Questions and Answers
Explain the difference between a stratified sample and a cluster sample.
In a stratified sample, random samples from each strata are included. In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
Explain the difference between a simple random sample and a systematic sample.
In a simple random sample, every sample of size n has an equal chance of being included. In a systematic sample, the only samples possible are those including every kth item from the random starting position.
Does every student have an equal chance of being selected for the sample?
Is it possible to include students sitting in row 3 with students sitting in row 2 in your sample?
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Is your sample a simple random sample?
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Describe a process you could use to get a simple random sample of size 20 from a class of size 40.
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How could you get a random sample of four students from your statistics class? (Select all that apply.)
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Why would the first four students walking into the classroom not necessarily form a random sample? (Select all that apply.)
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Why would four students coming in late not necessarily form a random sample? (Select all that apply.)
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Why would four students sitting in the back row not necessarily form a random sample? (Select all that apply.)
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Why would the four tallest students not necessarily form a random sample? (Select all that apply.)
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What are examples of population members that might have been omitted if you use the sampling frame of students present next Monday?
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What are examples of population members that might have been omitted if you use the student roster of the high school as the sampling frame?
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Study Notes
Sampling Methods
- Stratified sampling involves selecting random samples from various strata or groups within a population.
- Cluster sampling selects entire clusters randomly and includes all members from those chosen clusters.
- Simple random sampling gives every potential sample of size n an equal chance to be chosen, while systematic sampling selects every kth item from a randomly determined starting point.
Classroom Sampling Scenario
- In a classroom scenario with students arranged in four rows, the random selection process using a coin flip creates a potential bias leading to no equal chances for all students.
- Students in cluster samples are grouped, which restricts the representation of individuals from different rows.
Types of Random Samples
- Random selection methods must ensure that all individuals have equal opportunities to be chosen to avoid bias.
- The first four students entering a class could be influenced by their eagerness or schedule, suggesting they may not represent the entire class.
- Choosing students based on physical characteristics or specific seating does not ensure randomness and can introduce biases.
Undercoverage Examples
- In sampling scenarios, undercoverage occurs when certain members of the population (like absentee students) are not included, leading to skewed results.
- Not sampling students who skip class, are on school trips, or are unwell exemplifies this issue in a classroom setting.
- When using a high school student roster to sample 15-year-olds, undercoverage can exclude dropouts and home-schooled students, affecting the accuracy of findings.
Key Terms
- Undercoverage: When certain members of a population are not represented in a sample due to sampling frame limitations.
- Sampling Frame: The actual list or group being used to select samples from the population.
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Description
Test your understanding of various sampling methods including stratified, cluster, simple random, and systematic sampling. This quiz assesses your knowledge of how these methods work and their applications, particularly in classroom scenarios and their potential bias. See how well you can identify the best sampling techniques for different situations.
