University of Sydney · S2 2026 · FACULTY OF STATISTICS

DATA2002 Data Analytics: Learning from Data

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The Complete Exam Bible · S2 2026

DATA2002 Overview

Data Analytics: Learning from Data

— Week by week guide to USyd DATA2002: which test a data design actually permits, from chi-squared tables through the t and rank families to regression and classification, built for the 60% two hour final.

The University of Sydney
Semester 2, 2026
Level 2 undergraduate unit
Mathematics and Statistics
Six credit points

DATA2002 is the University of Sydney's intermediate unit in statistics and data science, taught by Mathematics and Statistics and worth six credit points.

Assessed by A 60 per cent written final exam of two hours, a three part group project worth 20 per cent, an individual project report worth 10 per cent, and weekly in class feedback exercises worth 10 per cent between them.
The organising idea Almost every mark is paid for choosing the procedure the data design permits and for writing a conclusion a reader could act on. The arithmetic in between is done by software.
Where the marks hide The weekly feedback exercises are sat in the workshop and are worth as much as the individual project report, so workshop attendance is worth ten per cent by another name.
Hardest habit Reporting a result in five lines every time: hypotheses, assumptions, statistic with its distribution, p-value, and a conclusion that names the variables and the population.
What the exam rewards Fast recognition of which test a scenario allows, and reading a printed result rather than producing one. The paper is sat without a calculator, so questions ask for the expression more often than the number.

DATA2002 · The University of Sydney

An independent, AskSia-authored study guide. AskSia is not affiliated with, endorsed by, or sponsored by The University of Sydney; the course code and name are used for identification only.

Assessment

How DATA2002 is assessed

Component	Weight	Format
Final Exam	60%	Written exam in the formal examination period, two hours, generative AI prohibited. The released sample paper for this offering is closed book with no calculator, thirty equally weighted multiple choice questions worth three quarters of the paper and one extended answer question worth the remaining quarter, with an Exam Guide of key procedures printed after the last question.
Group Project Report (Project 1)	10%	Group written work, due in Week 6, marked against a rubric published on the unit site. Not eligible for a simple extension because it is group work.
Individual Project Report (Project 2)	10%	Individual written work, due in Week 12, drawing on the whole unit. Eligible for special consideration and for an extension of up to ten days.
Individual Feedback Exercise	9%	An in class exercise sat in the weekly two hour workshop, assessing participation and understanding. Generative AI allowed.
Group Project Presentation (Project 1)	5%	Group presentation, due in Week 6, marked against a rubric. Not eligible for a simple extension because it is group work.
Individual GitHub Contribution (Project 1)	5%	A portfolio assessment of your own visible contribution to the group repository. Not eligible for a simple extension because it assesses collaboration inside the group work.
Individual Early Feedback Task	1%	The Week 3 feedback exercise, designated the early feedback task and sat in the two hour workshop. Generative AI allowed.

These seven components and their weights are what the University publishes on the unit of study page for the single 2026 offering, and they add to exactly 100 per cent. No component is a hurdle: the unit page states plainly that none of the tasks are hurdle tasks, so there is no double pass requirement and an overall mark of 50 is enough to pass. That is separate from a rule which is easy to confuse with a hurdle: the final exam is compulsory and must be attempted, and not attempting it results in an AF grade for the unit.

The two feedback exercise rows describe one stream. The unit runs eleven exercises across Workshops 1 to 5 and 7 to 12, each worth 1.25 per cent, and counts the best eight, capping the stream at 10 per cent, which is why the published table splits it into a 1 per cent early feedback task and a 9 per cent weekly row. Missing up to three is already priced into that rule and is not eligible for special consideration; missing more than three is what the reweighting provision exists for.

One rule links the two projects: if your Group Project Report mark is lower than your Individual Project Report mark, the individual mark replaces it, but that replacement does not apply when the Group Project Report mark is below 50 per cent. Late written work loses 5 per cent of the maximum mark for each calendar day and scores zero after ten calendar days. Weights and rules come from the unit of study page; confirm the exact submission settings on your own unit site.

Current dates · verify in LMS

Current DATA2002 dates

Date	Item	Control
6 September 2026	Group Project Presentation due	Week 6, at 23:59; closing date the same day
13 September 2026	Group Project Report due	Week 6, at 23:59; closing date 23 September 2026
13 September 2026	Individual GitHub Contribution due	Week 6, at 23:59; closing date the same day
1 November 2026	Individual Project Report due	Week 12, at 23:59; closing date 11 November 2026

Dates are as published in the unit of study page for the 2026 Semester 2 offering. Confirm exact deadlines and submission settings in the live LMS.

