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Monte

Frameworks

Five tools that work on any statistics problem. Use the first one when you freeze: answer three questions and it hands you the formula.

1. Which formula? Answer the questions

What is the question about?

2. The three moves in every probability question

  • OrAdd them, then subtract the overlap. Heart or face card = 13 + 12 − 3.
  • AndMultiply. Update the second count if there is no replacement.
  • GivenShrink the list to what you were told, then count inside it. The given goes on the bottom.

3. Four S for any word problem

  1. 1SketchDraw it: a bell with the cutoff, a tree, a two-way table. Ten seconds, and half the mistakes disappear.
  2. 2Set upWrite the formula with symbols before numbers. Name μ, σ, n, p. Decide sample or population.
  3. 3SolvePlug in. Say the ballpark out loud first, then use the calculator.
  4. 4Sanity checkIs it between 0 and 1? Is the SD smaller than the range? Is the average less noisy than one value? Put units on the answer.

4. The study loop

  1. 1LearnOne line and an example.
  2. 2LabDrag the control until the number makes sense.
  3. 3QuizAnswer before you reveal.
  4. 4DrillFresh numbers, on a clock.
  5. 5Due todayThe misses come back.

This is spaced retrieval practice with interleaving, the two study techniques with the strongest evidence (Dunlosky et al., 2013). Ten minutes a day through the loop beats an hour of rereading. Your topics on Practice only fill in from drills, on purpose.

5. Reading a question: the words that decide everything

If it says: at least one1 − P(none)Go to Probability, binomial
If it says: claim, significant, evidence that, test at 5%Hypothesis test: (estimate − H₀) / SE, then the p-valueGo to Hypothesis tests
If it says: given, of those, amongConditional: shrink the worldGo to Probability
If it says: average of n, sample mean, total of nStandard error σ/√n, or σ√n for a totalGo to CLT
If it says: per minute, per hour, arrivals, occurrencesPoisson; rescale λ to the windowGo to Poisson
If it says: n trials, each a success or failure, how manyBinomialGo to Binomial
If it says: within ± E, margin, how many to sampleSample size, round upGo to Confidence intervals
If it says: length of the intervalE is half the lengthGo to Confidence intervals
If it says: s instead of σ, small nt, not zGo to Confidence intervals
If it says: holding the others fixedA multiple regression coefficientGo to Multiple regression

6. Why the page is built this way

Plain sentence, then example, then formulaConcrete before abstractCognitive load research (Sweller)
A picture next to every ideaDual codingPaivio; Mayer's multimedia principles
Solved problems with the answer highlightedWorked examplesSweller's worked-example effect
Quiz mode and drillsRetrieval practiceRoediger and Karpicke; rated high utility in Dunlosky et al. (2013)
Missed questions come back laterSpaced practiceCepeda et al.; Dunlosky et al. (2013)
Drills mix topicsInterleavingRohrer and Taylor
Desk and court analogiesElaborative encodingDunlosky et al. (2013)
Timed sets pitched just above your levelFlowCsikszentmihalyi; self-determination theory (Deci and Ryan)