COURSE 4: THE POWER OF STATISTICS

Module 3: Sampling

GOOGLE ADVANCED DATA ANALYTICS PROFESSIONAL CERTIFICATE

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TABLE OF CONTENT

INTRODUCTION – Sampling

In this comprehensive overview, participants will delve into the essential practice of using smaller samples to draw meaningful conclusions about large datasets, a crucial aspect of the data analysis process. The module begins by elucidating the various methods employed by data professionals to collect and analyze sample data effectively, emphasizing the importance of avoiding sampling bias to ensure the integrity of the analysis. Participants will gain insights into the intricacies of sampling distributions, understanding their role in making accurate estimates and enhancing the reliability of conclusions drawn from limited data samples.

Furthermore, the module not only imparts theoretical knowledge but also emphasizes practical applications, ensuring that participants acquire hands-on skills in navigating and mitigating challenges associated with sample-based data analysis. By the end of this module, learners will be equipped with a nuanced understanding of sampling methodologies, empowering them to make informed decisions and draw reliable conclusions when working with large datasets in diverse data analysis scenarios. This comprehensive exploration underscores the module’s commitment to bridging theoretical concepts with practical proficiency, preparing participants for the dynamic challenges of the data analysis field.

Learning Objectives

  • Use Python for sampling
  • Explain the concept of standard error
  • Define the central limit theorem
  • Explain the concept of sampling distribution
  • Explain the concept of sampling bias
  • Describe the benefits and drawbacks of non-probability sampling methods such as convenience, voluntary response, snowball, and purposive
  • Describe the benefits and drawbacks of probability sampling methods such as simple random, stratified, cluster, and systematic
  • Explain the difference between probability sampling and non-probability sampling
  • Describe the main stages of the sampling process
  • Explain the concept of a representative sample

PRACTICE QUIZ: TEST YOUR KNOWLEDGE: INTRODUCTION TO SAMPLING

1. A data professional is conducting an election poll. As a first step in the sampling process, they identify the target population. What is the second step in the sampling process?

  • Determine the sample size
  • Collect the sample data
  • Select the sampling frame (CORRECT)
  • Choose the sampling method

Correct: The second step in the sampling process is to select the sampling frame.

2. Fill in the blank: In a _____ sample, every member of a population is selected randomly and has an equal chance of being chosen.

  • snowball
  • voluntary response
  • cluster
  • simple random (CORRECT)

Correct: In a simple random sample, every member of a population is selected randomly and has an equal chance of being chosen.

3. Non-probability sampling includes which of the following sampling methods? Select all that apply.

  • Stratified random sampling
  • Systematic random sampling
  • Convenience sampling (CORRECT)
  • Purposive sampling (CORRECT)

Correct: Non-probability sampling methods include convenience and purposive sampling. In convenience sampling, researchers choose members of a population that are easy to contact or reach. In purposive sampling, researchers select participants based on the purpose of their study.

PRACTICE QUIZ: TEST YOUR KNOWLEDGE: SAMPLING DISTRIBUTIONS

1. A data professional is analyzing data about a population of aspen trees. They take repeated random samples of 10 trees from the population and compute the mean height for each sample. Which of the following statements best describes the sampling distribution of the mean?

  • The probability distribution of all the sample means (CORRECT)
  • The average value of all the sample means.
  • The sampling distribution of the mean is the sum of all the sample means.
  • The sampling distribution of the mean is the maximum value of all the sample means.

Correct: The sampling distribution of the mean is the probability distribution of all the sample means. A probability distribution represents the possible outcomes of a random variable.

2. The central limit theorem implies which of the following statements? Select all that apply.

  • The sampling distribution of the mean approaches a normal distribution as the sample size decreases.
  • If you take a large enough sample of the population, the sample mean will be roughly equal to the population mean.
  • The sampling distribution of the mean approaches a normal distribution as the sample size increases. (CORRECT)
  • If you take a small enough sample of the population, the sample mean will be roughly equal to the population mean. (CORRECT)

Correct: The central limit theorem states that the sampling distribution of the mean approaches a normal distribution as the sample size increases. If a large enough sample of the population is taken, the sample mean will be roughly equal to the population mean.

3. What is a standard error? 

  • An estimate of a population parameter
  • A list of all the items in the target population.
  • The probability distribution of a sample statistic
  • The standard deviation of a sample statistic (CORRECT)

Correct: A standard error is the standard deviation of a sample statistic.

PRACTICE QUIZ: TEST YOUR KNOWLEDGE: WORK WITH SAMPLING DISTRIBUTIONS IN PYTHON

1. Which Python function can be used to simulate random sampling?

  • pandas.DataFrame.hist()
  • pandas.DataFrame.sample() (CORRECT)
  • pandas.DataFrame.describe()
  • pandas.DataFrame.mean()

Correct: The sample() function can be used to simulate random sampling.

