DSC6008 Design of Experiments

How DSC6008 is assessed

The formal course outline publishes four weighted components, and the numeric weights total 100%. The final project instructions give the internal 5%, 20%, 10% and 5% split shown in the table.

Current DSC6008 dates

These dates are the published due dates visible on the course syllabus page for this offering. Confirm exact deadlines and submission settings in the live LMS.

What DSC6008 covers

Ten chapters move from experimental language and statistical evidence through regression, randomization, power, causal reasoning and one-way ANOVA.

A numerical method cannot recover information that was lost when treatments were assigned badly, experimental units were confused with repeated measurements, or a nuisance variable moved together with the factor of interest.

The guide therefore begins with the practical structure of an experiment and keeps returning to it whenever a formula is used.

The language that controls the analysis

A response is the measured outcome. A factor is an input studied because it may change that response, while a level is one chosen setting. A treatment is the complete combination of factor levels.

The experimental unit is the smallest object that can receive a treatment independently. Those definitions decide how many treatments exist, what counts as replication and which observations enter the denominator of a standard error.

They also reveal pseudoreplication: several readings on one assigned unit can improve measurement but do not become several independent experimental runs.

Probability and statistical evidence

The early statistical chapters separate variation among observations from uncertainty in a statistic.

Sampling distributions, standard errors, t references, confidence intervals and p-values are presented as consequences of repeated sampling under a stated design. A confidence interval gives a range of parameter values compatible with the data and assumptions; a p-value measures how extreme a test statistic is under the null reference. Neither quantity measures practical importance on its own.

Error rates belong to the decision rule, so the significance level must be chosen before the observed result is interpreted.

Regression as a model of conditional means

Simple and multiple regression express how the expected response changes with predictors. Coefficients are read in the units of the variables and conditional on the other terms in the model.

Indicator coding turns a categorical level into a comparison with a named reference group. Interactions allow the effect of one predictor to depend on another.

Residual plots then check whether a straight-line mean, constant variance and approximately normal error description remain plausible enough for the intended inference.

Three principles of experimental design

Randomization protects treatment comparisons against systematic allocation patterns. Replication supplies independent information about experimental variation.

Blocking groups similar units or run conditions so a known nuisance source is separated from the treatment contrast. These principles solve different problems, and none substitutes for another.

A randomized design with no replication cannot estimate pure experimental error, while extensive replication does not remove a bias created by assigning one treatment only on one day.

Randomization tests and simulation

A randomization test builds its reference distribution from assignments that could have occurred under the design.

The observed statistic is compared with statistics recalculated after repeated valid reallocations of treatment labels. Monte Carlo implementation replaces an exhaustive list with many random reallocations, so the estimated tail probability carries simulation error as well as sampling uncertainty.

The validity comes from respecting the assignment mechanism, not from shuffling labels without constraints.

Paired designs and trials

Pairing creates dependence deliberately by matching related observations, such as two measurements from the same subject or two similar units. The analysis reduces each pair to a within-pair difference and treats those differences as the independent values.

Clinical trial structure adds questions about treatment allocation, masking, comparison groups and the population to which a conclusion can travel.

The guide keeps the unit of randomization separate from the unit of observation because trial data can contain several measurements per participant.

Power and sample size

Power is the probability that a specified procedure rejects the null when a particular alternative is true.

It grows when the scientifically important effect is larger, the noise is smaller, the significance threshold is more permissive or the independent sample size is larger. Sample-size planning therefore requires an effect worth detecting, an estimate of variability, a target power and an allocation rule.

Changing any one input changes the design rather than merely changing an arithmetic answer.

Causal effects and observational comparisons

A causal effect compares potential outcomes for the same unit under different treatments, although only one can be observed. Random assignment makes groups comparable in expectation and supplies a design-based route to causal inference.

Observational studies need additional assumptions because treatment choice can share causes with the outcome. Confounding is represented as a common cause, and adjustment is justified only for variables that occur before treatment and help recover the intended comparison.

One-way ANOVA and diagnostics

One-way ANOVA partitions total variation into variation among group means and variation within groups.

The F statistic compares those mean squares and tests a global null that all group means are equal. A significant global test does not identify which means differ, so any multiple comparisons need a controlled follow-up procedure.

Residuals are then examined for changing spread, nonlinearity, unusual observations and distributional departures before the result is translated back into the experimental context.

How the published assessment fits together

The formal course outline assigns 30% to four assignments, 25% to a midterm covering Weeks 1 to 6, 5% to weekly quizzes and 40% to a cumulative final project.

The best five of six quizzes count. The project is completed in a group of two and includes a proposal, final report, five-minute video presentation, self-reflection and individual contribution.

The project instructions require randomization, genuine replication, blocking and at least three factors with at least two levels each.

Using this guide efficiently

For each chapter, begin by naming the experimental unit and the comparison being estimated. Recompute the numerical example without looking at the answer, then change one assumption and predict how the result should move.

