8 Sample and Population
When you want to study a system—for example, a social issue—you cannot ask everyone every question. Doing so would require immense resources, and making participation mandatory would effectively mean forcing your will on the public, which is not ideal. Therefore, statisticians use sampling. From the entire population, they select a smaller group of people to survey. Some may choose to answer, while others may not.
The subset of people who actually provide responses is called the sample, while the entire group of interest (e.g., all citizens of a nation) is called the population. Although the sample size is usually much smaller than the population, statisticians can still produce accurate predictions if the sample is representative.
8.1 Sampling Bias
Consider a scenario where you are surveying the lifestyle of people in India. If you only take samples from highly developed states like Tamil Nadu or Maharashtra, your results will be skewed and unrepresentative of the country as a whole. To get an accurate picture, sampling must be done in a way that includes people from all states and diverse backgrounds.
Another type of bias can arise from population density. For instance, states like Arunachal Pradesh or Meghalaya have significantly fewer people than Bihar or Uttar Pradesh. If you collect samples without considering the population size, or if you disproportionately favor less populous states, your data can become skewed.
Effective sampling requires prior knowledge of the system. With this knowledge, one must carefully design a sampling strategy to ensure the results accurately reflect the population.
8.2 Food for Thought
- If you were a statistician working for the Afghan government and were denied the opportunity to survey women, do you think you could reach accurate conclusions about the country’s state?
- If a survey is conducted exclusively via a mobile app, it might be used more by millennials than by older generations. In what ways would this data be skewed?
- If a survey is only conducted using pencil and paper, who is it likely to target, and who might it exclude? How could you mitigate this?
- If a company executive only asks the board of directors about the company’s health, rather than the employees, is he conducting a valid and comprehensive survey?