Predict
Show the question and ask learners to commit to a prediction. Their reasoning matters more than whether they guessed correctly.
Instructor resources · Working draft
Don't press Run yet.
A good interactive lesson begins before anything moves. Ask students what they expect, run the experiment, and find out whether their explanation survives.
Use in class: These are instructor prompts for the current thirteen browser laboratories, not a complete instructor manual or validated assessment bank. The examples are marked fictional or historical in their respective lessons, and the explanations rely on their stated assumptions.
The three-part laboratory routine
Change exactly one thing
Keep as much of the model fixed as possible. If the answer changes, ask students to identify precisely which assumption or input moved.
Explain and qualify
Ask what the output supports, what it does not, and what additional evidence would matter for a real study.
Print a prediction worksheet → · View proposed syllabus
Fourteen weekly homework briefs → · Four unit-examination answer keys →
Demonstration scripts
Center and spread
Before: For 40, 45, 50, 55, and 60, what are the mean and median? What if the final value becomes 600?
Change: Move only the fifth observation and read the mean, median, and sample standard deviation.
After: Explain which summary stays resistant and why neither a mean nor median alone tells the whole distribution.
Visualizing distributions
Before: Will moving from four to sixteen histogram bins change the original observations, mean, or quartiles?
Change: Hold the synthetic data fixed while adjusting the number of equal-width bins; expand the frequency table.
After: Describe how a visualization choice changes perceived structure without changing the raw data.
Correlation and outliers
Before: Can moving one observation alter the sample Pearson correlation? Can it establish a cause?
Change: Move observation eight above and below the seven-point trend; inspect r and the full table.
After: Describe influence on a linear summary and explain why observational association is not a causal effect.
Survey nonresponse selection
Before: A population's views are fixed at 54% support. Could an honest survey report 63% without anyone changing their mind?
Change: Change the two groups' response probabilities; compare the respondent-weighted percentage with the fixed population percentage.
After: Use the expected response counts to explain group-composition bias; distinguish it from random sampling error.
Central limit theorem
Before: If individual observations come from a strongly skewed distribution, must their sample means also be just as skewed?
Change: Choose an exponential population; compare means from samples of 1, 5, 30, and 80 observations.
After: Identify which distribution becomes approximately normal and which remains right-skewed; discuss sample-size assumptions.
Normal probability
Before: What proportion lies between −1.96 and +1.96 under a standard normal model?
Change: Move the symmetric interval endpoints and watch both the curve area and numerical probability.
After: Distinguish density height, interval probability, and the interpretation of a confidence interval.
Bayesian base rates
Before: With 1% prevalence, 90% sensitivity, and 95% specificity, will most positive screening results be genuine?
Change: Hold test properties fixed and increase prevalence; inspect true and false positive expected counts.
After: Explain in ordinary language why sensitivity does not equal positive predictive value. The example is fictional.
Confidence interval coverage
Before: If a 95% confidence procedure makes fifty intervals, must exactly forty-eight contain the true parameter?
Change: Run several batches at 95%, then change to 90% or 99% and compare misses and interval width.
After: Explain the fixed-parameter/repeated-random-interval framework and why observed coverage fluctuates.
Exact binomial hypothesis test
Before: Under a fair-coin null model, should 18 heads in 20 tosses be surprising on a two-sided test?
Change: Change the observed count while preserving the null model, and identify the shaded extreme outcomes.
After: Interpret the exact p-value conditional on the null; distinguish it from P(null given data).
Simpson's paradox
Before: Could one recorded treatment success percentage be higher in both stone-size groups but lower overall?
Change: Switch between pooled and stone-size-specific historical success proportions.
After: Explain the differing case mixes and why neither pooled nor stratified observational rates prove causal superiority.
Bootstrap sampling
Before: If you repeatedly resample the same twelve observed waits with replacement, will every replicate have the same mean?
Change: Compare 200 and 3,000 replicates, inspect interval endpoints and the effect of the 39-minute wait.
After: Separate the bootstrap's Monte Carlo variability from information missing in the original sample.
Exact randomization inference
Before: For eight people randomly assigned in groups of four, how many balanced allocations are possible?
Change: Compare the two-sided and one-sided exact p-values for the fixed fictional outcomes.
After: Explain how design-based inference relies on the actual random assignment mechanism and pre-specified alternative.
Regression residual diagnostics
Before: Can the least-squares algorithm fit the optimal straight line and still miss a curved relationship?
Change: Increase the synthetic data curvature and compare fitted lines, R², and residual structure.
After: Describe a systematic residual pattern and why a high in-sample R² is not proof of causality or model validity.
Use the R Workbench responsibly
For a computation-heavy demonstration, first predict the sign or rough size of the statistic, then run a supplied base-R script, and finally change one assumption. The same approach works with the historical air-quality field notebook: ask how many observations will survive an `NA` audit before running the model.
A correct-looking answer is not enough. Require an interpretation with units, population, design, uncertainty, and at least one relevant limitation. Record which software and dataset were used.