Question

Through their Roper Reports Worldwide, GfK Roper conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. Within 30 countries, the researchers interview 1000 people aged \(13-65 .\) Their samples are designed so that they get 500 males and 500 females in each country. (www.gfkamerica.com) a) Are they using a simple random sample? Explain. b) What kind of design do you think they are using?

Short answer

a) No, they are not using a simple random sample. b) They are using stratified sampling.

Step-by-step solution

Understand Simple Random Sampling

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. In a simple random sample, every group of the same size has the same chance of being selected.

Evaluate the Sampling Method

In the described survey method, researchers are selecting 1000 people in each country, with exactly 500 males and 500 females. This means the sample is constructed to include equal gender representation, rather than giving every individual an equal chance regardless of gender. This does not align with the principles of simple random sampling.

Identify the Survey Design

Since the sample is intentionally divided into 500 males and 500 females, the design used here is a form of stratified sampling. In stratified sampling, the population is divided into distinct subgroups (strata) and samples are taken from each stratum, ensuring that specific groups are adequately represented in the sample.

Key concepts

Simple Random Sample

The concept of a Simple Random Sample involves selecting members from a larger population in such a way that each individual has an equal chance of being chosen. It is a fundamental technique in statistical sampling that aims to minimize bias and ensure that results are as generalizable as possible. A good example of a simple random sample is drawing names from a hat, where each name has an equal likelihood of being picked.
In this method:

• Every member of the population has the same probability of being included in the sample.
• The selection is entirely random and not influenced by any particular traits of the population.
• It ensures that each possible sample of a given size has an equal chance of selection.

This kind of sampling is beneficial in situations where you want each subgroup to have the same opportunity to be part of the study, but it might not be practical or feasible in all real-world applications, especially when studying diverse populations with key distinctions.

Stratified Sampling

Stratified Sampling is a method used when researchers divide a population into distinct subgroups or strata, based on shared characteristics, and then randomly sample from each subgroup. This technique ensures that each subgroup is adequately represented in the final sample, making it especially useful for heterogeneous populations.
Here's how it works:

• The population is divided based on specific traits, such as age, gender, or income.
• Random samples are taken from each stratum, proportional to their size in the overall population.
• It increases the precision and accuracy of the results by ensuring diversity and balance.

In the GfK Roper survey, the distinct allocation of 500 males and 500 females within each country's sample is an example of stratified sampling. This approach ensures gender balance and provides nuanced insights that might not be captured through simple random sampling. The method is ideal when you know that certain groups within your population will react differently to the variables being studied.

Survey Design

Survey Design is a broad term that encompasses the planning and structure of a questionnaire to gather data effectively. Quality survey design ensures that the data collected is both reliable and valid for making meaningful inferences about the population.
Key considerations in designing a survey include:

• Choosing the right sampling method, like stratified or random sampling, to best capture the target population.
• Structuring questions to avoid bias and ambiguity.
• Ensuring that questions are relevant and address the objectives of the study.

A well-designed survey makes use of appropriate sampling methods, such as what is employed by GfK Roper. Their intentional use of stratified sampling within their survey design ensures balanced representation, offering valuable insights across different demographics. In essence, designing a survey goes beyond question selection; it is a strategic process that determines how insights are gleaned from the data and how accurately they reflect the population's views.