Question

The Web site www.gamefaqs.com asked, as their question of the day to which visitors to the site were invited to respond, \({ }^{4}\) Do you ever use emoticons when you type online? "Of the 87,262 respondents, \(27 \%\) said that they did not use emoticons. a) What kind of sample was this? b) How much confidence would you place in using \(27 \%\) as an estimate of the fraction of people who use emoticons?

Short answer

a) A convenience sample; b) Low confidence due to potential bias.

Step-by-step solution

Identify the Sample Type

The survey was conducted online on a specific website, which means that the respondents were visitors to www.gamefaqs.com. This makes the sample a convenience sample, because it is composed of people who are easily accessible and self-selected as they chose to participate.

Analyze the Representation

A convenience sample is not necessarily representative of the general population. Visitors to gamefaqs.com might share certain interests or demographics, like being gamers, which might influence their likelihood to use emoticons differently than the general public.

Evaluate Confidence in the Estimate

Because the sample was obtained through convenience sampling, using the 27% result to generalize about the entire population could be problematic. Such sampling methods typically suffer from biases, as they don't ensure that every member of the population has an equal chance of being included.

Key concepts

Convenience Sampling

Convenience sampling is a method used in observational studies where the sample consists of individuals who are easy to reach or contact. This approach centers around ease and convenience for the researcher, often neglecting thorough randomization. In this method, respondents are generally self-selected, meaning they choose to participate. This was evident in the exercise where visitors to the website www.gamefaqs.com could freely respond to the survey. Since the participants were drawn from a specific site, without any rigorous methodology to ensure they represent the broader public, it exemplifies convenience sampling.
Convenience sampling is frequently utilized in initial exploratory research due to its simplicity and cost-effectiveness. However, the lack of randomness can lead to a non-representative sample, limiting the findings' applicability to a larger population. It's crucial to recognize when this method is appropriate and acknowledge its limitations in drawing broad conclusions.

Sample Bias

Sample bias occurs when certain groups or demographics are overrepresented or underrepresented within a sample. This bias negatively impacts the reliability of the results. Since convenience sampling depends on easily accessible participants, it often introduces sample bias. For instance, the respondents of the www.gamefaqs.com survey were primarily those interested in video games, potentially excluding other demographics who may use emoticons differently.
There are several reasons for bias within convenience sampling:

• The participants self-select, meaning only those interested in the survey topic may respond.
• The environment where the sample is taken (e.g., a gaming site) can influence responses due to shared traits among participants.

Recognizing sample bias is essential for interpreting data correctly and understanding the limitations of the results generated from such surveys.

Representation

Representation in sampling means how well the sample reflects the entire population. A sample is said to be representative when the characteristics of the sample closely match those of the population from which it is drawn. In the case of the survey from www.gamefaqs.com, there is a concern about whether the respondents accurately represent the broader population's emoticon usage.
Ensuring representation requires a well-thought-out sampling method, typically involving randomization, which was missing in the given convenience sample. Without a representative sample, results such as the 27% figure for non-emoticon users in the exercise might not apply to the entire population.
To improve representation, researchers might use methods such as stratified sampling, where the population is divided into subgroups, or ensure that every member has a chance of being selected. This would help produce more reliable data and conclusions that are more generalizable.