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  • 识别随机抽样

    Suppose you were handed a bag full of a large number of small, unknown items, and asked to try to identify the contents without looking in the bag.  Naturally the easiest way to investigate would be to reach inside and grab a handful to see what turned up.  If you reached in and then pulled out a handful of nothing but marbles of various colors off the top, you’d quite reasonably state that this must be a bag of marbles.
    ::假设你被交给了一个袋子,袋子里装满了一大堆微小的、未知的物品,并被要求在不看袋子的情况下试图辨别里面的东西。 当然,最简单的调查方式就是到里面去,抓住一小撮人,看看有什么发现。 如果你进去,然后从顶部拿出一小撮除了各种颜色的弹珠外的弹珠,你就可以相当合理地说这一定是一袋弹珠。

    Is it possible that you might be wrong?  How?  What could you have done to improve your guess?

    Identifying Random Sampling 
    ::识别随机抽样

    A random sampling is easily the most commonly known method of choosing representatives of a population to comprise a statistical sample .  Since the most likely error in developing an accurate statistical sample comes from some sort of personal bias , careful researchers try to allow as little influence from personal decisions to affect the choice of the sample members as possible.  The easiest way to avoid conscious or subconscious bias is to use a random method of selection.  However, true random sampling may be more difficult than it appears.  A good definition of random sampling is: “A sample consisting of individuals each chosen entirely by chance, in such a way that, at every stage of the process, every potential member of the sample has the same probability of being chosen as every other member.”
    ::随机抽样是选择人口代表组成统计抽样的最常见方法。由于开发准确统计抽样的最可能错误来自某种个人偏差,仔细的研究人员试图尽可能少地允许个人决定的影响影响抽样成员的选择。最容易避免意识或潜意识偏差的方法是使用随机选择方法。然而,真正的随机抽样可能比看上去更困难。随机抽样的良好定义是 : “ 由完全由偶然选择的个人组成的抽样,在过程的每个阶段,抽样的每个潜在成员都有与每个其他成员相同的被选择的概率。 ”

    In order to have a truly random sample , all of the factors involved with the choice of representatives must be entirely random processes, and out of the control of any influence which might have any sort of bias. A simple random sample is the process of assigning a number to each member of the population under study, and then using a random number generator to pick the samples. In subsequent lessons, we will learn how to individually identify and implement other types of random samples , including: Stratified Random Samples, Systematic Random Samples, and Clustered Random Samples.
    ::为了进行真正随机的抽样,与代表选择有关的所有因素都必须是完全随机的过程,并且超出了任何可能具有任何偏差的影响的控制范围。一个简单的随机抽样是将数字分配给每个受研究人口成员的过程,然后使用随机数字生成器来采集样本。在接下来的教训中,我们将学习如何个别地识别和实施其他类型的随机样本,包括:批定随机样本、系统随机样本和集束随机样本。

    Identifying Random Samples 
    ::识别随机抽样

    1. In order to randomly pick 15 students out of a class of 210, a researcher enters the names into a spreadsheet and numbers them 1-210.  Using a random number generator, he picks 15 numbers between 1 and 210, and uses the names associated with those 15 numbers.
    ::1. 为了随机挑选210个班级的15名学生,研究人员将名字输入电子表格,编号为1-210,使用随机数字生成器,在1至210之间取15个数字,并使用与这15个班数有关的名字。

    Is this a random sample?
    ::这是随机抽样吗?

    Yes, this is a random sample.  In fact, this is probably the most common method of randomizing the choice of names from a list.  By converting the names to numbers, the researcher minimizes the chance that he/she will be influenced by a subconscious preference for a particular name.  Further, by using a random number generator to pick the 15 numbers, he keeps his own thoughts away from the actual number selection process.
    ::是的,这是一个随机抽样。事实上,这可能是从列表中随机选取名字的最常用方法。通过将名字转换为数字,研究人员可以最大限度地减少他/她受特定名字的潜意识偏好影响的可能性。此外,通过使用随机数字生成器来选择15个数字,他把自己的想法与实际数字选择过程分开。

    2. A researcher is conducting a survey on how many students at a particular high school go off-campus for lunch.  He decides to pick every 5 t h person in line at the school cafeteria and ask how often he/she goes out to get lunch instead of eating at the cafeteria.
    ::2. 一名研究人员正在调查某一高中有多少学生去校外吃午餐,他决定在学校食堂每排排第5个人,并询问他/她经常出去吃午餐,而不是在食堂吃饭。

    Is this a random sample?  Is it appropriate for the study?
    ::这是随机抽样吗?

