Collecting data and the statistical cycle
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課程筆記
The Statistical Cycle
- The statistical cycle is a four-stage process: pose a question, collect data, process and represent data, and interpret results.
- The cycle is iterative: interpreting results often leads to new questions, starting the cycle again.
- Each stage must be planned carefully to ensure the data collected can actually answer the original question.
- A clear, focused problem definition is essential before any data is collected.
Primary and Secondary Data
- Primary data is collected first-hand by the person or team carrying out the investigation.
- Secondary data is data that has already been collected by someone else, such as from a website, book, or government report.
- Primary data is more reliable for your specific question but can be time-consuming and expensive to collect.
- Secondary data is quicker and cheaper to obtain but may not perfectly match your question or may be outdated.
Populations and Samples
- A population is the entire group of people or items that you want to understand.
- A sample is a subset of the population, selected to represent the whole.
- Collecting data from the whole population is called a census; it is often impossible, too costly, or too time-consuming.
- Sampling provides insights when measuring the entire population is infeasible.
- A good sample should be representative of the population, meaning it reflects its characteristics accurately.
Random Sampling
- Random sampling gives every member of the population an equal chance of being selected.
- Random sampling helps to avoid bias and produce a representative sample.
- Methods include using random number generators, lottery methods, or picking names from a hat.
- A large sample size alone does not guarantee accuracy if the sampling method is biased.
Sources of Bias
- Bias occurs when a sample is not representative of the population.
- Bias can arise from the sampling method, the way questions are asked, or who chooses to respond.
- A famous example is the 1936 Literary Digest poll, which predicted a Republican win but was biased because names were taken from magazine subscription lists and telephone directories, which over-represented Republicans.
- Even a very large sample can be deeply flawed if it is biased.
- To reduce bias, use random sampling and ensure questions are neutral.
Designing a Questionnaire
- Questions should be clear, concise, and easy to understand.
- Avoid leading questions that suggest a particular answer, e.g. 'Don't you agree that...?'
- Avoid biased questions that make one answer seem more acceptable, e.g. 'How much do you enjoy our excellent service?'
- Avoid double-barrelled questions that ask about two things at once, e.g. 'Do you like the food and the staff?'
- Provide balanced response options and avoid overlapping categories.
- Pilot the questionnaire on a small group to check for problems before full data collection.
Processing and Representing Data
- After collection, data must be processed: cleaned, organised, and summarised.
- Common representations include tables, bar charts, pie charts, and averages.
- The choice of representation should suit the type of data and the question being asked.
- Processing may involve calculating statistics such as the mean, median, mode, or range.
Interpreting Results and Drawing Conclusions
- Interpretation involves analysing the processed data to answer the original question.
- Conclusions should be based on evidence and should acknowledge any limitations or possible bias.
- It is important to distinguish between correlation and causation; a relationship does not prove cause.
- Results from a sample are estimates for the population and may have a margin of error.
- For example, sample counts in Singapore elections give an indicative result with a 4% margin of error at a 95% confidence interval, but are not official results.
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練習題
免費預覽——62 題中的 8 題。註冊即可查看全部。
1.Which of the following best describes a population in statistics?
Easy- AThe complete set of all people or items with the characteristics being studied
- BA small group selected from a larger group
- CThe number of people living in a country
- DThe data collected from a sample
2.Which of the following is an advantage of using a sample instead of a census?
Easy- AIt is cheaper and faster to collect data
- BIt gives exact information about every individual in the population
- CIt eliminates all bias
- DIt requires no sampling method
3.A sample should be representative of the population to allow valid conclusions.
EasyTrue or false?
4.A researcher wants to know the average height of students in a school. She selects every 10th student from an alphabetical list of all students. What type of sampling method is this?
Medium- ASystematic sampling
- BSimple random sampling
- CStratified sampling
- DQuota sampling
5.Which of the following are potential sources of bias in a sample? (select all that apply)
Medium- AUsing a convenience sample
- BUsing a random number generator to select participants
- CNon-response bias
- DUndercoverage of certain groups
- EUsing a large sample size
6.In the 1936 Literary Digest poll, more than two million people responded, but the prediction was wrong. What was the main reason for the error?
Medium- AThe sample was biased because it was drawn from magazine subscribers and telephone directories
- BThe sample size was too small
- CThe poll was conducted too early
- DThe respondents lied about their voting intention
7.Match each term with its correct definition.
Medium- Population
- Sample
- Census
- Bias
- The complete set of all items or individuals of interest
- A subset of the population selected for study
- Data collected from every member of the population
- A systematic error that makes results unrepresentative
8.Put the stages of the statistical cycle in the correct order.
Medium- Pose a question
- Collect data
- Process and represent data
- Interpret results
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