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What is an example of the situation of lottery sampling?

Lottery sampling, also known as chance sampling, is a sampling technique where we select a random sample from a larger population. The sample is chosen entirely by chance, like a lottery drawing. This means every member of the population has an equal chance of being selected.

When is lottery sampling used?

Lottery sampling is used when:

  • The population is very large and a list of all members is unavailable
  • There is no bias in selecting the sample and each member of the population has an equal chance of being selected
  • A probability sample is required but time/resources do not allow more advanced techniques
  • The researcher wants a simple random sample

While simple random sampling requires a sampling frame listing all members of the population, lottery sampling simply selects members at random without a sampling frame. This makes it useful when you have limited information about the population or it is prohibitively large.

Example of lottery sampling

Here is an example of when lottery sampling may be used:

A market researcher wants to conduct a survey of consumer preferences across the entire United States. The population size is over 300 million people. It is not feasible to obtain a complete list of all U.S. residents for simple random sampling. The market researcher decides to use lottery sampling.

The researcher obtains a random sample of 10,000 mailing addresses from the U.S. Postal Service. Surveys are mailed out to each address. As long as each address has an equal probability of being selected, this constitutes a lottery sample. The people who respond to the survey become the sample. Statistical analysis can then be applied to make inferences about consumer preferences in the overall U.S. population.

Some key points about this example:

  • The population is very large (300+ million)
  • There is no master list or sampling frame of all U.S. residents
  • Each mailing address has equal chance of selection for the initial sample
  • The final sample is self-selecting from those who respond to the mailed survey

Advantages of lottery sampling

Some advantages of using lottery sampling include:

  • Simple to implement – No need for complex algorithms or sampling frame.
  • Can generalize to large populations – As long as the lottery sample is random, results can be generalized to the broader population.
  • Equal chance of selection – Removes selection bias since every population member has equal probability of selection.
  • Cost-effective – Relatively inexpensive compared to more complex probability sampling techniques.

Disadvantages of lottery sampling

Some disadvantages and limitations of lottery sampling include:

  • Self-selection bias – Those who respond may differ from the broader population.
  • May need very large samples – To properly represent a large, diverse population.
  • No control over final sample – The researcher has no control over who specifically is included.
  • Potential duplication – Same population members may be sampled more than once.

How to conduct lottery sampling

The process for conducting lottery sampling generally includes these steps:

  1. Define the population – Determine what larger population you want to sample from.
  2. Create sampling frame – Obtain list or source of population members to randomly select from. This is the “lottery” pool.
  3. Simple random selection – Use lottery method to randomly select members from sampling frame. Common approaches include:
    • Computerized random number generator
    • Random number table
    • Drawing names/numbers from a hat
  4. Contact selected members – Reach out to randomly selected members to participate in research.
  5. Conduct research – Those who respond become the sample. Gather data and analyze results.

The lottery selection mechanism should be truly random to avoid bias. All members should have equal probability of selection. Larger sample sizes help ensure the sample represents the overall population.

Lottery sampling methods

There are a few main methods used to implement lottery sampling:

Simple random sampling

This involves putting names, numbers, or other identifiers for the entire population into a hat or pool. We then draw random members from this lottery to select the sample. For example, writing every student’s name on a piece of paper and drawing names from a hat.

Random number tables

Published tables of random numbers can be used to select random samples. We match random numbers to members of the population. For example, using a random number table to select phone numbers.

Computerized random number generators

Specialized computer programs quickly generate random numbers. These programs can rapidly select random samples of any size from a population. For example, using the RAND() function in Excel.

Geographic/address selection

Selecting random mailing addresses, phone numbers, or geographic coordinates. Surveys are then mailed/called to those selected. For example, calling random phone numbers with a given area code and prefix.

Examples of populations for lottery sampling

Lottery sampling can be used to select random samples from any large population where a complete list of members is unavailable. Some examples include:

  • All registered voters in a country
  • All households in a city
  • All customers of an insurance company
  • All students at a large university
  • All viewers of a TV channel

If complete lists exist for the populations above, simple random sampling would be better. But lottery sampling allows drawing a probability sample when such lists are infeasible to obtain or nonexistent.

