而是暴露。（观察性研究）
一项生态性研究会在整个英国以县为单位，比较医院中风入院数据和偏头痛药物处方。（这里学习了with的两种用法，一是表并列，并列有两种，成分并列，和句子并列；二是表伴随）
临床试验是一种试验。临床研究者决定每个人接受哪种干预，然后在结束时间跟踪每一个人去观察这个影响。正如描述，这项研究没有设计任何干预。（干预性研究）
词汇积累：
Stroke;中风
transient ischaemic attack：短暂性脑缺血发作
their general practitioners：全科实践者，全科医生
intervention干预
prescriptions处方
county县级
1.Despite the word（ in this study “cases” of migraine and “controls” without migraine ）are in fact the beginning of a study（ looking forward over time to the final outcome of stroke or transient ischaemic attack）.
长难句的理解：找出简单句。Word is beginning.
主要在于后半截理解：beginning，study look time to outcome.
我的直译：案例和对照这些词是一个（为了寻找时间结束时中风或短暂性缺血发作的结局）研究的开始
公众号给出的翻译：尽管本研究中的措词是偏头痛的“病例组”和不是偏头痛的“对照组”，但实际上是一项研究的开始，随着时间的流逝，我们期待中风或短暂性脑缺血发作的作为最终结果。
公众号的翻译我阅读会存在很多疑惑。
Question 07-18：normally distributed（20210816周一）
Question
If a statistician tells you that your data are not normally distributed and the distribution has “fat tails,” which if any of the following will be true?
a) Extreme values may be more frequent than in a normal distribution1
b) 95% confidence intervals can not be computed
c) Parametric statistics can not be used
d) 95% confidence intervals will be narrower than those suggested by a normal distribution.
Answer
The tails of a distribution are the regions furthest from the middle or main body of the distribution. Many things measured in medicine do look like normal distributions, but not all of them do. When extreme values happen more often than expected in a normal distribution this is described as a distribution with fat tails. As more observations lie outside the 95% confidence limits of a normal distribution2, the true 95% confidence interval for a fat tailed distribution will be wider than expected on the basis of a normal distribution.
The distribution of stock market values has distinctly fat tails. More large falls and gains/ occur /than expected. In general, when multiple correlated factors/ influence/ an outcome then extreme values are more likely to occur.Cardiovascular risk can follow this pattern.
Lack of conformity to a normal distribution does not mean one has to immediately give up all hope of using parametric statistics. A transformation using logarithms, square root or other suitable procedure may produce a normal fit. Cardiovascular risk is not always normally distributed and the Framingham model uses a different statistical parameter (the Weibull distribution) as the basis for its predictions. So long as a suitable statistical distribution can befound, 95% confidence intervals may still be computed.
积累词汇：
1.Extreme values，极致值
2.Parametric，参数
3.the regions furthest，最远的区域
4.stock market values，股票市场价值
5.distinctly，明显的
6. Cardiovascular risk心血管风险
7. pattern模式
8.Lack of conformity，一致性，联合，统一
9. Framingham model弗雷明翰心血管风险模型
10. computed，计算机和计算
翻译：
1. 极致值的出现可能比正态分布更加频繁
什么是extreme valve?
为什么extreme valve of not normally distributed比normally distibuted更加频繁？
2.正如很多观察者，（躺在）95%的置信下限的外部
当更多的观测值超出正态分布的95%置信限时
lie躺; 平躺; 平卧; 平放; 处于，保留，保持(某种状态); n. 谎言; 位置; AS翻译有误，应该为“当”。
Question 08-20: normal distribution(20210817周二)
Which, if any, are true of a normal distribution?
a) It is symmetrical
b) The mean is equal to the median
c) The mean is equal to the mode
d) The skewness is positive
Answer
The normal distribution is the familiar bell shaped curve and is symmetrical in reflection about the mid-value. Because every point on one side of the curve is matched by a corresponding value on the other side,the mean occurs at the same place on the curve as the middle value, or median.Furthermore, the middle value is also the most frequent value or mode.
Skewness describes the degree to which a distribution is not symmetrical, so the normal distribution is not skewed.
词汇积累
Symmetrical，Sym+meter
Mode，众数
Skew,斜度
Bell，钟
Question 09-04: sample size (20210817周二)
Which of the following will affect the sample size calculation for a clinical trial? (There may be more than one correct statement.)
a) Power
b) Significance level
c) Size of effect to detect
d) Variability of primary outcome
Answer：
These are the four pieces of information required for a sample size calculation.
Larger sample sizes will result in increased power.
Formal“significance” may be set at any P value1. The smaller the P value chosen as indicating significance /the larger will be the required /sample size8.
Large clinical differences/ are easier to detect/ that small ones. The smaller the clinical effect that it is desired to detect, the larger will be the required sample size2.
If the outcome (measure) is highly variable /this will act like “noise,” making it difficult to detect the “signal” of the clinical effect3 .Variability in a continuous measure may be assessed by the standard deviation4. The larger this is, the larger will be the required sample size to detect a certain clinical effect5. Trials are sometimes designed to reduce variability by using strictin clusion criteria to ensure that people in the trial are more similar (for example, similar stage of illness, similar age, similar ethnicity)6. This will reduce the required sample size at the expense of reducing wider generalis ability7.
