INTRODUCTION – Sampling
Participants will learn the exact model where small samples are used to reach intelligent conclusions about larger data-gathering-a fundamental effective data analysis model. Following an exposition on methods used by data professionals for collecting and analyzing sample data, the module focuses on avoiding any instance of sampling bias to maintain integrity and accuracy of the analytical results. Participants will observe how sampling distributions work their magic in getting precise estimates and improving reliability in outcomes derived from scanty data.
The diversity encountered in this module represents both theoretical concepts surrounding sampling and the hands-on practice where participants become learned in addressing challenges presented by analyses based on samples. By the end of this module, participants will hold a general comprehension of sampling methods that will enable them to make sound use of that knowledge while using proper judgment and drawing insights when analyzing various contexts of large datasets. The module connects theory and application to support participants in traversing the competitive and fast-changing career landscape that characterizes data analysis.
Learning Outcomes
- Sampling tasks using Python.
Understand and explain in detail what standard error refers to. - Define and apply the central limit theorem correctly.
- Analyze the purpose and importance of sampling distributions.
- Diagnose and address sampling bias.
- Experience the pros and cons of non-probability sampling techniques such as convenience, voluntary response, snowball, and purposive sampling.
- Benefits and limitations of probability sampling methods including simple random, stratified, cluster, and systematic sampling.
- Differentiate probability sampling techniques from non-probability ones.
- Outline the steps involved in the sampling process.
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: Choosing the sampling frame is the second stage of the sampling procedure. An exhaustive catalogue or representation of all elements in a population is a sampling frame from which the sample is drawn. This process is very crucial, for it determines the accuracy and reliability of a sample according to how well the sampling frame reflects the target population.
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: A simple random sample is one in which each individual in the population is randomly drawn and each 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: Because of non-probability sampling, there exist convenient sampling methods, such as purposive sampling. Convenience sampling involves selecting individuals in the population who are relatively easy to access or contact. Whereas purposive sampling involves selecting study participants according to purpose or objective for the 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 means is the probability distribution in which all possible sample means are shown. A probability distribution is a representation of possible outcomes for 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: As sample sizes increase, the central limit theorem states that the sampling distribution of the mean will approximate normality. The sample mean will be strongly concentrated around the population mean if the sample is large enough and drawn from the population.
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: More formally, a standard error is defined as the standard deviation of a sample statistic, for example, of the sample mean. It quantifies the spread or the variation of the sample statistic from the true population parameter.
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 is used for simulating random sampling, selecting a given number of elements at random from a population or dataset. Sampling can be done with or without replacement, depending on the settings.
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 simply an initial value employed to seed the random number generation process. Any value can act as a seed, and reapplying the same random seed will always yield the same series of random numbers. Thus: reproducibility in experiments or simulations.
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 is one that accurately reflects the characteristics of the hypothesized population from which it is taken. If a sample is not representative, any conclusions or predictions drawn from it are likely to be highly flawed. This may have an unfavourable effect on the decision-making processes and consequences, either directly or indirectly, to those involved or those within 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 stage in the sampling process is the definition of the target population. The process of sampling represents that the sample accurately represents the population and is not biased so that one can make reliable and valid inferences.
24. Fill in the blank: Probability sampling uses ____ selection to generate a sample.
- Random (CORRECT)
- Non-random
- Biased
- Unrepresentative
Correct: Assembling a sample through random selection, probability sampling comprises four major types: simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Since each type involves random selection, it is particularly favored by most professional data handlers because it assures an unbiased and representative sample.
25. Sampling bias occurs when a sample is not representative of the population as a whole.
- True (CORRECT)
- False
Correct: When the sample does not accurately portray the population, that is, an inappropriate sample, it may lead to distorted conclusions. Models built on representative sample data are more likely to produce fair and unbiased decisions because such data tend to represent true characteristics of the population.
26. What term describes a probability distribution of a sample statistic?
- Point estimate
- Sampling variability
- Sampling distribution (CORRECT)
- Sampling bias
Correct: Thus, a sampling distribution is defined as a probability distribution for a sample statistic (say the sample mean). A probability distribution indicates the outcomes of a random variable, while a sampling distribution indicates the outcomes of a sample statistic obtained from many samples extracted from the population.
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: It is known that as the amount of a sample increases, the mean of the sampling distribution approaches that of a normal shaped curve, sometimes called a bell curve, by the central limit theorem. A sample of this size will tend to yield almost the same sample means for different sample methods for the population mean, irrespective of how the population is distributed.
CONCLUSION – Sampling
This module provides a solid theoretical base for cracking sample size smaller enough to reveal good insights from huge datasets. It covers various methodologies around sample collection and sample analysis and includes challenges associated with sampling bias. It does not stop at the theory: it exposes real-life applications so that the participant can not only learn theoretically but also practice skills essential for getting a better decision-making ability in the real world. In this in-depth teaching-learning experience, a participant will learn to use sampling techniques, devise sound conclusions, and thus play an active role in an evolving field of data analysis.