2. Which of the following statements describe a random seed when specifying random_state in pandas.DataFrame.sample()? Select all that apply.

  • Only a negative number may be chosen to fix the random seed.
  • Any non-negative integer can be chosen to fix the random seed. (CORRECT)
  • The same random seed may be used over again to generate the same set of numbers. (CORRECT)
  • A random seed is a starting point for generating random numbers. (CORRECT)

Correct: A random seed is a starting point for generating random numbers. Any number can be chosen to fix the random seed, and the same random seed can be used over again to generate the same set of numbers.

MODULE 3 CHALLENGE

1. Which of the following scenarios would benefit from replacing their current sample with a representative sample? Select all that apply.

  • A researcher conducts a survey on the experience of high school students. For their sample, they choose students from a variety of academic, social, and cultural backgrounds.
  • A researcher conducts a survey on computer skills among university students. For their sample, they choose students who major in computer science. (CORRECT)
  • A researcher conducts a poll for an upcoming national election. For their sample, they choose voters from a single city. (CORRECT)
  • A researcher conducts an employee satisfaction survey for a company. For their sample, they choose employees who have worked at the company for at least 25 years. (CORRECT)

2. Fill in the blank: In statistics, _____ refers to the number of individuals or items chosen for a study or experiment.

  • target population
  • sampling frame
  • sample size (CORRECT)
  • sampling method

3. Which of the following statements accurately describe non-probability sampling? Select all that apply.

  • Non-probability sampling typically uses random selection.
  • Non-probability sampling is often based on convenience. (CORRECT)
  • Non-probability sampling is often based on the personal preferences of the researcher. (CORRECT)
  • Non-probability sampling can result in biased samples. (CORRECT)

4. Which sampling method involves dividing a population into groups and randomly selecting some members from each group for the sample?

  • Simple random sampling
  • Stratified random sampling (CORRECT)
  • Systematic random sampling
  • Cluster random sampling

5. Which sampling method involves choosing members of a population who are easy to contact or reach?

  • Voluntary response sampling
  • Convenience sampling (CORRECT)
  • Purposive sampling
  • Snowball sampling

6. Fill in the blank: Standard error measures the _____ of a sampling distribution.

  • standard deviation (CORRECT)
  • mode
  • median
  • mean

7. What concept states that the sampling distribution of the mean approaches a normal distribution as the sample size increases?

  • Sampling frame
  • Central limit theorem (CORRECT)
  • Bayes’ theorem
  • Standard error

8. A data professional is working with data about annual household income. They want to use Python to simulate taking a random sample of income values from the dataset. They write the following code: sample(n=100, replace=True, random_state=230). What is the sample size of the random sample?

  • 100 (CORRECT)
  • 230
  • 23
  • 10

9. Fill in the blank: A _____ sample accurately reflects the characteristics of a population.

  • Representative (CORRECT)
  • nonrepresentative
  • biased
  • very small

10. What stage of the sampling process refers to creating a list of all the items in the target population?

  • Determine the sample size
  • Collect the sample data
  • Select the sampling frame (CORRECT)
  • Choose the sampling method

11. Which of the following statements accurately describe a sampling distribution? Select all that apply.

  • A sampling distribution is a probability distribution of a population parameter.
  • A sampling distribution can be visualized with a histogram. (CORRECT)
  • A sampling distribution represents the probability distribution of a statistic under random sampling. (CORRECT)
  • The distribution of a sample mean and the distribution of a sample proportion are examples of sampling distributions. (CORRECT)

12. A data professional is conducting an employee satisfaction survey. First, they list all the employees alphabetically by first name. Then, they randomly choose a starting point on the list and pick every third name to be in the sample. What sampling method are they using?

  • Systematic random sampling (CORRECT)
  • Cluster random sampling
  • Simple random sampling
  • Stratified random sampling

13. Which of the following scenarios best describe snowball sampling?

  • Researchers select members of a population who are easy to contact or reach.
  • Researchers select members of a population based on random sampling.
  • Researchers recruit initial participants to be in a study, then ask them to recruit other people to participate in the study. (CORRECT)
  • Researchers select participants based on the purpose of their study.

14. Which of the following statements accurately describe the standard error of the mean? Select all that apply.

  • The higher the standard error, the more precise the sample mean is.
  • The standard error of the mean measures variability among the sample means obtained in repeated sampling. (CORRECT)
  • A larger standard error indicates that, in repeated sampling, the sample means are more spread out. (CORRECT)
  • The lower the standard error, the more precise the sample mean is. (CORRECT)

15. Fill in the blank: The central limit theorem states that the _____ of the mean approaches a normal distribution as the sample size increases.