Contents · every chapter, one map

What DATA2002 covers

DATA2002 runs over thirteen weeks in four official modules. Weeks 1 to 3 work with categorical data, where a test statistic can be built from first principles and compared with a distribution you can name. Weeks 4 to 6 move to measurements and the normality question, answering it three ways: assume it and use a t test, avoid it with ranks, or dispense with it by resampling.

Weeks 7 to 9 generalise from two groups to many, which creates two new problems at once, the error rate across many comparisons and how to separate one factor from another. Weeks 10 to 12 change the goal from explaining the sample to predicting a new observation, which is why cross-validation exists. Week 13 is revision.

A weekly two hour workshop runs underneath the whole unit and is where the assessed feedback exercises are sat.

Working with data in R and reproducible reports

The analysis loop from import to plot, the four variable types that route every later method, cleaning decisions that must be recorded, and the version control the unit assesses in its own right. (Week 1)

The unit opens with software rather than statistics, and the reason is assessment shaped.

The analysis loop: import, inspect, clean, summarise, visualise, and the arrow back to cleaning
Two ways to call a function, and why naming the package is worth the keystrokes in written work
The pipe read aloud as and then, so a chain of steps reads as a sentence
Rows are observations, columns are variables, cells are values, and what to do when a heading is a value
Four variable types, and which module of the unit each one routes to
Numbers stored as text and categories stored as numbers: the two errors that survive longest

Study design: surveys, experiments and observation

Sampling and the three named bias families, the randomised controlled double blind design and what randomisation buys, confounding and its two conditions, and the reversal of an association when a third variable is conditioned on. (Week 1)

This chapter contains no test statistic and it decides the marks on the questions that do. Every method later in the unit ends in a sentence, and what that sentence is allowed to say is fixed here, by how the data came to exist.

Parameter against statistic: what the researcher wants to know against what the researcher knows
Why sample at all, and the sampling procedure questions that follow
Selection bias, non response bias and measurement bias, each with what goes wrong
The two stage failure in the 1936 survey, and why a larger frame would not have fixed either stage
Precision against accuracy, and which of the two sample size buys
The randomised controlled double blind design as five ordered steps

Hypothesis testing and chi-squared goodness of fit

The six reporting slots the unit marks against, where the chi-squared statistic comes from, degrees of freedom and the price of estimating a parameter, the expected count condition and pooling, and goodness of fit to a named count distribution. (Weeks 1 to 2)

This is where the unit stops describing data and starts making statements about the population behind it.

The six reporting slots, and why the first three can be written before any number
A hypothesis is a statement about population parameters, never about the sample
Two sentences the unit repeats: a large p-value is not evidence of the null, and the level is chosen in advance
Where the statistic comes from: square, divide by the expected count, add
Why only the upper tail is used, and why there is no lower tail p-value here
Degrees of freedom as two separate subtractions with two separate reasons

Diagnostic accuracy and measures of risk

Nine measures from one two by two table and the margin each conditions on, the base rate effect on predictive value, relative risk and the odds ratio, and the study design that decides which of the two you may compute. (Week 2)

A two by two table of counts is the smallest interesting object in this unit, and almost every quantity here is a ratio of two of its cells.

Two table layouts in one week, and why the first move is naming which one you have
The four cells, and why the first word grades the test rather than the news
Nine measures grouped by denominator: whole table, conditioned on truth, conditioned on result
Sensitivity against positive predictive value, and why only one is a property of the test
Conditional probability run in the direction a patient cares about
Working in natural frequencies rather than probabilities, which matters without a calculator

Contingency tables: homogeneity, independence, exact tests

Two tests that share every line of arithmetic and differ in what they may conclude, where the row times column rule comes from, and the exact and simulated methods for tables too small for the approximation. (Week 3)

This is the chapter that rewards reading a question twice. Two of the most frequently examined tests in the unit produce the same expected counts, the same statistic, the same degrees of freedom and the same p-value from the same table of numbers.

