Population vs Sample

Summary

This video script introduces the fundamental concepts of population and sample in statistical analysis. It explains that a population encompasses all items of interest, while a sample is a subset used due to practical constraints like time and cost. The script highlights the importance of random and representative sampling to ensure the sample accurately reflects the population. It uses the example of surveying New York University students to illustrate these points and emphasizes that while sampling can be challenging, statistical tests are designed to work with such data, making minor sampling errors less critical.

Takeaways

• 📚 The first step in statistical analysis is to determine if the data is a population (all items of interest) or a sample (subset of the population).
• 🔢 Parameters are the numbers obtained from a population, while statistics are derived from samples.
• 🏛️ The population for a study can be extensive and include various groups such as on-campus, distance education, and part-time students.
• 🕵️‍♂️ A sample should ideally be easy to contact, less time-consuming, and less costly to gather compared to a whole population.
• 📈 Random sampling ensures that each member of the population has an equal chance of being selected for the sample.
• 🍽️ The example of interviewing students in the university canteen is highlighted as a non-random and non-representative sampling method.
• 🎯 Representativeness in a sample means it accurately reflects the characteristics of the entire population.
• 📊 A truly representative sample for NYU students would require random selection from a comprehensive student database.
• 🔎 Recognizing representative samples becomes easier with experience, and minor sampling errors are often manageable with statistical tests.
• 🎓 The course aims to make understanding populations and samples, as well as the nuances of sampling, straightforward for the learners.

Q & A

What is the difference between a population and a sample in statistical analysis?

A population is the complete collection of all items of interest in a study, denoted by uppercase N, while a sample is a subset of the population, denoted by lowercase n.

Why are parameters and statistics important in statistics?

Parameters are the numbers obtained from a population and represent the true values of the population. Statistics are the numbers obtained from a sample and are used to estimate the parameters.

What is the population in the context of a survey about job prospects at New York University?

The population includes all students studying at New York University, including those on campus, at home, on exchange, abroad, in distance education, part-time students, and even those who are enrolled but still at high school.

Why is it challenging to define and observe a population in real life?

Populations are hard to define and observe because they can include a vast and diverse group of individuals that may be spread across different locations and situations.

What are the advantages of using a sample over analyzing an entire population?

Sampling is less time-consuming and less costly compared to analyzing an entire population. It allows for more manageable and feasible data collection within limited resources.

Why might interviewing 50 students in the NYU canteen not provide a true representation of the whole university?

The sample is neither random nor representative because the students were not chosen by chance and only represent those who were present at the canteen during lunchtime.

What is a random sample, and why is it important?

A random sample is one where each member is chosen from the population by chance, ensuring each member has an equal likelihood of being selected. This is important for ensuring that the sample is unbiased and can accurately represent the population.

What is a representative sample, and how does it reflect the population?

A representative sample is a subset of the population that accurately reflects the characteristics of the entire population. It should include a diverse mix of individuals that mirrors the population's demographics and other relevant attributes.

How can one ensure a sample is both random and representative?

Ensuring a sample is both random and representative can be achieved by using a random selection method, such as accessing a complete database and selecting individuals at random, which helps in capturing the diversity of the population.

What are the two big advantages of using samples in statistical analysis despite the challenges?

The two advantages are that with experience, it becomes easier to recognize a representative sample, and statistical tests are designed to work with incomplete data, making small sampling errors less critical.

What is the role of statistical tests when working with samples?

Statistical tests help in analyzing and interpreting data from samples to make inferences about the population. They account for the variability and incompleteness of sample data, allowing for robust conclusions despite potential sampling errors.

