FIT4005 Chap.9 Inferential Statistics and Hypothesis Testing
Inferential Statistics and Hypothesis Testing
Most quantitative data is a sample, but the question is usually about a population. Week 9 explains how inferential statistics reason from one to the other and why that step is only valid when the sample is representative. It sets out probability sampling methods, simple random, systematic, stratified and cluster, and non-probability methods, convenience, purposive, snowball and voluntary response.
It defines hypothesis testing and the difference between parametric and non-parametric tests, and shows how within-subjects and between-subjects designs shape which test fits. The chapter adds the standard meanings of independent, dependent and confounding variables, and warns that a statistically significant difference is not automatically a large one.
The step from description to inference changes what you may claim.
A bar chart of a sample's answers describes that sample; saying how the whole population would answer is an inference, and it is only as good as the sample. That is why the unit spends time on sampling methods before tests, and why the design of the study, including who was measured and how often, determines which test is appropriate.
What this chapter covers
- 01
From sample to population
- 02
Representativeness and random sampling
- 03
Probability sampling methods
- 04
Non-probability sampling methods
- 05
Hypothesis testing
- 06
Parametric and non-parametric tests
- 07
Within-subjects and between-subjects designs
- 08
Independent, dependent and confounding variables
Worked example · free
Set up a comparison study
- +1Independent variable: interface version. Dependent variable: time taken to complete a booking.
- +1Design: randomly assign 20 students to each interface, a between-subjects design that avoids learning the task twice.
- +1Hypotheses: the null states that mean booking time is equal for both interfaces; the alternative states that it differs.
- +1Threat: if more experienced library users end up in one group, experience is a confounding variable; random assignment reduces this risk.
Key terms
- Population
- The entire group a researcher wants to draw conclusions about.
- Sample
- The subset of the population from which data are collected.
- Hypothesis testing
- A procedure for judging, from sample data, whether a claim about a population is adequately supported.
- Parametric test
- A statistical test that makes assumptions about the distribution of the population being sampled.
Inferential Statistics and Hypothesis Testing FAQ
Why does representativeness matter so much?
The Week 9 slides state that valid statistical inference depends on the sample resembling the population it stands for. That is why random sampling is used: it reduces the bias that would otherwise make conclusions about the population unreliable.
What is the difference between within-subjects and between-subjects designs?
Within-subjects designs measure the same participants more than once, under each condition. Between-subjects designs use separate groups, each measured once. The choice affects which statistical test is appropriate and which biases you must control.
Is voluntary response sampling acceptable?
It is a legitimate non-probability method for exploratory work, but people who opt in often differ from those who do not, so results cannot be generalised to the whole population with confidence.
What are parametric and non-parametric tests?
Parametric tests make assumptions about the distribution of the population being sampled, while non-parametric tests do not require those assumptions. Which one fits depends on your data and design, which is why the design must be settled before the test is chosen.
What should I ask before trusting a significant result?
Ask who the sample represents, how it was selected, whether a confounding variable could explain the difference, and how large the difference actually is. A statistically significant result can still be too small to matter in practice.
How does sampling differ between probability and non-probability methods?
In probability sampling each member of the population could be selected, through simple random, systematic, stratified or cluster methods. Non-probability sampling uses a non-random criterion, such as convenience, the researcher's judgement, referrals or volunteers, so generalising is riskier.
Assessment move
For each study you read, practise naming the population, the sample, the sampling method and whether it is probability based. Then identify the independent and dependent variables and one possible confounder. Keep the parametric and non-parametric definitions and the two design types side by side, since quiz items often turn on those distinctions.
When you see a significant result, ask how big the difference is and whether the sample supports the claim being made. Practise describing one study in four lines: population, sample and method, variables, and the claim the design can support.
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