Which margins the design fixed, and why that is invisible in the table of counts
Homogeneity: several populations, each sampled at a size the investigator chose
Independence: one population, cross classified on two variables
Why both nulls produce the same expected counts and the same arithmetic
The expected count derived as an estimate of a product, rather than recalled as a rule
Two free arithmetic checks: expected rows sum to row totals, expected columns to column totals

Testing means with the t-test family

Where the t distribution comes from, the general estimator over standard error shape, one sample, two independent samples pooled and unpooled, and the paired design that changes the answer on identical numbers. (Week 4)

Module 1 counted observations into categories. From here the response is a measurement, and the first question about a measurement is almost always about its mean.

The general shape: estimator minus parameter over standard error, and the two conditions it needs
Where the t distribution comes from, and why its tails are heavier than a normal's
Estimator, estimate and standard error, and why the unit keeps the three words apart
The one sample test, its statistic and its degrees of freedom
The pooled two sample test, and the weighted average that produces the pooled variance
The unequal variance version, its approximate degrees of freedom, and why it is not a proper t statistic

Confidence intervals, power and sample size

Critical values under the unit's lower tail notation, the interval as the set of hypotheses a test would not reject, the two error rates, power as a curve rather than a number, and sizing a study with the round up rule. (Week 4)

A test can be wrong in two directions and the two are not treated symmetrically. The significance level fixes one of them by decree: when the null hypothesis is true, the chance of rejecting is exactly what you chose. Nothing guarantees the other.

The error table, and why only one of its two rates is guaranteed by the procedure
Why a very small significance level destroys the ability to detect anything
The lower tail definition of the critical value, and the three decision rules that follow
Splitting the level between two tails, and where the half comes from
One decision drawn on three scales: p-value, statistic, and the measurement itself
The interval as the set of hypothesised values a two sided test would not reject

Rank-based tests when normality fails

Checking normality honestly, the sign test as a binomial test on directions, the signed-rank test and the information it recovers, the rank-sum test for independent samples, and the statistic software prints instead of the one you computed. (Week 5)

Everything in the previous two chapters assumed the measurements came from a normal population.

Checking normality graphically, and why a histogram is unreliable at these sample sizes
The distribution free assumptions the three rank procedures actually need
The sign test as a binomial test on directions, with no degrees of freedom
Why zero differences are discarded, and how that changes the sample size
The four p-value branches, and doubling the tail the observation is actually in
The signed rank construction: rank the absolute differences, sum the positive ranks

Permutation tests and the bootstrap

Building a null distribution by rearranging labels, exchangeability as the single assumption, resampling with replacement for an interval, the percentile method, and the two readings of a confidence interval the unit rules out. (Week 6)

Every test so far has needed a named distribution for its statistic under the null hypothesis, and that requirement is what forced the assumptions. The previous chapter avoided it by changing the data into ranks.

The null hypothesis restated as a statement about labels rather than about parameters
Exchangeability, and the kinds of data that fail it
Why the statistic is free, and why a t statistic does not bring the t distribution with it
Enumerating every split when the samples are small, so the p-value is exact
Sampling the rearrangements at random when enumeration is impractical
The paired version, which permutes signs rather than labels

Multiple testing and error rate control

The outcome table for many hypotheses, three error rates side by side, how fast the family wise rate grows, the Bonferroni threshold and what conservative means, and the step up procedure that controls the false discovery rate instead. (Week 7)

Nothing in this chapter says any individual test was wrong. Each one, at the five per cent level, rejects a true null hypothesis five per cent of the time, exactly as designed.

The outcome table for many tests, and which of its six quantities you can ever see
The arithmetic that starts the argument: level times number of tests
The false positive rate, the family wise error rate and the false discovery rate, side by side
How fast the family wise rate grows with the number of independent tests
Which procedure controls which rate, stated as the pairing to memorise
The Bonferroni threshold, and the equivalent adjusted p-value

One-way ANOVA and post hoc comparisons

The sums of squares decomposition, the F ratio and its two degrees of freedom, contrasts and the union bound behind the Bonferroni multiplier, three multiplier methods and what each permits, and what to do when the assumptions fail. (Weeks 7 to 8)

With three or more groups the obvious move is a t test on every pair, and the previous chapter explains why that is a poor instrument: the comparisons multiply, the family wise error rate climbs, and each test throws away the information in the groups it is not looking at.

Why several t tests is the wrong instrument for more than two groups
What pooling the variance across all groups buys the comparisons
The decomposition identity, and why the cross terms vanish
Sums of squares and degrees of freedom both dividing, with two free arithmetic checks
The F ratio as a relative rather than an absolute comparison
The two degrees of freedom in order, numerator first

Two-way and two-factor analysis of variance

Blocking as the removal of a nuisance source and what it buys, the two way table, replication and the fourth row it creates, interaction and how to read an interaction plot, and the rank based test that ranks within blocks. (Weeks 8 to 9)

Real experiments rarely vary one thing at a time. Material arrives in batches, subjects differ from one another, machines drift between days.

