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Alright. Before crunching any numbers and making decisions,
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we should introduce some key definitions.
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The first step of every statistical analysis you will perform is to determine whether the data you are
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dealing with is a population, or a sample.
A population is the collection of all items of interest
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to our study and is usually denoted with an uppercase N. The numbers we've obtained when using a population
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The numbers we've obtained when using a population are called parameters.
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A sample is a subset of the population and is denoted with a lowercase n, and the numbers we've obtained
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when working with a sample are called: statistics.
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Now you know why the field we are studying is called statistics.
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Let's say we want to make a survey of the job prospects of the students studying in the New York University.
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What is the population?
You can simply walk into NYU and find every student, right?
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Well probably that would not be the population of NYU students.
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The population of interest includes not only the students on campus, but also the ones at home, on exchange,
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abroad,
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distance education students, part time students, even the ones who are enrolled but are still at high school.
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Though exhaustive, even this list misses someone. Point taken.
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Populations are hard to define and hard to observe in real-life.
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A sample, however, is much easier to contact.
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It is less time consuming and less costly.
Time and resources are the main reasons we prefer drawing samples
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compared to analyzing an entire population.
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So, let's draw a sample then.
As we first wanted to do, we can just go to the NYU campus.
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Next let's enter the canteen because we know it will be full of people.
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We can then interview 50 of them.
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Cool.
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This is a sample.
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Good job! But what are the chances of these 50 people provide us answers that are a true representation
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of the whole university?
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Pretty slim, right?
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The sample is neither random, nor representative.
A random sample is collected when each member of the
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sample is chosen from the population strictly by chance.
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We must ensure each member is equally likely to be chosen.
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Let's go back to our example.
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We walked into the university canteen and violated both conditions.
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People were not chosen by chance.
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They were a group of NYU students who were there for lunch.
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Most members did not even get the chance to be chosen as they were not on campus.
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Thus we conclude the sample was not random.
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What about the representativeness of the sample?
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A representative sample is a subset of the population that accurately reflects the members of the entire population.
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A representative sample is a subset of the population that accurately reflects the members of the entire population.
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Our sample was not random but was it representative?
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Well, it represented a group of people but definitely not all students in the university to be exact.
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It represented the people who have lunch at the university canteen.
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Had our survey been about job prospects of NYU students who eat in the university canteen we would have done well.
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Had our survey been about job prospects of NYU students who eat in the university canteen we would have done well.
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By now, you must be wondering how to draw a sample that is both random and representative.
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Well, the safest way would be to get access to the student database and contact individuals in a random manner.
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Well, the safest way would be to get access to the student database and contact individuals in a random manner.
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However, such surveys are almost impossible to conduct without assistance from the university.
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We said populations are hard to define and observe.
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Then we saw that sampling is difficult.
But samples have two big advantages.
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First, after you have experience, it is not hard to recognize, if a sample is representative.
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And second statistical tests are designed to work with incomplete data.
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Thus, making a small mistake while sampling is not always a problem.
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Don't worry.
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After completing this course samples and populations will be a piece of cake for you!
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Thanks for watching!
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