Question

Describe the difference between an unbiased sample and a biased sample. Give one example of each.

Short answer

In simple terms, an unbiased sample gives each member of the population an equal chance of being included, ensuring a fair representation (like randomly selecting households for a TV viewing survey). A biased sample, on the other hand, includes members of the population unevenly, leading to a skewed representation (like surveying only private high school students about education).

Step-by-step solution

Define Unbiased Sample

An unbiased sample is a subset of a population in which each member of the sample has an equal chance of being selected. This means that the sample fairly represents the entire population and is devoid of any personal judgment or preferences.

Example of Unbiased Sample

An example of an unbiased sample could be conducting a country-wide survey about people's television viewing habits, where every household in the country has the same chance of being chosen. This might involve randomly selecting postal codes, and then randomly selecting households within those postal codes to participate in the survey.

Define Biased Sample

A biased sample, on the other hand, is a subset of a population in which certain members are more or less likely to be included than others. This could occur due to intentional or unintentional factors like selection bias or non-response bias.

Example of Biased Sample

An example of a biased sample might be a survey about high school education, conducted by only interviewing students attending expensive, top-ranking private high schools. This sample would be biased because it doesn't fairly represent all students, from a variety of socio-economic backgrounds and education types.

Key concepts

Unbiased Sample

An unbiased sample is an essential concept in statistics and research. It ensures that every individual in a population has an equal chance of being selected.
This type of sample is like giving every person in a crowd an equal opportunity to toss a coin and be part of the final group chosen. When researchers aim to draw conclusions about a population, having an unbiased sample ensures that their findings are legitimate and accurately reflect reality.
A fair example of an unbiased sample could be a national television viewing survey where each household, regardless of location, has the same opportunity to participate. This could involve random selection of postal codes and further randomization within those codes. This randomness ensures all segments of the population are represented evenly, making conclusions drawn from the sample credible.

Biased Sample

A biased sample stands out due to its lack of fairness in selection.
In this type of sampling, some individuals have a higher or lower chance of being selected compared to others in the population. This skew can drastically influence the outcome of research and lead to misleading conclusions.
Imagine surveying opinions on public schools but only consulting students from elite private institutions. Such a sample would be biased as it disregards the diverse experiences in public schooling, making the results unrepresentative of the larger student population. Bias can arise from a variety of sources including methodological errors or personal judgment.

Selection Bias

Selection bias is a common challenge in achieving a proper sample.
This type of bias occurs when the sample is not representative of the population due to the way individuals are chosen. It often happens subconsciously or accidentally, leading to overrepresentation or underrepresentation of certain groups.
For instance, if a survey about health habits only uses data from gym-goers, it introduces selection bias. This is because people who frequently visit gyms may have different health habits than the general population. Such bias can distort findings and should be carefully avoided.

Survey Methods

Survey methods are the tools and techniques used to gather data from a sample of a population.
Choosing the right survey method is crucial to minimize bias and enhance the reliability of the data collected.

• Random Sampling: Each member of the population has an equal opportunity to be selected. This minimizes biases and enhances representativeness.
• Stratified Sampling: Dividing the population into subgroups and surveying within these groups allows for more precise insights.
• Systematic Sampling: Selecting every 'nth' person in a list. This can be effective but only if the list is random.
• Cluster Sampling: Large populations are divided into clusters, with a random sample of these clusters being surveyed.

In all cases, it is imperative to design surveys carefully to ensure they reflect the true diversity of the population.