Two roles for a second grouping variable, and the different table each produces
Blocking as the removal of a nuisance source, and the signature of a nuisance factor
What blocking buys, shown by analysing the same data with and without it
Why a block design cannot detect an interaction, as a property of the design
The three row table, and the degrees of freedom that must add
The block row as a housekeeping note rather than a finding

Linear regression and model interpretation

Least squares, the four assumptions and the plot that checks each, inference on a coefficient, r-squared and why it cannot select a model, confidence against prediction intervals, and the conditional reading of a multiple regression coefficient. (Week 10)

Module 4 changes the goal. Until now the explanatory variable has been a label naming a group; from here it can be a measurement, and the object of interest is a relationship rather than a set of differences.

The model as a claim about the mean response rather than about individual points
Least squares, and why the distances measured are vertical
The fitted line through the point of means, and the divisor of the variance estimate
Residuals as the raw material for every check and every standard error
Whether the intercept is interpretable, and the extrapolation test for deciding
The four assumptions and the plot that checks each

Model selection and assessing performance

Why in-sample fit always improves, information criteria and the direction of the comparison, stepwise and exhaustive search and why the two need not agree, and k-fold cross-validation with the whole procedure inside the loop. (Week 10)

The previous chapter ended on an uncomfortable fact: adding a predictor can never increase the residual sum of squares, so it can never reduce r-squared.

Why in sample fit always improves, as arithmetic rather than as evidence
Over fitting defined by what it does, and why it is invisible in the output
The shape of an information criterion: reward for fit, price per parameter
Lower is better, and how large a difference has to be to mean anything
Why a selected model can retain a term that is not individually significant
Forward selection, backward elimination and exhaustive search

Classification: logistic regression, trees, neighbours

Log-odds, odds and probability and where the neutral value sits on each, the confusion matrix and the accuracy figure that flatters a useless model, the complexity constant that runs backwards, and the number of neighbours that cannot be chosen in sample. (Weeks 11 to 12)

The response is now a category rather than a number, and two things change with it.

Why a straight line cannot model a zero or one response
Log-odds, odds and probability, and where the neutral value sits on each
The three step conversion, and why rounding partway through changes the answer
Why the printed statistic is a z and carries no degrees of freedom
The classification threshold as a separate decision from the model
The confusion matrix, its orientation, and what transposing it silently swaps

Dimension reduction and clustering

Supervised against unsupervised, components as directions of maximal variance, loadings against scores, how many components to keep when two rules disagree, reading a dendrogram by height, and what an unsupervised result can claim. (Week 12)

Every method in the unit so far has had a target: a count to model, a mean to compare, a number to predict, a label to get right. This chapter removes it.

Supervised against unsupervised, and what disappears when the target does
Dimension reduction works on the columns; clustering works on the rows
Why standardising first is the default for both
The maximal variance definition, and the unit length constraint that makes it well posed
The second component as the best direction uncorrelated with the first
Loadings against scores, one per variable and one per observation

It takes the hypothesis test you met in first year and turns it into a decision procedure: given data that arrived in a particular way, which analysis is defensible, what does it assume, and what may the conclusion say? The unit is organised into four official modules that widen the question in stages.

Module 1 works with categorical data, where a statistic can be built from first principles and compared with a distribution you can name, and it covers goodness of fit, diagnostic accuracy, measures of risk, and tests of homogeneity and independence with their exact small sample alternatives.

Module 2 changes the response from a count to a measurement, which forces the normality question, and answers it three ways: assume it and use the t test family, avoid it by working with ranks, or dispense with it by permuting and resampling.

Module 3 goes from two groups to many, which immediately creates two new problems, the error rate across many comparisons and how to separate the effect of one factor from another, and it answers them with multiple testing corrections and the analysis of variance.

Module 4 changes the goal altogether: instead of explaining the sample you predict a new observation, which is why in sample measures stop being sufficient and cross-validation appears, and it closes on classification and on methods that have no response variable at all.

Running underneath the whole unit is R, assessed directly through a reproducible report and a version controlled repository, and a weekly two hour workshop where the assessed feedback exercises are sat.

