Items run from scaffolded to unassisted. Whatever support you use is recorded alongside your answer, because a correct answer after substantial help is not the same evidence as an independent one.
Review set
The questions ask you to complete a decomposition and to say what a significant result does and does not establish. The arithmetic returns easily; the pull toward reading a particular group comparison out of an omnibus result is what needs unlearning.
Review set
The questions ask you to convert between odds, risks and probabilities using a baseline rate, and to catch a result stated on a scale it was not estimated on. The conversion returns easily; noticing the silent substitution in someone else's prose is what needs practice.
Review set
The questions ask you to work out which estimator a design requires and to judge somebody else's analysis, rather than to repeat a calculation you have already done. Computing a weighted average comes back easily; noticing that an analysis has quietly discarded the design does not.
Review set
The questions ask you to say what a confidence level describes and to read magnitude and precision from an interval rather than only whether it excludes zero. The construction returns easily; the pull toward treating the interval as a probability about the parameter is what needs unlearning.
Review set
The questions ask you to decide which allocations a design permits and to judge what somebody else's p-value established, rather than to repeat an enumeration you have already done. Counting allocations comes back easily; knowing which set to count does not.
Review set
The questions ask you to work out which standard error a described study supports and to judge what somebody else concluded from a p-value. The formulas come back readily; spotting a paired design described in unfamiliar words does not.
Review set
The questions ask you to say what a coefficient means given how the model was parameterised, and to recover a group gap that varies. The algebra returns easily; remembering that a main effect is the effect at a particular point is what needs practice.
Review set
The questions ask you to form weights and to say what their distribution reveals about whether a comparison is supported. Forming a weight comes back readily; reading a weight of 400 as a limit of the evidence rather than a computational annoyance is what needs unlearning.
Review set
The questions ask you to say what a coefficient reports and to resist the two upgrades regression output invites, from association to cause, and from explained variation to a good model. The formulas return readily; the reflex to treat a high fit statistic as reassurance is what needs unlearning.
Review set
The questions ask you to name the quantity a matching scheme targets and to notice when a matched comparison is being described as though a coin had been tossed. The procedure returns easily; tracking which units the estimate still describes is what needs practice.
Review set
The questions ask you to judge an interval someone else computed and to say what it does and does not cover, rather than to repeat the calculation. Recomputing a standard error is the part that comes back easily; knowing what the number leaves out is the part worth checking.
Review set
The questions here ask you to separate what a study observed from what it never could, in settings you have not seen before, rather than to repeat the easiest thing you can still do. Hints stop short of supplying the answer, because recalling it is the point.
Review set
The questions ask you to judge a fitted assignment model by the right evidence and to say what it leaves untouched, rather than to restate a definition. The formula returns easily; the habit of reaching for classification accuracy is what needs unlearning.
Review set
The questions ask you to meet an unfamiliar procedure and decide whether it is randomization at all, and to compare designs that look alike but license different conclusions. Recognising a named mechanism is not what has to survive the delay; judging an unfamiliar one is.
Review set
The questions ask you to screen a specification and say what the adjustment is doing, rather than to restate a rule. Which covariates are admissible comes back readily; the reflex to treat controls as a remedy for a broken design is what needs unlearning.
Review set
The questions ask you to say what a standard error describes and to notice when the data are not the independent observations a formula assumes. The arithmetic returns easily; the habit of counting rows instead of independent units is what needs unlearning.
Review set
The questions ask you to state what a study assumes and to say which part of it the data could speak to, rather than to recall a definition. The two assumptions are easy to name and easy to conflate, and the difference between them is what decides whether a balance table means anything.
Review set
The questions hand you a point and ask which constraints hold with equality there, including the nonnegativity restrictions that are easiest to overlook. Taking the set returns quickly; deciding position by the rank of the normals rather than by counting them is what needs practice.
Review set
The questions ask which bases are adjacent, which way the edge between them runs, and how far you can walk along it. Computing the direction returns quickly; remembering that adjacency is about shared columns rather than distance, and that only falling variables bound the step, is what needs practice.
Review set
The questions give you a column set and ask what it determines, sometimes a feasible point, sometimes a point outside the region, sometimes nothing at all. The construction returns quickly; keeping the sign test as a step of its own, rather than assuming it from a clean solve, is what needs practice.
Review set
The questions ask you to spot a degenerate solution from its components and to say what follows for an algorithm walking between corners. The count is quick to recall; telling degeneracy from multiple optima, and reading a tie in the ratio test as a warning, is what needs practice.
