Week 5 · Central Limit Theorem. t-distribution. Confidence intervals
Hypothesis testing II: from the population distribution to the sampling distribution of the mean, and the t-test in practice
Week 4 used t-tests; Week 5 explains where they come from. Starting from a normally distributed population, the deck derives the sampling distribution of the mean, the Central Limit Theorem and the standard error, introduces the t-distribution and confidence intervals, and then practises one-sample and two-sample t-tests on three examples. A self-study section and a set of t-score tables close the deck.
Slides
| Material | WS 2024/25 | WS 2023/24 |
|---|---|---|
| 🖥 Interactive slides | Week 05. Hypothesis testing II. Central Limit Theorem. T-distribution. Confidence intervals. t-test | not rendered (sources were revised for 2024/25) |
| 📄 PDF from Ilias | Week 05. Hypothesis testing II.pdf · 99 pages · added 12 Nov 2024 | Week 05. Hypothesis testing II.pdf · 80 pages · added 16 Jan 2024 |
| 💻 Source | mk68-05-slides-v2.qmd, which includes cct-2-simple.qmd, pop-dist-clt.qmd, ci-t-dist.qmd, mk68-05-slides-ex1.qmd, t-test.qmd and mk68-05-slides-t-scores.qmd |
mk68-05-slides-v2.qmd |
What the deck covers
- t-test with conditional cash transfers, the example carried over from Week 4.
- Normally distributed population and confidence intervals: the population distribution, the 95% interval for the mean, and 90%, 95% and 99% intervals; the population can have any distribution.
- The Central Limit Theorem, the standard error, a summary and the CLT in practice.
- The confidence interval and the t-distribution: how to find a CI, the t-distribution and how it differs from the normal, from the population to a sample, the t-distribution in use on the travel-time example, interpreting and calculating a confidence interval, and more on the t-distribution and the t-test.
- Practice: Example 1, the effect of a drug on sleep (one-sample t-test: the test of significance, confidence intervals, p-value, conclusion); Example 2, travel time between treatment and control (two-sample t-test, equal variances); Example 3, the causal effect of treatment on school enrolment.
- Extra materials for self-study: the four steps of a t-test, from hypothesis formulation to conclusion, with examples.
- t-scores: critical values of the t-distribution for 1 to 150 degrees of freedom.
- Homework on two published field experiments and the key concepts checklist.
Data used
sleep(Student’s sleep data) from base R, for Example 1.- A one-variable example dataset from the data-to-viz project, downloaded at render time.
- Simulated populations and samples for the travel-time and enrolment examples.
Where the course goes next
← Week 4 · Cause and effect in the RCT. Hypothesis testing. t-tests · → Week 6 · Simple and multiple regression. Bias. Linearity