CVEN9405 Chap.3 Transport Data and Statistical Inference
Transport Data and Statistical Inference
Transport datasets contain people, households, trips, days and zones, and those units cannot be exchanged casually. This chapter begins by identifying the independent observation before using sample size. It then develops sampling distributions, standard errors, confidence intervals and two-tailed hypothesis tests using the methods demonstrated in the workshop.
Statistical precision is kept separate from coverage, response and measurement quality. Worked examples show why the sample standard deviation and standard error answer different questions, how a critical value creates a margin of error, and why a statistically detectable effect still needs a planning-scale interpretation.
What this chapter covers
- 01
Observation units and dependence among repeated trip records
- 02
Sampling distributions and the central limit result
- 03
Standard deviation versus standard error
- 04
Confidence intervals and repeated-sampling interpretation
- 05
Null and alternative hypotheses for two-tailed tests
- 06
Statistical significance, practical magnitude and survey bias
Worked example · free
Test a stated mean and form the matching interval
- +1Standard error = 5.0/square root of 100 = 0.5 minutes.
- +1Test statistic = (8.6 - 7.5)/0.5 = 2.2.
- +1Since |2.2| exceeds 1.984, reject the stated null at the supplied threshold.
- +1Interval = 8.6 ± 1.984×0.5 = 8.6 ± 0.992, or 7.608 to 9.592 minutes.
Key terms
- Observation Unit
- The entity represented by one independent analytical record, such as a person, household, trip, day or zone.
- Sampling Distribution
- The distribution of a statistic across repeated samples drawn under the same design.
- Standard Error
- The estimated spread of a statistic's sampling distribution and therefore a measure of estimation precision.
- Confidence Interval
- An interval produced by a method with a stated long-run coverage rate under its assumptions.
- Null Hypothesis
- A precise reference statement about a population quantity against which sample evidence is compared.
Transport Data and Statistical Inference FAQ
Why are twenty thousand trip rows not necessarily a sample of twenty thousand people?
One person can contribute several trips, making those rows dependent for person-level behaviour. Precision calculations must use the correct observation unit or account for clustering and the survey design. Treating repeated trips as independent people can make standard errors far too small.
What is the difference between standard deviation and standard error?
Standard deviation describes variation among observed values, such as travellers' trip times. Standard error describes uncertainty in an estimated statistic, such as the sample mean. For a simple mean it is the sample standard deviation divided by the square root of sample size.
Does statistical significance mean a policy effect is important?
Not automatically. A large sample can detect an effect too small to influence a planning decision, while a meaningful effect can remain uncertain in a small sample. Interpret magnitude, interval, affected population, cost and operational relevance after reporting the statistical result.
Why should survey weights be used in transport estimates?
Sampling probabilities and response rates often differ across places or traveller groups. A weight lets each responding unit represent the appropriate share of the target population. Use the supplied design information, state the weighted population and apply variance methods that respect clustering and stratification rather than treating weights as simple frequency multipliers.
What does a confidence interval add to a point estimate?
A point estimate gives one best-supported value, whereas an interval communicates sampling uncertainty under the stated design and model. Its width helps distinguish a precise small effect from an uncertain large one. The interval does not automatically cover measurement error, nonresponse bias or a flawed sampling frame, which require separate assessment.
How should missing travel observations be investigated?
First describe missingness by variable, survey stage and relevant traveller groups. Determine whether absence is plausibly unrelated to the value, explained by observed information or associated with unobserved behaviour. Complete-case analysis, weighting adjustment and imputation rely on different assumptions, so report the chosen method and test sensitivity to credible alternatives.
Exam move
Start each data question by writing the observation unit and checking whether records are independent. Make a two-column card contrasting standard deviation with standard error, then derive the square-root sample-size relationship so you can catch implausible precision claims. Practise one confidence interval and one hypothesis test from the same sample because they share the standard error and critical value.
State the null and alternative before calculation, mark whether the test is one- or two-tailed, and write the test statistic with its sign. After the statistical decision, add two separate sentences: one about practical magnitude and one about data quality. For workshop-style datasets, trace how person, household and trip tables connect and count unmatched keys before calculating any rate.
Use small invented samples to check formulas by hand, then repeat with a spreadsheet. When revising, deliberately diagnose common errors: using the raw standard deviation in an interval, treating clustered trip rows as independent, choosing the tail after seeing the data, or claiming that failure to reject proves equality.