    This is a random sample, but not of the correct population.  The concept of ‘every  5 t h person’ is convenient and effective as a method of choosing random students from the line, but choosing students from the lunch line at school excludes the students who are already off campus for lunch!
    ::这是随机抽样,但不是对正确人口的随机抽样。 `第五个人 ' 的概念是方便而有效的,可以作为从一线选择随机学生的方法,但从学校午餐线上选择学生,不包括已经不在校园午餐的学生!

    Choosing a Random Sample 
    ::选择随机抽样

    Evan is conducting a study of the types of seashells on the 2-mile stretch of beach near his home.
    ::埃文正在研究 在他家附近的2英里长的海滩上 贝壳的种类

    How might he choose a random sample to represent the population of seashells on the beach?  Would simply walking around without aim and picking up seashells be effective?  Why or why not?
    ::他如何选择随机样本来代表海滩上的贝壳群? 光是徒步走,不瞄准就捡贝壳会有效吗? 为什么或为什么不行?

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    Just walking around without direction will not actually result in a random sample, since Evan may have conscious or unconscious preferences that would affect where he would choose to walk.  Also, ‘just picking up’ seashells would further influence the sample with his own preferences since he would be picking up the shells he chooses.
    ::光是走来走去而没有方向实际上不会产生随机的样本,因为埃文可能有意识或无意识的偏好会影响到他选择走路的地点。 此外,“只是捡起”贝壳会进一步影响样本,因为他会自己选择的贝壳。

    If Evan wanted to randomize the sample, he could do so with a set of dice.  He could roll the dice before leaving, and use the number to set a distance to travel before stopping.  He could pick up any seashells within reach at the stop, and roll the dice again.  If he turned right on even rolls, and left on odd rolls, the results would be much more random.
    ::如果埃文想随机排列样本,他可以使用一套骰子。他可以在离开前滚骰子,用数字来设定停留前的旅行距离。他可以在车站接住任何可以到达的贝壳,然后再次滚骰子。如果他右转,甚至滚动,然后以奇数滚动,结果会更加随机。

    Earlier  Problem Revisited
    ::重审先前的问题

    If you reached in and then pulled out a handful of nothing but marbles of various colors off the top, you’d quite reasonably state that this must be a bag of marbles.
    ::如果你伸手进去,然后从顶部取出一小撮除了各种颜色的弹珠外的弹珠,你就可以相当合理地说,这一定是一袋弹珠。

    Is it possible that you might be wrong?  How?  What could you have done to improve your guess?
    ::有没有可能你错了?怎么搞的?你能做些什么来改进你的猜测?

    It is entirely possible that you are correct, but it is also pretty clear that the results would be suspect at best.  By only grabbing a single handful of items off the top of the bag, you are limiting your results to items that worked their way to the top.  There may well have been other items at the bottom of the bag that you did not get a sample of by just grabbing off the top.  You could certainly improve the reliability of the sample by first shaking the bag well so that your sample is appropriately randomized.
    ::完全有可能你是对的, 但同样非常清楚的是, 最终结果最有可能被怀疑。 通过从袋子顶部抓取一小撮物品, 你只能将结果限制在工作到顶部的物品上。 在袋子底部可能有其他物品, 你可能没有通过从上面抓取来样本。 你当然可以先把样品摇动一下, 从而适当随机化, 从而提高样品的可靠性 。

    This is an example of convenience sampling , which is selecting a sample more because it is easily obtained than because it is random or representative.
    ::这是方便取样的一个实例,它选择样本的原因更多是因为它容易获得,而不是因为它是随机的或具有代表性的。

    Examples
    ::实例

    For each question below, first decide if the example describes a random sample, second describe why you believe it is/isn’t random.
    ::对于下面的每一个问题,先决定示例是否描述随机抽样,然后描述为什么你认为这是/不是随机抽样。

    Example 1
    ::例1

    Several apples are selected from each bin of different types at the market. 
    ::从市场上的每个不同类型垃圾桶中选取几个苹果。

    This is probably not a random sample.  The question does not specify how the apples are chosen from each bin.  You would have an unconscious preference for shinier apples if you just selected one from a bin.
    ::这很可能不是随机的样本。 问题并不指定苹果是如何从每个垃圾箱中选择的。 如果您只是从垃圾箱中选择一个苹果, 您将会在无意识中偏爱光苹果 。

