Final study guide
The information below provides an overview of the final exam: what it covers, how to prepare, and the format. The final is tentatively scheduled for Monday, June 8 at 1:10pm.
Scope
The final is comprehensive in scope — any material covered in lecture, labs, or assignments could appear. The material for the course broadly falls under two umbrellas:
Statistical inference from continuous data
- one- and two-sample \(t\)-tests and confidence intervals
- analysis of variance (ANOVA) and effect sizes
- nonparametric alternatives to \(t\)-tests and ANOVA
- simple linear regression
Statistical inference from categorical data
- exact and approximate tests and intervals for proportions
- \(\chi^2\) tests (goodness of fit and independence)
- relative risk and odds ratios
- treatment efficacy
All of the methods above are instances of population parameter estimation, hypothesis tests, and confidence intervals. Thus, you are expected to be fluent with respect to the following general concepts and their specific manifestations in the above-listed methods:
- population/model parameters
- sample statistics and point estimates
- standard errors and sampling variability
- sampling distributions
- interval coverage and construction
- statistical hypotheses and alternatives
- test statistics and \(p\)-values
- type I and type II errors
- statistical power
These ideas are very general and provide a core conceptual framework for statistical methodology that extends well beyond the scope of this class.
Textbook references
| Topic | V&H sections |
|---|---|
| Study design and data semantics | 1.1–1.5 |
| Descriptive statistics | 1.4–1.5 |
| Point estimation and sampling variability | 4.1 |
| Confidence intervals | 4.2 |
| One-sample \(t\)-tests | 4.3 |
| Two-sample \(t\)-tests | 5.2–5.3 |
| One-way ANOVA | 5.5 |
| Nonparametric methods | (lecture notes) |
| Simple linear regression | 6.1–6.3 |
| Inference for proportions | 8.1 |
| \(\chi^2\) tests | 8.4 |
| Relative risk and odds ratios | 8.5 |
Conventional reporting style
Results should be reported using precise, context-specific language. The templates below illustrate the expected style.
Point estimate
The mean total HDL cholesterol among the U.S. adult population is estimated to be 5.043 mmol/L (SE 0.0191).
Confidence interval
With 95% confidence, the mean total cholesterol among U.S. adults is estimated to be between 5.006 and 5.080 mmol/L.
Hypothesis test (one-sample \(t\)-test; two-sided)
The data do not provide evidence that the mean body temperature differs from 98.6°F (T = −1.328 on 38 degrees of freedom, p = 0.192).
The data provide evidence that the average U.S. adult does not sleep 8 hours per night (T = −42.53 on 3178 degrees of freedom, p < 0.0001).
\(\chi^2\) test
The data provide evidence of an association between asthma and sex (\(\chi^2\) = 3.62 on 1 degree of freedom, p = 0.057).
Relative risk
With 90% confidence, the risk of asthma is estimated to be between 1.08 and 2.28 times greater for women than for men.
Note that test statistics, degrees of freedom, and \(p\)-values are always reported parenthetically, and interpretations are stated in terms of the research question rather than in terms of the hypotheses themselves.
Format
The test comprises a series of short data analyses in which quantitative results are provided for you. In each analysis, there are several prompts which require you to interpret results in context or perform simple subsequent calculations.
The test is closed-computer. You may consult any written or printed (i.e., non-digital) notes and are allowed the use of a calculator. Digital devices are not permitted.
My recommendation: prepare a concise reference sheet covering key formulas, definitions, and result templates, and bring printed copies of any class notes you find useful.
Preparation
I recommend preparing a set of review notes based on the above. One straightforward strategy would be to list the “core concepts” for each main method and identify one example from a past assignment.
The one-sample \(t\)-test.
Method
- Population/model parameters: population mean \(\mu\)
- Sample statistics: sample mean and SD \(\bar{x}, S_x\)
- Point estimate: \(\hat{\mu} = \bar{x}\)
- Standard error: \(SE(\bar{x}) = \frac{S_x}{\sqrt{n}}\)
- Sampling distribution: \(t_{n - 1}\) model for \(\frac{\bar{x} - \mu}{SE(\bar{x})}\)
- Interval: \(\bar{x} \pm c \times SE(\bar{x})\), where \(c\) is a quantile from the \(t\) model
- Statistical hypothesis and alternatives: \(H_0: \mu = \mu_0\) and \(H_A: \mu \mathrel{\substack{>\\\neq\\<}} \mu_0\)
- Test statistic: \(T = \frac{\bar{x} - \mu}{SE(\bar{x})}\)
- \(p\)-value: from \(T\) model, proportion of samples exceeding observed test statistic in the direction of the alternative
I also recommend reviewing the following:
- Lecture slides and notes
- Textbook readings (see table above)
- Lab activities and homework assignments
- The midterm and midterm practice problems
- The final practice problems