Example lottery sampling survey

Here is a step-by-step example of using lottery sampling to conduct a survey:

  1. A market researcher wants to survey public opinion across the U.S. regarding a new product. The target population is all 250 million U.S. adults.
  2. With no national registry of adults, obtaining a complete sampling frame is impossible. The researcher decides to use random postal mailings for lottery sampling.
  3. The researcher obtains a CD-ROM of random U.S. mailing addresses from the Census Bureau. The disc contains 50,000 random addresses.
  4. 10,000 random addresses are selected from the CD-ROM using the RAND() formula in Excel. Surveys are mailed to each address.
  5. Approximately 1,200 completed surveys are returned. This becomes the lottery sample.
  6. The researcher analyzes results. Since the original 10,000 addresses were randomly selected, the 1,200 responses can generalize to the overall target population.

This example demonstrates the key principles of using lottery sampling when conducting surveys with large general populations. Geographic random selection is an easy way to approximate an overall population sample.

Lottery sampling in political polling

Lottery sampling is sometimes used in political opinion polling and exit polls. Surveys aim to represent the target population of all voters rather than a registered voter list. Steps may include:

  1. Obtain random phone numbers or household addresses for the targeted geographic area (e.g. city, state, country).
  2. Call the randomly selected numbers. The person who answers becomes the survey respondent.
  3. Analyze results to infer opinions and trends in the overall target population of local voters.

While phone surveys have declined due to call screening, random digital polling has become more common. This sends survey invitations to random email addresses or social media users. Geo-targeted online ads can also randomly expose users to survey links. Both methods use lottery sampling principles to approximate a random sample of the target population.

Using lottery sampling to study rare populations

It is difficult to create sampling frames for small, rare, or hidden populations. Examples may include:

  • Members of a small religious sect
  • Homeless people in a city
  • Sufferers of a rare disease
  • Exotic pet owners

There may be no registries or lists available for such groups. Lottery sampling provides a way to study them. We can intercept randomly-selected people through marketing lists, phone numbers, or by approaching them in public areas. Those that meet the population criteria become the sample.

This method relies on the population members frequenting public places where they can be randomly intercepted. It may have bias since some members may be reclusive. But the random selection element aims to create a representative cross-section.

Ethics of lottery sampling

While lottery sampling is useful in some cases, ethical concerns include:

  • People may feel exploited by random cold-contact surveys.
  • Repeated surveys of the same individuals can occur by chance.
  • Rare populations require care not to study members without consent.
  • Personal data like postal addresses should have privacy protections.

Researchers should weigh whether simpler sampling or public archival data could substitute. If direct contact is required, transparency, consent procedures, and confidentiality safeguards help uphold ethics.

Limitations of lottery sampling

Some limitations to consider with lottery sampling:

  • Results may reflect only the opinions of people who respond to surveys, not the entire target population.
  • Large samples are required, often 1,000+ members.
  • Samples may unintentionally exclude portions of the population with lower probability of selection.
  • The methodology assumes respondents are truthful about their demographics.
  • Repeated surveys of the same people may occur by chance over time.

Despite limitations, lottery sampling offers a practical way to approximate probability sampling when full population lists are unavailable. Demographic questions help assess respondent diversity.

Comparing lottery sampling to other methods

Method Sampling Frame Needed? Equal Probability of Selection? Cost
Simple random sampling Yes Yes Medium
Systematic sampling Yes No Low
Stratified sampling Yes No High
Cluster sampling Yes No Medium
Multi-stage sampling Partial No High
Convenience sampling No No Low
Lottery sampling Partial Yes Medium

This table compares lottery sampling to other common sampling techniques. The main advantage of lottery sampling is equal probability of selection from the population without needing a full sampling frame.

Conclusion

In summary, lottery sampling provides a probability sampling method when full population lists are lacking. By randomly selecting members, all individuals have an equal chance of inclusion. This avoids selection bias. While limitations exist, lottery sampling enables statistically valid inferences to be made about the broader population from the sample data.

Lottery sampling is thus a useful technique for market research, opinion polling, studying rare groups, and other sampling situations where complete population information is unavailable. As long as randomness is assured in selection, results can be generalized to the overall target population. With large enough sample sizes, lottery sampling offers a feasible way to approximate true random probability sampling.