    Example 2
    ::例2

    Each student is assigned a number and a die is rolled. Starting with that number each 4th student is chosen until the quota is met. 
    ::每个学生被分配到一个数字,死亡被滚动。从这个数字开始,每个第四名学生被选中,直到配额达到为止。

    This is a valid random sampling, specifically a systematic random sample .  Each student has the same opportunity to be chosen as any other.
    ::这是一个有效的随机抽样,具体而言,是一个系统的随机抽样,每个学生都有与任何其他学生相同的被选中机会。

    Example 3
    ::例3

    To build a sample of students in his state, Brian first made a list of school districts and assigned each a number. He then randomly chose 4 districts and assigned each school in those districts to a number and randomly chose 3 schools from each district. Once he has the schools, he assigned numbers to each students in each school, and used a random number generator to pick 15 students from each school. 
    ::布赖恩首先对各州的学生进行抽样调查,首先列出了各学区名单,并指定了每个学区的数字。然后,他随机选择了四个学区,将这些地区的每所学校分配到一个学区,并从每个学区随机选择三所学校。 一旦他拥有学校,他为每所学校的每个学生分配了数字,并使用随机数字生成器从每所学校挑选15名学生。

    This is a valid random sampling method, specifically a multi-stage cluster sample .  Each student in the state has the same opportunity to be chosen for the sample.
    ::这是一种有效的随机抽样方法,具体来说是一种多阶段的集群抽样,该州每个学生都有相同的机会被选用。

    Example 4
    ::例4

    Katrina closed her eyes and reached into a beverage stand, randomly selecting a soda. 
    ::卡特里娜闭上眼睛 走到酒柜里 随机挑选苏打水

    This is not a random sample.  Katrina would be more likely to pick one within reach than to select from the top or bottom, and would be unlikely to reach behind the front sodas to select one further back.  Some sodas have a greater chance of being chosen than others.
    ::这不是随机的样本。 卡特里娜比从顶部或底部选择更容易挑选到一个可以达到的样本,而且不太可能在前苏打水后面再选择一个。 有些苏打水比其他苏打水更有可能被选中。

    Review 
    ::回顾

    State whether each example describes a random sample:
    ::说明每个示例是否说明随机抽样:

    1. Consumer Reports is conducting a poll to evaluate consumer opinions on the latest console gaming platform.  The publisher includes a postcard in an issue of Consumer Reports , and asks readers to fill out the form and return it.
      ::消费者报告正在进行一次民意测验,以评价消费者对最新的控制台赌博平台的意见。 出版商在《消费者报告》一期中包括一张明信片,并要求读者填写表格并退还。
    2. Kelly closes her eyes, opens the dictionary and randomly points to a word on the page.  She repeats the process 10 times.
      ::Kelly闭上眼睛,打开字典,随机指向页面上的一个字。她重复了10次这个过程。
    3. Shake a bag of marbles well, reach in and select a marble with eyes closed.
      ::摇一袋大理石 钻井,伸手 并选择大理石 闭上眼睛。
    4. Number the students in your class 1-32, and roll six standard dice to choose a random student, discarding any number greater than 32.
      ::学生人数在你的班级 1-32 和滚动六标准骰子 选择随机学生, 丢弃任何超过32个以上的学生。
    5. Walk along a pebbled path and randomly pick up a stone.
      ::沿着一条支离破碎的道路走 随意捡起一块石头
    6. Roll standard 4 dice and choose a name starting with the letter associated with that number if the alphabet is numbered 1-26.
      ::滚动标准 4 骰子, 如果字母编号为 1-26 , 请选择一个以该编号相关字母开头的名称 。
    7. Walk around a park and randomly pick up fallen leaves to see what kind of trees are in the park.
      ::漫步在公园周围 随机拾起落叶 看公园里有什么树
    8. Search for “dog” on Google to get a random sample of popular dogs.
      ::寻找谷歌上的“狗”,
    9. Ask shoppers in a hardware store if they know how to replace a light switch to learn the percentage of people that know how.
      ::询问五金店的店主,他们是否知道如何更换灯开关,以了解知道如何使用灯开关的人的百分比。
    10. Spin a spinner numbered 1-25 to decide how much to charge for a glass of lemonade.
      ::旋转一个编号为1-25的旋转器 来决定一杯柠檬水要付多少钱

    Review (Answers)
    ::回顾(答复)

    Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
    ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。