prep

1. Sampling (WHO you study)

Key idea:

You usually don’t study everyone, so you take a sample.

  • Population = everyone you care about

  • Sample = the group you actually study

  • Sampling frame = the list you pick your sample from

👉 Example:

Population = all NZ students

Sample = 1000 students surveyed



Types of Sampling

Good (less bias)

  • Simple random → everyone has equal chance

  • Stratified → split into groups (e.g. age), then sample

  • Systematic → every 10th person



Bad (biased)

  • Convenience → whoever is easiest

  • Voluntary → people choose to respond

👉 Why bad?

Because they don’t represent the population properly



2. Bias (WHAT can go wrong)

Bias = results are not trustworthy

3 main types you must know:



1. Coverage error

Some people are missing completely

👉 Example:

Online survey → excludes people without internet



2. Non-response bias

People were selected but didn’t respond

👉 Example:

1000 people selected, only 300 reply



3. Response bias

People’s answers are influenced

👉 Causes:

  • leading questions

  • wanting to look good

  • pressure



3. Surveys (HOW questions affect answers)

Bad questions:

  • Leading → pushes you toward an answer
    👉 “Don’t you agree…?”

  • Double-barrelled → 2 questions in one
    👉 “Do you like school and your teachers?”

  • Confusing wording → unclear meaning



Types of questions

  • Open → write your own answer
    → good detail, hard to analyse

  • Closed → choose from options
    → easy to analyse



4. Validity vs Reliability (VERY IMPORTANT)

This is one of the most tested ideas.



Validity = are we measuring the RIGHT thing?

👉 Example:

  • Measuring happiness with an IQ test ❌
    → wrong thing → not valid



Reliability = are results CONSISTENT?

👉 Example:

  • Scale gives different weight each time ❌
    → not reliable



5. Experiments (CAUSE and EFFECT)



Two types of studies:

Observational study

  • Just observe

  • people choose their behaviour
    ❌ cannot prove cause



Experiment

  • researcher assigns treatment
    ✅ can show cause and effect



Key ideas:

Explanatory variable

→ the cause (what you change)

Response variable

→ the outcome (what you measure)



Confounding variable (VERY IMPORTANT)

👉 A hidden factor that affects BOTH things

Example:

  • Students attend tutorials AND get better grades
    BUT…
    → maybe they also study more

👉 That’s a confounder



Randomisation

👉 Randomly assign people to groups

WHY?

→ spreads confounding variables evenly



Control group

👉 Group that gets NO treatment

WHY?

→ gives something to compare against



6. Data (mean vs median)

Mean (average)

  • affected by extreme values

Median (middle value)

  • NOT affected by outliers

👉 Rule:

  • Skewed data → use median



7. Margin of Error (MOE)

Formula:

MOE = \frac{1}{\sqrt{n}}



What it means:

It tells you how uncertain your result is

👉 Example:

60% ± 3%

→ real value likely between 57% and 63%



Important:

  • Bigger sample → smaller MOE

  • MOE ≠ bias



8. Variables



Categorical

→ groups

👉 e.g. gender, colour



Measurement

→ numbers

👉 e.g. height, weight



Discrete

→ counts

👉 e.g. number of students



Continuous

→ measurements

👉 e.g. height, time