Learning Objectives
- Understand the difference between Primary and Secondary Data.
- Explain what a Simple Random Sample is and how to generate one.
- Identify sources of Bias in data collection and survey design.
- Design fair, unbiased questionnaires.
- Distinguish between Observational Studies and Designed Experiments.
Interactive Study Tools
These tools are here to help students slow down and think about the method before rushing to an answer.
Study Planner
Use this to break a topic into small study sessions.
Method Reminder
This quick guide reminds students what to do when they feel stuck.
- Read the story: what is the question really asking?
- Choose the method: identify the correct idea before calculating.
- Show the reason: do not skip the logic.
- Check the answer: make sure it fits the situation.
1. Primary vs. Secondary Data
Before doing any statistics, you must get your data. There are two main categories of data sources:
- Primary Data: Data collected by the investigator themselves for a specific purpose (e.g., you handing out a survey in your school, or doing an experiment in a lab).
- Secondary Data: Data that has already been collected by someone else (e.g., looking up the national census results online, reading a newspaper article, or using historical weather records).
Advantage: Exact data needed for their specific project. Disadvantage: Takes a lot of time.
Advantage: Very fast and usually massive sample sizes. Disadvantage: Might not have the exact specific details the student wanted.
2. Simple Random Sampling
A sample is only useful if it represents the population accurately. The gold standard is a Simple Random Sample (SRS).
Definition: A sample selected in such a way that every member of the population has an equal chance of being chosen, and every possible sample of that size has an equal chance of being chosen.
3. Bias and Survey Design
Bias occurs when a sample or a survey method systematically over-represents or under-represents a certain group, leading to inaccurate results.
Sources of Bias:
- Selection Bias: The sample does not reflect the population (e.g., asking only gym members about their exercise habits).
- Leading Questions: Phrasing a question to push the respondent towards a specific answer.
- Non-response Bias: When people chosen for the survey refuse to answer, and those who do answer have very different opinions.
Correction: "How would you rate the healthiness of the canteen food?" (Provide options: Very Unhealthy to Very Healthy).
Correction: If someone is 20, they don't know which box to tick! It should be [0-10] [11-20] [21-30].
4. Observational Studies vs. Designed Experiments
How does the researcher interact with the subjects?
- Observational Study: The researcher simply observes and records data without interfering or trying to change anything. (e.g., Watching a junction to see how many cars run a red light).
- Designed Experiment: The researcher intentionally applies a "treatment" or changes a variable to see what effect it has. (e.g., Giving half a group a new study pill, and the other half a placebo, to test memory).
This is an Observational Study. The doctor didn't force them to drink the coffee.
This is a Designed Experiment. A treatment was applied!
📝 Exam Style Questions
Easy Q1: State one advantage and one disadvantage of using a postal questionnaire to collect primary data.
Medium Q2: A student writes the following survey question: "Most intelligent people love Maths. Do you love Maths? [Yes] [No]". Identify two flaws in this question.
Hard Q3: A researcher wants to find the average height of adult men in Ireland. They go to a professional basketball match in Dublin and randomly select 50 men from the crowd to measure. Explain why this sample is biased and how it will affect the results.
A1: Advantage: People can take their time to answer it privately (good for sensitive topics) and it can reach a wide geographical area. Disadvantage: Very low response rate (most people throw them in the bin!).
A2: Flaw 1: It is a Leading Question. By stating "Most intelligent people love Maths", it pressures the respondent to say Yes so they feel intelligent. Flaw 2: There is no "Don't Know", "Sometimes", or "Neutral" option. It forces a strict binary choice.
A3: Bias: Basketball matches tend to attract taller people (players, families of players, fans of the sport). Because they only sampled at a basketball game, they have excluded men who do not attend these games. Effect: The average height calculated will be significantly higher than the true national average. It is an unrepresentative sample.
🔥 Challenge Questions (No Peeking!)
Easy C1: Is the data collected in the Irish National Census primary or secondary data to the Irish Government?
Medium C2: You want to design a survey to find out how much money students spend on lunch. Write a well-designed question with appropriate tick-boxes to gather this data.
Hard (HL) C3: Explain the concept of a "Control Group" in a designed experiment.
(Answers at the very bottom of the page)
📌 Quick Summary
1. Primary = You collect it. Secondary = Someone else collected it.
2. Simple Random Sample: Everyone has an equal chance. Use a random number generator.
3. Survey Rules: No leading questions, no overlapping boxes (1-5, 6-10), and always provide a "Zero" or "Other" option.
4. Experiment vs Observation: If you apply a treatment/change things, it's an experiment. If you just watch, it's observational.
🎓 Final Examiner Advice
When critiquing a survey question on the exam, be specific. Don't just say "It's a bad question." Say "The boxes overlap," or "It is a leading question that introduces bias." Knowing the exact terminology will turn a 2-mark attempt into a 5-mark perfect answer. Always imagine yourself filling out the survey: if you wouldn't know what box to tick, there's a flaw in the design!
Challenge Answers:
C1: It is Primary Data to the government (because they collected it themselves for their own purposes). If YOU use it for a school project, it becomes Secondary Data to you.
C2: "How much do you typically spend on lunch per school day?" [€0] [€0.01 - €2.00] [€2.01 - €4.00] [€4.01 - €6.00] [More than €6.00]. (Notice: No overlaps, covers all possibilities including zero).
C3: A Control Group is a group in an experiment that does NOT receive the active treatment (they might receive a fake pill/placebo instead). This provides a baseline to compare the actual treatment against, proving that any changes were actually caused by the treatment and not just natural time or the placebo effect.