The final examination is worth 60 per cent, runs for two hours in the formal examination period, and the released sample paper for this offering describes it as closed book, sat without a calculator, with thirty multiple choice questions carrying three quarters of the paper and a single extended answer question carrying the rest.

Worked example · free

Route a scenario to a test before computing anything

Q [6 marks]. A hospital records, for 240 patients admitted through one emergency department over a month, whether each was discharged within four hours and which of three triage categories they were assigned. A second study takes 80 patients from each of the same three categories, in three separate samples, and records the same outcome. For each study, name the test, write the null hypothesis in words, and give the degrees of freedom. Then say what changes if the smallest expected count is 4.1. (6 marks. The mark allocation is ours, sized to the number of judgements, and is not a University marking scheme.)

The same absolute gap is worth different amounts depending on where it happens. Categories one and two are both off by 12, yet the second contributes more, because dividing by a smaller expected count magnifies the discrepancy. That is the whole reason the statistic divides. Reading a table this way is also the fastest route to a good sentence about where the model failed, which a bare total never gives you.

+2Read the sampling sentence in each study before anything else. In the first, one group of 240 patients was collected and then classified two ways, so only the grand total was fixed. In the second, three sample sizes of 80 were chosen in advance, so the row totals are design constants.
+1First study: a test of independence. The null hypothesis is that discharge within four hours and triage category are unrelated in this population, so the joint probabilities factor into their marginals.
+1Second study: a test of homogeneity. The null hypothesis is that the proportion discharged within four hours is the same in all three triage populations.
+1Degrees of freedom are the same for both, because the tables have the same shape: three rows and two columns give (3 minus 1) times (2 minus 1), which is 2. Only the wording of the hypothesis and the conclusion differ.
+1An expected count of 4.1 is below five, so the chi-squared approximation is not reliable and the ordinary test should not be reported. With a three by two table, either pool two triage categories if that still answers the question, or compute a simulated p-value with the margins held fixed.

Independence for the first study and homogeneity for the second, both on 2 degrees of freedom, with an exact or simulated method substituted when an expected count falls below five. The arithmetic is identical in the two studies and the conclusions are not: one names an association between two variables in one population, the other names a difference between three populations that were sampled separately.

Sia tip — Write the design sentence before you write anything you can compute. The two tests in this unit that share their entire arithmetic are told apart only by whether somebody chose how many observations would come from each row.

Glossary

Key terms

Test statistic: A quantity computed from the sample whose distribution is known when the null hypothesis is true. Comparing the observed value with that distribution is what produces a p-value, so a test statistic without a stated null distribution is not yet a test.
P-value: The probability, computed assuming the null hypothesis is true, of a test statistic at least as extreme as the one observed. It is not the probability that the null hypothesis is true, and a large one is a failure to find evidence rather than evidence of no effect.
Expected count: The count a cell of a table would contain on average if the null model held, computed as the row total times the column total divided by the grand total. The chi-squared approximation requires every expected count to be at least five, and the condition is checked on the expected counts rather than the observed ones.
Homogeneity: The hypothesis that several populations, each sampled separately with a size the investigator chose, share the same distribution of an outcome. Its arithmetic is identical to a test of independence and its conclusion is about groups rather than about two variables.
Odds ratio: The odds of an outcome under exposure divided by the odds without it, equal to the cross product of a two by two table. It is the same number whichever margin the table is conditioned on, which is why it can be estimated from a retrospective study when relative risk cannot.
Power: The probability of rejecting the null hypothesis when a specified alternative is true. It is a function of the true effect rather than a single number, and it rises with sample size and effect size and falls when the significance level is made smaller.
Exchangeability: The assumption that permuting the observations leaves their joint distribution unchanged. It is the single condition a permutation test needs, and it is weaker than the normality assumptions it replaces, though data with a time trend or a clustered structure do not satisfy it.
Family wise error rate: The probability of making at least one false positive across a family of tests. It grows quickly with the number of tests and is the quantity the Bonferroni correction bounds.
False discovery rate: The expected proportion of the results declared significant that are actually false. Controlling it is more permissive than controlling the family wise rate and is the usual choice when a screen produces a shortlist for follow up.
Interaction: The part of a cell mean in a two factor design that the two margins do not predict. When it is present the effect of one factor depends on the level of the other, so each main effect becomes an average over conditions in which the factor behaves differently.
Cross-validation: Splitting the observations into folds, holding each out in turn, fitting on the rest and predicting the held out fold. It estimates how a procedure will perform on data it has not seen, which no measure computed on the fitting data can do.
Loading: The weight a variable receives in a principal component, as distinct from a score, which is the value of that component for one observation. Loadings say what a component means; scores say where an observation sits along it.