Review set
The questions ask you to state a system both ways and to pick the reading that answers what is being asked. Naming the two pictures returns easily; reaching for the column reading when the question is whether something is possible at all is what needs practice.
Review set
Selection, exclusion, implication and fixed charges, arriving in situations described in prose rather than as named patterns. Writing the constraint is quick once the pattern is named; noticing that a sentence is an implication, and that a written constraint forbids nothing, is what needs practice.
Review set
The questions ask which variables genuinely need whole-number values and what the restriction does to the problem. Naming the three program types returns quickly; resisting integrality on divisible quantities, and remembering that the vertex account does not survive, is what needs practice.
Review set
The questions give you a relaxation value, sometimes with a candidate plan beside it, and ask what follows. The bound's direction returns quickly; keeping it apart from an achievable value, and refusing the rounding that always looks available, is what needs practice.
Review set
The questions give you an objective and ask which way the contour travels, including minimisations and negative coefficients. Drawing the family returns easily; keeping the direction right when the problem is a minimisation, and settling a doubtful direction by the sign of a dot product, is what needs practice.
Review set
The questions ask you to read a reduced system and say which of the three outcomes holds, and to resist deciding it from the shape of the original. Elimination returns readily; telling redundancy from contradiction, and describing a set rather than a point, is what needs practice.
Review set
Construct the point a basis determines, decide whether it is feasible, and price the nonbasic columns. The two competences are drilled together because the common failure is to run the optimality test on a basic solution that is not feasible, where the verdict means nothing.
Review set
Situations described in words, to be turned into variables, an objective and constraints. The descriptions vary in what they leave implicit, a unit that must be inferred, a restriction stated as a ratio, a quantity that sounds like a variable and is data, because reading the description is the part that does not transfer from worked examples.
Review set
Plot the region, locate the direction of improvement, and push the objective until it leaves. Cases are chosen so the answer is not always a single corner: one has parallel contours giving a whole edge of optima, one recedes without limit, and one is empty.
Review set
Problems arriving without a label saying which technique they want. Deciding that is the competence assessed here, and it is the one a set of chapter-grouped exercises cannot train: a learner who has practised each method in its own section has never had to choose between them.
Practice set
Practice distinguishing the terminal outcomes of a linear program. Each case is paired with the feature that makes it hard: an unbounded feasible set that still has a finite optimum, and constraints that are satisfiable in pairs but not all at once.
Review set
Programs carried through successive pivots until a stopping condition fires. Both representations appear, and not every run ends in an optimum: one terminates on an entering column with no positive entry, and one produces a degenerate basis on the way.
Practice set
Formulate a program, drive a named solver with it, and verify the answer against the model as written. Tool use is an item permission rather than a requirement: a learner without Excel or MATLAB is never excluded from the objective, only from the items that name those tools.
Review set
Programs arriving in every shape the conversion rules have to handle: a maximisation, a constraint pointing the wrong way, a variable free in sign, a bound that is not zero. Mixed rather than grouped by rule, since deciding which conversion a line needs is the part that is assessed.
Review set
The questions ask you to move between the row and column readings of a product and to choose whichever answers the question posed. Computing
Review set
The questions hand you a program, a tableau, or a solver line and ask which outcome holds and what decides it. Naming the four cases comes back quickly; deciding feasibility without reaching for the objective, and telling a genuine tie from two close numbers, is what needs practice.
Review set
The questions ask you to place a boundary and then say which side the inequality permits, including constraints that have been multiplied through by a negative. Drawing the line comes back quickly; testing a point rather than trusting the inequality symbol is the habit these are here to keep.
Review set
The questions hand you a model and a report and ask which checks pass. Running the checks is quick; remembering to test against the model as you wrote it, rather than against the input the solver read, is what needs practice.
Review set
The questions ask which substitution a restriction calls for and what it leaves behind. The substitutions themselves come back quickly; remembering the constant a shift puts in the objective, and that a split pair is not unique, is what needs practice.
Review set
The questions ask you to say what a dot product measures in a situation, and to recognise one inside a constraint that never uses the word. The arithmetic returns quickly; noticing that a coefficient row applied to a point is the same operation is what needs practice.
Practice follows each lesson, so what you are asked matches where you are in the route.
Data Visualization and Reporting
Causal Inference from Experiments and Observational Data
Inferential Foundations for Experimental Research
Knowledge Representation and the Semantic Web