Outlines

00:00

📚 Introduction to Populations and Samples

This paragraph introduces fundamental concepts in statistics, emphasizing the distinction between a population and a sample. A population, denoted by an uppercase 'N', encompasses all items of interest in a study, while a sample, denoted by a lowercase 'n', is a subset of the population. Parameters are the characteristics obtained from a population, and statistics are derived from samples. The example of surveying job prospects at New York University illustrates the complexity of defining a population, which includes not just on-campus students but also those at home, on exchange, abroad, in distance education, part-time, and even those who are still in high school but enrolled. The paragraph highlights the practical challenges of accessing entire populations, leading to the preference for more manageable samples.

Keywords

💡Population

A population in the context of the video refers to the complete set of items or individuals that are the subject of a study. It is denoted by an uppercase 'N'. The video emphasizes that a population is not just the students on campus but includes all students associated with an institution, such as those studying remotely, on exchange, or even those enrolled but still in high school. This broad definition illustrates the complexity of defining a population in real-life scenarios.

💡Sample

A sample, indicated by a lowercase 'n', is a subset of a population that is used to represent and make inferences about the whole. The video uses the example of interviewing students in the New York University canteen to illustrate a sample. It highlights that while samples are easier to obtain, they must be carefully selected to be representative and random to ensure the validity of statistical analysis.

💡Parameters

Parameters are the numerical values that describe a population. They are derived from the entire population and are constants. The video mentions that parameters are obtained when using a population, which is why they are crucial for understanding the overall characteristics of the population.

💡Statistics

Statistics, in contrast to parameters, are numerical values that describe a sample. They are estimates of the parameters and are used to make inferences about the population. The video explains that statistics are derived from samples and are denoted with a lowercase 'n', emphasizing the importance of sample selection in statistical analysis.

💡Random Sample

A random sample is one where every member of the population has an equal chance of being selected. The video points out that the sample taken in the university canteen was not random because it was based on convenience rather than chance, which can lead to biased results.

💡Representativeness

Representativeness refers to the degree to which a sample accurately reflects the characteristics of the entire population. The video discusses that the sample of students in the canteen was not representative of the entire NYU student body, as it only included those present on campus during lunchtime, thus limiting the generalizability of the findings.

💡Statistical Analysis

Statistical analysis is the process of analyzing sample data to make inferences about a population. The video introduces the concept by explaining the difference between populations and samples and the importance of using samples for this analysis due to the practical limitations of studying entire populations.

💡Inference

Inference is the process of drawing conclusions about a population based on the analysis of a sample. The video suggests that even though samples may not perfectly represent the population, statistical tests are designed to work with such data, allowing for reasonable inferences to be made.

💡Resources

Resources, as mentioned in the video, refer to the time, money, and effort required to conduct a study. The video argues that sampling is often preferred over analyzing an entire population because it is less resource-intensive, making it a more practical approach for research.

💡Database

A database in the context of the video is a systematic collection of information, such as a list of all students, which can be used to draw a random and representative sample. The video suggests that accessing a student database would be an ideal way to ensure a random sample but acknowledges that such access often requires institutional support.

💡Survey

A survey is a research method used to gather data from a population or sample through interviews or questionnaires. The video uses the example of a survey about job prospects to illustrate the importance of sample selection and how it can impact the validity of survey results.

Highlights

Introduction to the concept of population and sample in statistical analysis.

Definition of population as the complete set of items of interest.

Parameters are the numbers obtained from a population.

Definition of a sample as a subset of the population.

Statistics are the numbers obtained from a sample.

Explanation of why the field is called statistics.

Example of defining the population for a survey on NYU students.

Challenges in defining and observing populations in real life.

Advantages of samples over populations in terms of time and cost.

The process of drawing a sample from the NYU campus canteen.

Discussion on the representativeness of the sample from the canteen.

Importance of a random sample where each member is chosen by chance.

Critique of the canteen sample for not being random or representative.

Definition of a representative sample that reflects the entire population.

Suggestion to use the student database for a random sample.

Reassurance that small sampling errors are not always problematic.

Encouragement for learners to master the concepts of samples and populations.

Transcripts

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 we’ve 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

we’ve 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!