Sample Notes: Data And Its Collection

1. Data and Its Collection

1.1 General Ideas of Sampling

• Population:
  The complete group of items or people being studied.
  Example: All students in a school.
• Sample:
  A subset of the population selected for the study.
  Used to make conclusions about the entire population without investigating every individual.
• Census:
  A data collection method where every member of the population is surveyed.
  • Pros: Highly accurate
  • Cons: Time-consuming, expensive, often impractical
• Sampling:
  The process of selecting a sample from the population.
• Representative Sample:
  A sample that accurately reflects the population’s characteristics (e.g. age, gender, region).
• Why sampling is used:
  • Saves time and cost
  • Can still provide reliable results
  • Useful when population is too large to survey completely

1.2 Types of Sampling

1. Simple Random Sampling (SRS)

• Every member of the population has an equal chance of being selected.
• Method: Use of random number tables or random number generator.
• Example: Choosing 10 students randomly from a list of 200 students using a random number generator.
• Pros: Unbiased if truly random
• Cons: May not reflect subgroups in the population

2. Systematic Sampling

• Select every nᵗʰ member from a list after choosing a random starting point.
• Example: If population = 100 and sample size = 10, select every 10ᵗʰ person starting from a random number between 1–10.
• Pros: Easy to implement
• Cons: May introduce bias if list is ordered in a pattern

3. Stratified Sampling

• Population is divided into strata (groups), e.g., age, gender, region. Then, a proportional sample is taken from each stratum.
• Example: In a school of 60% girls and 40% boys, a sample of 100 would include 60 girls and 40 boys.
• Pros: More representative
• Cons: Requires knowledge of population structure

4. Quota Sampling

• Interviewers are told to select people who fit into specific categories (e.g., 10 boys, 5 girls). No random selection within groups.
• Example: Interviewing 20 people—10 below 30 years, 10 above.
• Pros: Faster and easier to conduct
• Cons: Can introduce selection bias

1.3 Bias: How It Arises and Is Avoided

Bias:

An error that causes results to be skewed in a particular direction, leading to inaccurate conclusions.

Sources of Bias:

• Non-random sampling: Choosing only convenient people (e.g. friends, classmates).
• Leading questions: “How amazing was your experience?” vs “How would you rate your experience?”
• Non-response bias: When certain groups are less likely to respond.
• Small or unrepresentative sample: Sample doesn’t reflect the population.
• Interviewer influence: Body language or tone may influence answers.

How to Reduce Bias:

• Use random methods for selection.
• Ensure questions are neutral.
• Use larger sample sizes when possible.
• Ensure the sample represents all key subgroups.
• Avoid self-selection bias (e.g., online polls where only some types of people respond).

1.4 General Ideas of Surveys

What is a Survey?

A method for collecting information from a sample using a set of questions.

Designing a Survey:

1. Define objective – What information is needed?
2. Target population – Who is being surveyed?
3. Choose sample method – SRS, stratified, etc.
4. Design the questionnaire
5. Pilot test the survey – Try it on a small group first
6. Collect responses
7. Analyse and interpret data

Question Types:

• Closed questions: Have fixed options (e.g., Yes/No, Multiple Choice)
  • Easy to analyze but less detailed
• Open questions: Allow respondents to answer in their own words
  • More detail but harder to analyze

Best Practices:

• Avoid leading questions
• Keep wording clear and simple
• Avoid double-barrelled questions (e.g. “Do you like sports and music?”)

1.5 Types of Data and Variable

1. Types of Data:

Quantitative Data:

Numerical data that can be measured or counted.

• Discrete: Takes specific values only (e.g., number of children: 0, 1, 2…)
• Continuous: Can take any value within a range (e.g., height: 161.2 cm, 163.8 cm…)

Qualitative Data:

Descriptive data that deals with categories or labels.

• Examples: Colors, brands, gender, opinions

2. Types of Variables:

• Independent variable: The one being changed or controlled in an experiment.
  • Example: Type of fertilizer used in a crop study
• Dependent variable: The one being measured.
  • Example: Growth of plants (cm)
• Categorical variable: Data that can be divided into specific groups or categories.
  • Example: Blood type (A, B, AB, O)
• Numerical variable: Data represented by numbers.
  • Example: Age, test scores

Important Terms to Memorize

Example Exam Questions

1. Define the term “census” and give one advantage and one disadvantage of using it.
2. Explain the difference between stratified and quota sampling.
3. Identify one source of bias in surveys and explain how it can be avoided.
4. Give two examples each of discrete and continuous data.
5. Distinguish between qualitative and quantitative data using examples.