FAQ

DATA2002 FAQ

What does this unit actually cover, week by week?

Four modules over twelve teaching weeks, with a revision week at the end. Weeks 1 to 3 are categorical data: the hypothesis testing framework, chi-squared goodness of fit, measures of diagnostic accuracy and risk, and tests of homogeneity and independence with exact alternatives for small tables.

Weeks 4 to 6 move to measurements: the t test family, confidence intervals, power and sample size, rank based tests for when normality fails, and permutation and bootstrap methods. Weeks 7 to 9 handle several groups and several factors: multiple testing corrections, one way analysis of variance with post hoc comparisons, and two way and two factor designs including interaction.

Weeks 10 to 12 turn to prediction: linear regression, model selection and cross-validation, classification with logistic regression, trees and nearest neighbours, and finally dimension reduction and clustering. R runs underneath all of it and is assessed in its own right.

How is the mark made up, and is anything a hurdle?

The final exam is 60 per cent. The rest is a three part group project worth 20 per cent between a presentation, a report and an individual assessment of your contribution to the shared repository, an individual project report worth 10 per cent, and weekly feedback exercises worth 10 per cent between the Week 3 early feedback task and the remaining weeks.

No task is a hurdle: the unit page states that none of the tasks are hurdle tasks, so an overall mark of 50 passes and there is no separate exam threshold. One rule is easy to mistake for a hurdle and is not one, which is that the final exam is compulsory and must be attempted, and not attempting it results in an AF grade.

What is the exam like, and what can I take in?

The unit page gives the weight and the conditions: 60 per cent, two hours, formal examination period, generative AI prohibited. The sample paper released for this offering describes the format, and it is worth planning around: ten minutes of reading time before two hours of writing, closed book with no material permitted, no calculators, a twenty eight page booklet, and two sections.

Thirty equally weighted multiple choice questions carry seventy five per cent of the paper and one extended answer question with several parts carries the rest, with working required. An Exam Guide summarising key procedures with their contexts and assumptions is printed after the last question. Read your own cover sheet on the day, because a sample is strong evidence rather than a promise.

How much R do I need to memorise?

Very little, and the unit says so directly: you are not expected to memorise the code, you are expected to understand what a piece of code is doing and how to interpret its result in context. In a closed book paper sat without a calculator, that translates into one specific skill, which is reading a printed result and saying which number answers the question.

The projects are the opposite: there you write and run the code, and the reproducibility of the report and your contribution to the shared repository are both assessed.

How do the weekly feedback exercises actually count?

There are eleven of them, run in Workshops 1 to 5 and 7 to 12. Each is worth 1.25 per cent and the best eight are counted, which caps the stream at 10 per cent and is why the published table shows it as a 1 per cent row for the Week 3 early feedback task and a 9 per cent row for the rest. Missing up to three is already priced into the best eight rule and is not eligible for special consideration.

Missing more than three, for example through prolonged illness, is what the mark adjustment provision is for.

How do the two projects fit together?

Project 1 has three assessed components in Week 6: a group presentation, a group report and an individual assessment of your own contribution to the group's repository.

Project 2 is an individual report in Week 12. A progress mark adjustment runs between them: if your Group Project Report mark is lower than your Individual Project Report mark, the individual mark replaces it, but not when the Group Project Report mark is below 50 per cent.

So a weak group report is worth rescuing to the pass line first and only then worth improving through Project 2. The group components and the repository assessment are not eligible for simple extensions, because they are group work.

A question describes a study without naming a test. How do I choose?

Answer four questions in order. What is the response: a count, a measurement or a label? How many groups are being compared: one, two, or more than two? Are the observations paired, meaning each one is matched to exactly one in the other group? And what is the goal: to test a hypothesis, to estimate something with uncertainty, or to predict a new case?

Those four answers narrow the field to one or two candidates before you write anything. One extra sentence matters for tables of counts: if the sizes of the groups were chosen in advance the test is one of homogeneity, and if a single sample was classified two ways it is one of independence.

Is this a heavily mathematical unit?

It is quantitative rather than proof heavy. Formulas are derived rather than dropped in, so you see where the chi-squared statistic comes from and why the analysis of variance ratio is a ratio, but the assessment rewards choosing and interpreting procedures rather than reproducing derivations.

