EMET8002 Chap.1 Survey Data, Sampling and Hypothesis Tests
Survey Data, Sampling and Hypothesis Tests
Where the data come from
The course opens with survey data: how respondents are reached by door knock, telephone, post or web, how samples are drawn by simple random, stratified, cluster or multi-stage designs, and why weights restore representativeness.
The total survey error approach sorts the risks into errors of measurement and errors of representation.
Testing a claim
The second half sets out hypothesis testing: a null and an alternative written before the data are analysed, Type I and Type II errors, size and power, and the decision rules based on critical values and p-values.
The t-test, F-test and chi-squared test are matched to the kinds of variable being compared.
What the Week 2 lab rewards
The Week 2 lab sets three comparisons on ANU Poll data: age by gender, age by state, and gender by state.
Marks follow from naming the right statistic for each pair of variable types, writing the null in words before running anything, and reporting the p-value with the decision rather than a bare verdict. Exploring the age-group variable with descriptive statistics and graphs comes first, because a test on a variable you have not looked at is easy to misread.
What this chapter covers
- 01
Survey modes and their trade-offs
- 02
Simple random, stratified, cluster and multi-stage sampling
- 03
Total survey error
- 04
Dichotomous, categorical, ordinal and continuous responses
- 05
Null and alternative hypotheses
- 06
Type I and Type II errors, size and power
- 07
Rejection regions and p-values
- 08
Choosing a t, F or chi-squared test
Worked example · free
Reading a right-tailed test at the 5% level
- 1For a right-tailed test at 5%, the critical value is 1.645, the point with 5% of the standard normal area above it.
- 1The statistic of 2.33 lies above 1.645, inside the rejection region, so the null is rejected.
- 1The area above 2.33 is about 0.010, which is below 0.05 and agrees with the decision.
Key terms
- Stratified Sampling
- A design that divides the population into groups and samples within each group.
- Total Survey Error
- A framework that lists every source of error from measurement and representation to inference.
- Significance Level
- The probability of a Type I error that a test is designed to allow, often 5%.
- P-Value
- The probability, under the null, of a statistic as far from the null value as the observed one or further.
- Power
- One minus the probability of a Type II error, the chance of rejecting a false null.
Survey Data, Sampling and Hypothesis Tests FAQ
What is the difference between a Type I and a Type II error?
A Type I error rejects a null hypothesis that is actually true, like convicting an innocent defendant, and its probability is the significance level. A Type II error fails to reject a false null, like acquitting a guilty defendant; one minus its probability is the power of the test.
When should hypotheses be written?
The lecture insists they come before any data collection or analysis, grounded in theory or the literature and testable with the data available. Writing them first makes false positives less likely and gives a research project more credibility than adding variables to see what happens.
Which test compares a continuous variable across groups?
Use a t-test for two groups, such as age by gender, and an F-test for three or more, such as age across states and territories. Two categorical variables in a two-way table, such as gender by state, call for a chi-squared test of association.
Why does the course insist on weights in survey data?
Stratified, cluster and multi-stage designs select some groups with different probabilities from others. Without weights, the sample over-represents some people and under-represents others, so estimates describe the sample rather than the population. Weights restore the population shares, which is why the sampling slide ends on that single word.
What does failing to reject the null actually mean?
It means the sample does not provide enough evidence for the alternative at the chosen level. It does not prove the null is true, in the same way that a not-guilty verdict is not a finding of innocence. A larger sample or a more precise measure might still reveal an effect.
Assessment move
For each research question you meet, write the null, the alternative and its direction, then name the test the variable types call for. Practise reading one statistic two ways, against a critical value and through its p-value, until the two decisions always agree.
Finally, take one published survey you might use, such as an ANU Poll on the Australian Data Archive, and list which of the total survey error sources most threaten it, with one sentence on how each could bias your results.
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