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  • All right!

  • Before crunching any numbers and making decisions, we should introduce some key definitions.

  • The first step of every statistical analysis you will perform is to determine whether the

  • data you are dealing with is a population or a sample.

  • A population is the collection of all items of interest to our study and is usually denoted

  • with an uppercase N. The numbers weve obtained when using a population are called parameters.

  • A sample is a subset of the population and is denoted with a lowercase n, and the numbers

  • weve obtained when working with a sample are called statistics.

  • Now you know why the field we are studying is called statistics ?

  • Let’s say we want to make a survey of the job prospects of the students studying in

  • the New York University.

  • What is the population?

  • You can simply walk into New York University and find every student, right?

  • Well, probably, that would not be the population of NYU students.

  • The population of interest includes not only the students on campus but also the ones at

  • home, on exchange, abroad, distance education students, part-time students, even the ones

  • who enrolled but are still at high school.

  • Though exhaustive, even this list misses someone.

  • Point taken.

  • Populations are hard to define and hard to observe in real life.

  • A sample, however, is much easier to contact.

  • It is less time consuming and less costly.

  • Time and resources are the main reasons we prefer drawing samples, compared to analyzing

  • an entire population.

  • So, let’s draw a sample then.

  • As we first wanted to do, we can just go to the NYU campus.

  • Next, let’s enter the canteen, because we know it will be full of people.

  • We can then interview 50 of them.

  • Cool!

  • This is a sample.

  • Good job!

  • But what are the chances these 50 people provide us answers that are a true representation

  • of the whole university?

  • Pretty slim, right.

  • The sample is neither random nor representative.

  • A random sample is collected when each member of the sample is chosen from the population

  • strictly by chance.

  • We must ensure each member is equally likely to be chosen.

  • Let’s go back to our example.

  • We walked into the university canteen and violated both conditions.

  • People were not chosen by chance; they were a group of NYU students who were there for

  • lunch.

  • Most members did not even get the chance to be chosen, as they were not on campus.

  • Thus, we conclude the sample was not random.

  • What about representativeness of the sample?

  • A representative sample is a subset of the population that accurately reflects the members

  • of the entire population.

  • Our sample was not random, but was it representative?

  • Well, it represented a group of people, but definitely not all students in the university.

  • To be exact, it represented the people who have lunch at the university canteen.

  • Had our survey been about job prospects of NYU students who eat in the university canteen,

  • we would have done well.

  • By now, you must be wondering how to draw a sample that is both random and representative.

  • Well, the safest way would be to get access to the student database and contact individuals

  • in a random manner.

  • However, such surveys are almost impossible to conduct without assistance from the university!

  • We said populations are hard to define and observe.

  • Then, we saw that sampling is difficult.

  • But samples have two big advantages.

  • First, after you have experience, it is not that hard to recognize if a sample is representative.

  • And, second, statistical tests are designed to work with incomplete data; thus, making

  • a small mistake while sampling is not always a problem.

  • Don’t worry; after completing this course, samples and populations will be a piece of

  • cake for you!

  • Keep up the good work and thanks for watching!

All right!

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B1 中級

人口とサンプル (Population vs sample)

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    林宜悉 に公開 2021 年 01 月 14 日
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