The assumed knowledge is a first or second year unit in statistics or data science with a substantial coding component, and the unit expects you to be comfortable using R before you start.

Chapter questions

Questions students ask in each DATA2002 chapter

Do I have to memorise the R functions for the exam?: No, and the unit says so explicitly: you are expected to understand what a piece of code is doing and how to interpret its result in context, not to reproduce it from memory. The closed book paper reflects that by handing you printed output and asking which number answers the question. What is worth memorising is the shape of the common printouts, so that you can find the statistic, the degrees of freedom and the p-value at a glance, and the vocabulary of variable types, because that is what routes a scenario to a method. Chapter 01 · Working with data in R and reproducible reports
If a survey gets millions of responses, is it not reliable?: Not if the procedure that produced them is biased. The unit's opening example is the case in point: a survey with 2.4 million replies called an election wrongly while a much smaller well drawn sample called it correctly. Sample size buys precision, meaning a narrower interval around whatever the procedure is estimating. It does not buy accuracy, meaning that the thing being estimated is the quantity you wanted. A biased procedure applied at scale produces a confident wrong answer, which is worse than an uncertain one. Chapter 02 · Study design: surveys, experiments and observation
Why is the p-value always the upper tail here?: Because the statistic measures distance from the model in any direction and turns all of it into a positive number. A large value means the observed counts sit far from what the model predicted, which is evidence against it. A small value means they sit close, which is agreement rather than evidence, so there is nothing for a lower tail to detect. That is different from the t tests later in the unit, where the statistic is signed and the direction of the alternative decides which tail or tails are used. Chapter 03 · Hypothesis testing and chi-squared goodness of fit
Why does a very accurate test still mostly raise false alarms?: Because accuracy conditions on the truth and a positive result does not. Take a test that is 90 per cent sensitive and 95 per cent specific used where 2 per cent of people have the condition. In 20,000 people, 400 have it and 360 are flagged; 19,600 do not and 5 per cent of them, 980, are also flagged. So 360 of 1,340 positives are correct, about 27 per cent. Nothing is contradictory: sensitivity is computed among people who have the condition, predictive value among people who tested positive, and when the condition is rare the second group is dominated by healthy people. Chapter 04 · Diagnostic accuracy and measures of risk
If the arithmetic is identical, why does it matter which test I name?: Because the conclusion differs, and the conclusion is where the marks are. A test of homogeneity concludes that the groups which were sampled differ in their outcome distribution. A test of independence concludes that two variables are associated within one population. Those are statements about different things, and a script that computes the right number and attaches the wrong sentence has answered a question that was not asked. The hypotheses differ too, so the loss is usually more than one mark. Chapter 05 · Contingency tables: homogeneity, independence, exact tests
How do I tell a paired design from two independent samples?: Ask whether each observation in one group is matched to exactly one in the other by something in the design. The same subject measured before and after, two measurements on the same item, litter mates, the left and right of one object: all paired. If the two groups are simply two sets of units with nothing linking member to member, they are independent, and one visible clue is that their sizes need not be equal. A paired design with unequal group sizes is a contradiction and usually indicates that something has been lost. Chapter 06 · Testing means with the t-test family
Why does making the significance level smaller reduce power?: Because a smaller level moves the critical value further from zero, and the test then rejects less often whatever the truth is. Fewer false alarms and fewer genuine detections come together, so the Type II error rate rises as the Type I rate falls. The intuition that a stricter test is a better test is misleading here: strictness is precisely what a Type II error is made of. The only lever that reduces both error rates at once is collecting more data. Chapter 07 · Confidence intervals, power and sample size
If rank tests need fewer assumptions, why not always use them?: Because when the normality assumption really holds, the t test is more powerful and the rank tests will miss effects it would find. Discarding information buys immunity and costs sensitivity, and paying that cost when nothing is wrong is a waste of real data. The choice should be made from the diagnostic plot and the design before any p-value is seen, which is the one part of the decision that is not negotiable: running all three and reporting the most favourable is the genuinely indefensible move. Chapter 08 · Rank-based tests when normality fails
What is the difference between a permutation test and a bootstrap?: They answer different questions and are used at different points. A permutation test answers a testing question by rearranging labels under a null hypothesis, and it produces a p-value. A bootstrap answers an estimation question by resampling with replacement, and it produces an interval. The mechanics look similar because both involve repeated resampling, but a question asking whether there is a difference wants the first and a question asking how uncertain a number is wants the second. Chapter 09 · Permutation tests and the bootstrap