  • sampling frame
  • sampling variability
  • sampling distribution (CORRECT)
  • sampling bias

16. A data professional is working with data about annual household income. They want to use Python to simulate taking a random sample of income values from the dataset. They write the following code: sample(n=100, replace=True, random_state=230). What does the argument replace=True refer to?

  • Sampling without replacement
  • Sampling with replacement (CORRECT)
  • Replacing decimal values with whole numbers
  • Replacing whole numbers with decimal values

17. Which of the following statements accurately describe a representative sample? Select all that apply.

  • A representative sample represents some groups in the population but not others.
  • A representative sample suffers from sampling bias.
  • A representative sample reflects the characteristics of the overall population. (CORRECT) A representative sample helps data professionals make reliable inferences based on sample data.

18. Which of the following statements accurately describes the relationship between probability sampling and non-probability sampling?

  • Probability sampling is more biased than non-probability sampling.
  • Probability sampling is typically less expensive than non-probability sampling.
  • Probability sampling gives data professionals a better chance of generating a representative sample than non-probability sampling. (CORRECT)
  • Probability sampling is typically more convenient than non-probability sampling.

19. What is a key difference between stratified random sampling and cluster random sampling?

  • Stratified sampling is a probability sampling method; cluster sampling is a non-probability sampling method.
  • In stratified sampling, you randomly choose some members from each group to be in the sample; in cluster sampling, you choose all members from each group to be in the sample. (CORRECT)
  • In stratified sampling, you randomly choose all members from each group to be in the sample; in cluster sampling, you choose some members from each group to be in the sample.
  • Stratified sampling is a non-probability sampling method; cluster sampling is a probability sampling method.

20. A data professional is working with data about annual household income. They want to use Python to simulate taking a random sample of income values from the dataset. They write the following code: sample(n=100, replace=True, random_state=230). What is the random seed?

  • 100
  • 230 (CORRECT)
  • 23
  • 10

21. The instructor of a fitness class asks their regular students to take an online survey about the quality of the class. What sampling method does this scenario refer to?

  • Purposive sampling
  • Convenience sampling
  • Snowball sampling
  • Voluntary response sampling (CORRECT)

22. A representative sample does not reflect the characteristics of a population.

  • True
  • False (CORRECT)

Correct: A representative sample accurately reflects the characteristics of a population. If a sample does not accurately reflect the characteristics of a population, then the inferences will likely be unreliable and predictions inaccurate. This can lead to negative outcomes for stakeholders and organizations.

23. When working with sample data, what is the first step in the sampling process?

  • Identify the target population (CORRECT)
  • Select the sampling frame
  • Choose the sampling method
  • Collect the sample data

Correct: The first step in the sampling process is to identify the target population. The sampling process helps determine whether a sample is representative of the population and if it is unbiased.

24. Fill in the blank: Probability sampling uses ____ selection to generate a sample.

  • Random (CORRECT)
  • Non-random
  • Biased
  • Unrepresentative

Correct: Probability sampling uses random selection to generate a sample. There are four methods: simple, stratified, cluster, and systematic. All are based on random selection, which is the preferred method of sampling for most data professionals

25. Sampling bias occurs when a sample is not representative of the population as a whole.

  • True (CORRECT)
  • False

Correct: Sampling bias occurs when a sample is not representative of the population as a whole. Models based on representative samples are much more likely to lead to fair and unbiased decisions.

26. What term describes a probability distribution of a sample statistic?

  • Point estimate
  • Sampling variability
  • Sampling distribution (CORRECT)
  • Sampling bias

Correct: Sampling distribution describes a probability distribution of a sample statistic. Probability distribution represents the possible outcomes of a random variable; sampling distribution represents the possible outcomes for a sample statistic.

27. Fill in the blank: The central limit theorem states that the sampling distribution of the mean approaches a _____ distribution as the sample size increases

  • Binomial
  • Normal (CORRECT)
  • Bernoulli
  • Poisson

Correct: The central limit theorem states that the sampling distribution of the mean approaches a normal distribution as the sample size increases. In other words, as the sample size increases, the sampling distribution assumes the shape of a bell curve. If a large enough sample of the population is used, the sample mean will be roughly equal to the population mean.

CONCLUSION – Sampling

This module provides participants with a robust foundation in the critical practice of using smaller samples to derive meaningful insights from extensive datasets. By delving into various methods of sample collection and analysis, as well as addressing potential pitfalls like sampling bias, participants are well-equipped to navigate the complexities of data analysis.

The emphasis on practical applications ensures that learners not only grasp theoretical concepts but also develop hands-on skills essential for accurate decision-making in real-world scenarios. This comprehensive overview serves as a valuable resource, empowering participants to confidently employ sampling methodologies, make informed conclusions, and contribute effectively to the dynamic landscape of data analysis.

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