Vocabulary accumulation
detect,un+cover
significance,检验水准
translate
正式的“检验水准“会可以被设置为任意P值。
Size of effect指的是效应值,渴望被发现的临床效果越小，所需样本量就越大。
如果测量的结局有很高的差异性，这就像噪音一样起作用，去发现临床效果的“信号”就更加困难。
连续性变量的差异程度可以通过标准差来评估。
为了发现确定的临床效应量被要求更大的样本量。
试验被设计通过严格的入排标准确保参与试验的人的更加相似，来减少差异性（例如，相同的疾病情况，相同的年龄，相同的名族）。
减少更宽泛的能力的消费，这里减少了对样本量的要求。
作为检验水准指标的P值越小，所需样本量越大。
总结：power、p、different、effect、variable与n的关系。
How to reduce the variability?strictin clusion criteria
认识的名词：
power,significance,p,clinical different,clinical effect,varibility,standrard deviation；
疑问：
1.what is effect?
The different of mean or rate,ratio
2.what is varibility primary outcome?
比如研究某药物治疗高血压的主要结局是“有效率”，20-30岁有效率是30%，30-40岁有效率是25%，40-50岁有效率是20%；不同年龄之间的主要结局的差异程度；
Question 10-21：statistical test（2021/8/23 周一）
Which of the following statistical tests would be your first choice in each of the studies below?
Test:
1 χ2 for contingency tables 卡方列联表
2 Two sample t test
3 Log rank test
4 Poisson test
5 Pearson’s correlation coefficient
6 Paired t test
Study:
a) The occurrence of heart attacks on duty in the staff of two airlines
b) Change in uric acid concentrations in people with gout before and after starting a new diet
c) Cholesterol concentrations in people from high and low income households in a health survey
d) The association of car colour with owner’s personality type
Answer
a) Poisson distribution based test
b) Paired t test
c) Two sample t test
d) χ2 test
Heart attacks are likely to be a rare occurrence in airline staff on duty and to occur in a large pool of susceptible people. The Poisson distribution models this type of study well.
Uric acid can be measured on a continuous scale and follows a fairly symmetrical distribution. If concentrations are measured in each person before and after starting a diet,then the two measurements are paired within individuals and their difference will probably follow a normal distribution. The paired t test fits the bill.
Cholesterol concentrations in people from households with high and low incomes in a health survey/ can also be measured on a continuous scale. However, the people with a high or a low income are different and cannot be paired, so a two sample t test is appropriate. The test works best if the cholesterol concentration is normally distributed, which is the case in most populations.
Car colour falls into categories with no particular value or order and the same is true of personality type. χ2 tests may be used to assess associations between categorical variables. This could be done for all colours and all personality types in one table to produce a global assessment of “something is going on,” or this could be done for one colour and one personality type at a time by splitting the data into two categories, such as “red and not red”“extrovert and not extrovert.”
χ2 for contingency tables （chi-square test）列联表
what is poisson test?为什么我脑子里面的一点关于泊松分布的记忆都搜索不出来，只是有印象学过这个名词。
What is χ2 test?
What is t test?
What is poisson test?
一段时间内，抛n次硬币，求几次硬币向上的概率。
1.Duty,责任，值班。
2.Uric，尿的；杯子里面的小草被蜡烛烧起来，月亮看见有人撒了一泡尿，把火灭了。
3.Acid，酸（n，adj），sour（adj）；The concentration of acid，啊的一声，实验室发生了硫酸撒到皮肤的事故；
4.Gout，痛风，noun[U] 准备出去，突然头痛发作了。
a disease that causes painful swelling in the joints, especially of the toes, knees and fingers。
5.Cholesterol，胆固醇，chol（胆囊）+e+ster（固化）+ol; [kəˈlestərɔːl]
a substance found in blood, fat and most tissues of the body. Too much cholesterol can cause heart disease.
记忆法：月亮形状的椅子看见巨型鸡蛋就木棍敲碎了，吓破了胆，死特凝固看着鸡蛋和木棍。
6.within=with+in,在什么里面
7.pair，two things the same。
7.1 susceptible,易感人群
8. bill，账单，提议；
9.category,类别，种类
10. split，分开，分离，分类
11.extrovert，内向；extro+over 向外翻转
这两个测量值在个体内是配对的。
我的翻译：在一个表中所有的颜色和个性进行处理，为了产生“某事正在进行”的全球评估，在一个时间内一个颜色和一个个性通过分配这个数据进入两分类，进行处理。
作者翻译：可以针对一张表中的所有颜色和所有个性类型进行此操作，以对“某事正在发生”进行全局评估，也可以通过将数据分为两类，一次针对一种颜色和一种个性类型进行此操作，例如“红色和非红色”，“性格外向和非外向
global assessment翻译错误，全球就是全方位，全面的评估。