Which procedure controls which rate?: Bonferroni controls the family wise error rate, and the step up procedure controls the false discovery rate. The pairing is easy to swap under pressure, which is exactly why it is examinable. Attach each name to its own sentence: Bonferroni to at least one false positive, and the step up rule to the proportion of my discoveries that are false. If you can say those two sentences, both procedures follow from them. Chapter 10 · Multiple testing and error rate control
Why not just run a t test on every pair of groups?: Two reasons. The comparisons multiply, so the chance of at least one false positive climbs with the number of groups, which grows quadratically. And each pairwise test estimates the spread from only the two groups it involves, throwing away the information in the others. The analysis of variance asks one question once and estimates the spread from every observation, which makes the follow up comparisons sharper than standalone ones would have been. Chapter 11 · One-way ANOVA and post hoc comparisons
What does blocking actually buy me?: It moves a real source of variation out of the residual term and into a row of its own. Since every F ratio has the residual mean square in its denominator, shrinking that denominator makes every comparison sharper. The effect can be decisive: the same treatments can be strongly significant when the block effect is removed and unremarkable when it is not, from identical data. That is why recording a known nuisance variable at the design stage is worth the trouble even though its own row is rarely of interest. Chapter 12 · Two-way and two-factor analysis of variance
Which interval does a question want?: The wording tells you. Estimate the average response for cases with this value asks for the confidence interval. Predict the response for a new case with this value asks for the prediction interval. The word average or mean against the word predict or a new individual case is the discriminator, and it is often the only difference between two otherwise identical parts of a question. The prediction interval is always the wider of the two. Chapter 13 · Linear regression and model interpretation
Why can r-squared never fall when I add a predictor?: Because the model without the new predictor remains available as a special case: setting its coefficient to zero recovers the previous fit exactly. Least squares will therefore never do worse than that, so the residual sum of squares can only stay the same or fall, and r-squared can only stay the same or rise. A criterion that always rewards more complexity cannot be used to decide how much complexity to have, which is the whole reason this chapter exists. Chapter 14 · Model selection and assessing performance
Why does the same result get reported on three different scales?: They are three scales for the same information and the neutral value moves between them. A logistic coefficient is a log-odds, neutral at zero, and it may be any real number. Its exponential is an odds ratio, neutral at one, and it is always positive. Applying the logistic function gives a probability between zero and one. A negative coefficient therefore corresponds to an odds ratio below one, and comparing an odds ratio against zero rather than against one is the most common slip in reading this output. Chapter 15 · Classification: logistic regression, trees, neighbours
What changes when there is no response variable?: The tools for judging a result disappear. With a target you can measure an error, count correct labels and hold data out to see how a procedure behaves on cases it has not seen. Without one there is no accuracy and no cross-validation, so a result becomes a description that has to be argued for rather than a prediction that can be checked. That does not make the methods unscientific; it means the interpretation you supply is part of the finding and has to be stated with its assumptions. Chapter 16 · Dimension reduction and clustering

Study strategy

How to study for the exam

Build the routing table first and keep adding to it. One page with the four questions down the side, response type, number of groups, paired or not, and goal, and the tests down the other, will do more for your mark than rereading the formulas, because most multiple choice items in this unit are recognition questions rather than calculations.

Second, practise writing the five reporting lines for a method you only half remember: hypotheses, assumptions, statistic and its distribution, p-value, conclusion in context. Several of those lines carry marks on their own, so a structurally complete answer with a missing statistic scores most of the way while a blank scores nothing.

Third, keep a single sheet of directions, because this unit is full of statements that are easy to reverse: the prediction interval is the wider one, lower information criterion values are better, a larger complexity constant gives a smaller tree, the log-odds scale is neutral at zero and the odds ratio scale at one.

Fourth, do the workshop exercises when they are set rather than before the exam, since they are assessed weekly and only the best eight count, so an exercise skipped in Week 4 cannot be recovered in Week 10. Fifth, treat every printed result you meet as a comprehension exercise: cover the interpretation, decide which number answers the question, then check.

Since the paper is sat without a calculator, spend your final revision writing expressions and degrees of freedom rather than finishing arithmetic, and make sure that every practice answer you write ends with a sentence naming the variables and the population rather than stopping at the decision.

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