Data collection is the first major decision in any statistical study because the quality of the conclusions depends on the quality of the data. A strong research question helps determine whether to use surveys, experiments, observation, or existing records. Each method answers different kinds of questions and has different strengths, limits, costs, and risks of bias.
Choosing the right method makes results more reliable and easier to interpret.
Key Facts
- Survey: collects self-reported answers from a sample using questions, polls, or interviews.
- Experiment: changes one variable on purpose to study its effect on a response variable.
- Observation: records behavior or measurements without assigning treatments.
- Existing records: uses data already collected, such as medical files, school records, or government databases.
- Sample proportion: p-hat = x/n, where x is the number with a trait and n is the sample size.
- Larger random samples usually reduce sampling variability, but they do not automatically remove bias.
Vocabulary
- Population
- The entire group of individuals or items that a study wants to learn about.
- Sample
- A smaller group selected from the population to provide data for a study.
- Bias
- A systematic error that makes collected data or conclusions consistently favor one outcome.
- Treatment
- A condition or action assigned in an experiment to test its effect on a response.
- Response variable
- The outcome measured in a study to see how it changes or differs across groups.
Common Mistakes to Avoid
- Using a survey when behavior is the real target is a mistake because people may misremember, exaggerate, or give answers they think sound acceptable.
- Calling an observational study an experiment is wrong because an experiment requires the researcher to assign treatments or conditions.
- Assuming a large sample is automatically unbiased is wrong because a huge sample chosen badly can still give misleading results.
- Using existing records without checking how they were collected is a mistake because missing data, old definitions, or inconsistent measurement methods can distort conclusions.
Practice Questions
- 1 A school wants to estimate the proportion of 1,200 students who bike to school. A random sample of 80 students finds that 18 bike to school. Find p-hat and estimate the number of students in the whole school who bike.
- 2 A researcher wants to test whether a new fertilizer increases plant height. She randomly assigns 60 plants to two equal groups, one with the new fertilizer and one with the old fertilizer. How many plants are in each group, and what data collection method is being used?
- 3 A city wants to know whether adding more streetlights reduces nighttime accidents. Explain whether a survey, experiment, observation, or existing records would be most appropriate, and justify your choice.