In R, save the design table, model formula, diagnostic plots and session information together so that every reported result can be traced to an explicit analysis choice. For project work, freeze the randomization plan before collecting data and document any departure while it can still be explained honestly.

Worked example · free

Plan a balanced two-group comparison

Key terms

Response Variable

The measured outcome whose change the experiment is designed to explain.

Experimental Unit

The smallest unit that receives a treatment independently.

Factor

An input variable studied because it may influence the response.

Level

One selected setting or category of a factor.

Treatment

A complete combination of factor levels assigned to an experimental unit.

Randomization

Use of chance to determine treatment assignment or run order.

Replication

Independent application of a treatment to additional experimental units.

Blocking

Grouping similar units or conditions to isolate nuisance variation.

Standard Error

The estimated spread of a statistic across repeated samples under the design.

P-value

The null probability of a test statistic at least as extreme as the observed one.

Statistical Power

The probability that a procedure rejects the null under a specified alternative.

Causal Effect

A comparison between potential outcomes under different treatment conditions.

Mean Square

A sum of squares divided by its corresponding degrees of freedom.

Residual

The observed response minus the fitted response from a statistical model.

DSC6008 FAQ

Questions students ask in each DSC6008 chapter

Why is the experimental unit so important?

It decides what counts as independent information. Several readings from one assigned object may refine that object's measured response, but they do not create additional treatment assignments. Using the reading count as the sample size would make the reported uncertainty too small and the conclusion too confident. Chapter 01 · Experimental Questions and Design Vocabulary

Does the central limit theorem make the data normal?

No. It concerns the distribution of a statistic, usually a sample mean, across repeated independent samples. Individual observations can remain skewed. Confusing those two distributions leads to incorrect claims about what a raw-data histogram or residual plot should look like. Chapter 02 · Probability, Sampling and Diagnostic Plots

Is a p-value the probability that the null is true?

No. It is calculated under the assumption that the null model is true and measures how often that model would produce a statistic at least as extreme as the observed one. A probability assigned to the hypothesis itself would require a different inferential framework. Chapter 03 · Hypothesis Tests, Intervals and Error Rates

What does a regression intercept mean?

It is the fitted mean response when numeric predictors equal zero and categorical predictors are at their reference levels. That setting may or may not be scientifically realistic. If zero lies outside the useful range, centring a predictor can give the intercept a clearer interpretation. Chapter 04 · Regression Models and Coded Predictors

What does randomization protect against?

It prevents treatment assignment from following a systematic pattern tied to known or unknown influences. Randomization does not guarantee perfectly equal groups in one experiment, but it supplies a known assignment mechanism and makes design-based uncertainty calculations defensible. Chapter 05 · Randomization, Replication and Blocking

What makes a permutation valid?

It must be an assignment that the original design could have produced. A completely randomized experiment permits one set of reallocations, while paired or blocked designs require treatment labels to move only within pairs or blocks. Unrestricted shuffling changes the design and answers a different question. Chapter 06 · Randomization Tests and Monte Carlo Evidence

Why can pairing increase precision?

Pairing removes stable differences between matched units from the treatment contrast. When outcomes within a pair are positively related, the variation of their difference can be much smaller than the variation obtained by treating the groups as unrelated. Poor matching may offer little benefit. Chapter 07 · Paired Designs and Clinical Trials

Why must a power calculation specify an effect?

Power is not a property of a test alone. The chance of detection varies across alternatives, so planning needs a particular difference considered important enough to find. Choosing an unrealistically large effect can make the proposed sample too small for the scientific question. Chapter 08 · Power, Sample Size and Allocation

Why can only one potential outcome be observed?

A unit experiences one treatment condition at the relevant time, so its response under the alternative remains counterfactual. Experimental design addresses this missing-data problem by making groups comparable and estimating average effects, rather than revealing both outcomes for the same unit. Chapter 09 · Causal Effects and Potential Outcomes

What does the ANOVA F test compare?

It compares variation attributed to differences among group means with variation remaining among units within groups. Under the global null and model assumptions, both mean squares estimate the same error variance, so an unusually large ratio counts against equality of all means. Chapter 10 · One-Way ANOVA and Model Diagnostics

How to prepare for the assessments

Build one design-and-analysis ledger for the semester. For every exercise, record the research question, response, experimental unit, factors, levels, treatments, assignment rule, nuisance variables and intended statistic before calculating anything. Then solve the problem by hand far enough to predict signs, scales and degrees of freedom before using R.

After fitting a model, check residuals and translate the result into the original measurement units.

For midterm preparation, rotate among short definition checks, full calculations and design critiques because the published coverage spans Weeks 1 to 6. For the final project, freeze the run table and randomization plan before data collection, record genuine replicates separately from repeated measurements, and document blocks as they occur.

Rehearse the five-minute presentation around one visible chain: question, design, data, model, diagnostic, result and limitation. Keep an error log whose entries state the earliest wrong decision, not only the final wrong number. That habit turns each mistake into a reusable check for the next assignment or quiz.

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