Research Methodology — Cheat Sheet

Research types & philosophy

• Basic = discover knowledge; Applied = solve a problem.
• Quantitative (numbers/stats) · Qualitative (meaning/context) · Mixed (both).
• Positivism: one objective reality, observable only.
• Post-positivism: reality exists, knowledge is fallible/approximate.
• Constructivism: reality is socially constructed; knowledge co-constructed.

Research problem

• Problem = knowledge gap, phrased as a question.
• Iterative refinement: broad → context → population → variables → outcome → time.
• Fishbone diagram: problem (head) + cause categories (bones).
• 5-whys: dig to root cause.
• Aim (broad goal) · Objectives (specific/measurable) · Deliverables (outputs).
• Feasibility: Time, Resources, Ethics, Data, Scope.

Research design

problem -> objectives/hypothesis -> design -> sample -> instrument
        -> collect -> clean -> analyze -> interpret -> report

Validity = measuring the intended construct. Reliability = consistency. Triangulation = combining methods, investigators, theories, or data sources.

Sampling and statistics

P(A|B) = P(A intersection B) / P(B)
P(A intersection B) = P(A|B)P(B)

Power is the probability of detecting a real effect. Alpha is the tolerated false-positive rate. A p-value is interpreted relative to the null hypothesis and chosen decision rule; it is not the probability that the null hypothesis is true.

Ethics and CS research

• Protect participants with consent, minimisation, confidentiality, secure storage, access control, retention limits, and honest reporting.

• Experiment = real system; simulation = model. Validate simulations and report assumptions.

• H₀ (no effect) vs H₁ (directional or non-directional).

• Experimental = manipulate + control + randomise.

• Non-experimental = observe as-is (association only).

• Exploratory (discover) → Descriptive (what) → Causal (why).

• Randomisation: simple, block, stratified.

• Control group = baseline (no/wait-list treatment).

• Validity: construct, internal, external, statistical.

• Reliability: test-retest, parallel-forms, internal consistency (α).

• Triangulation: multiple methods/data sources.

Measurement & scaling (NOIR)

• Nominal (names) — mode, frequency, χ².
• Ordinal (order) — median, percentile, rank.
• Interval (equal gaps, no true 0) — mean, SD, r.
• Ratio (true 0) — geometric mean, CV, all statistics.
• Rating scales: Likert (agree), Thurstone (judged), semantic differential (bipolar).
• α ≥ 0.7 acceptable; reliability is necessary but not sufficient for validity.

Sampling

• Population (target) · Sampling frame (list) · Sample (studied).
• Probability: simple random, systematic, stratified, cluster, multi-stage.
• Non-probability: convenience, purposive, quota, snowball, judgment.
• Sample size (means): n = z²·σ² / d².
• Sample size (proportions): n = z²·p(1−p) / d² (use p=0.5 for max n).
• FPC for small populations: n_adj = n / (1 + (n−1)/N).
• Sampling error ∝ 1/√n (reduce); sampling bias (eliminate via design).
• Quantitative → power + precision; Qualitative → saturation.

Data analysis

• Descriptive: mean/median/mode; SD/variance/IQR; histograms, box plots, scatter.
• Pearson r: r = Σ((x−x̄)(y−ȳ)) / √(Σ(x−x̄)²·Σ(y−ȳ)²); correlation ≠ causation.
• Linear regression: y = a + bx; b = Σ((x−x̄)(y−ȳ))/Σ(x−x̄)²; R² = variance explained.
• Cleaning: validate, handle missing, outliers (z>3 or 1.5×IQR), standardise, dedupe.

Statistics / hypothesis testing

Step 1  H₀ (no effect)  vs  H₁ (effect; directional or not)
Step 2  Choose α (usually 0.05) and the test
Step 3  Compute statistic  z / t / F / χ²  and p-value
Step 4  If p < α  ⇒  REJECT H₀  (significant)
         else        ⇒  FAIL TO REJECT H₀

Test	When	Statistic	df
Z-test (one mean)	large n or σ known	z=(x̄−μ₀)/(σ/√n)	∞
t-test (one mean)	small n, σ unknown	t=(x̄−μ₀)/(s/√n)	n−1
Paired t-test	before/after same subjects	t = d̄/(s_d/√n)	n−1
Two-sample t	two independent means	t=(x̄₁−x̄₂)/√(s_p²(1/n₁+1/n₂))	n₁+n₂−2
F-test	compare two variances	F = s₁²/s₂²	n₁−1, n₂−1
χ² independence/fit	categorical counts	χ²=Σ(O−E)²/E	(r−1)(c−1)

• One-tailed: directional H₁ (more power, blind to opposite).
• Two-tailed: non-directional (safer).
• p = P(data | H₀), NOT P(H₀ | data).
• Report effect size + CI (significance ≠ importance).

Probability

• 0 ≤ P(A) ≤ 1; P(S)=1.
• P(A∪B) = P(A)+P(B) − P(A∩B) (subtract if not mutually exclusive).
• P(Aᶜ) = 1 − P(A).
• P(A|B) = P(A∩B)/P(B); independent iff P(A|B) = P(A).
• Bayes: P(A|B) = P(B|A)·P(A) / P(B).
• E[X] = Σx·P(x); Var(X) = E[X²] − μ².
• CLT: for large n, sample-mean ~ Normal ⇒ Z/t-tests justified.

Writing & IPR

• IMRaD: Introduction, Methods, Results, And, Discussion (+ Conclusions).
• Cite: APA (author-date), IEEE/ACM (numbered).
• LaTeX: separate content/formatting; BibTeX for refs; $$...$$ for maths.
• IPR: Patent (invention, ~20y) · Copyright (writing, long) · Trademark (brand) · Trade secret.
• Proposal structure: problem → gap → approach → contribution + timeline + risks.
• Evaluation plan (CS): dataset, baselines, metrics, statistics.

CS research

• CS = artefact + analysis + evaluation.
• Areas: AI/ML, Systems, Theory, HCI, Security, Networks, SE, Data, Graphics, IoT.
• Methods: experimental (real), simulation (model), analytical (proof).
• Proposal: problem → gap → approach (with evaluation plan) → contribution.

Ethics

• Belmont: Respect for persons · Beneficence · Justice.
• IRB/REC: protocol + consent + risk review; continuing review; vulnerable groups.
• Privacy: minimise, anonymise/pseudonymise, secure, comply (GDPR/HIPAA), retain then delete.
• Misconduct: Fabrication · Falsification · Plagiarism (FFP); HARKing; gift/ghost authorship.

Distributions (parameters)

Distribution	Mean	Variance
Bernoulli(p)	p	p(1−p)
Binomial(n,p)	np	np(1−p)
Poisson(λ)	λ	λ
Uniform(a,b)	(a+b)/2	(b−a)²/12
Normal(μ,σ²)	μ	σ²
t(df)	0	df/(df−2)

Key thresholds

• α = 0.05 (standard), 0.01 (stringent).
• α ≥ 0.7 (Cronbach's).
• n ≥ 30 (CLT/large-sample rule of thumb).
• Expected counts ≥ 5 per cell (χ² assumption).
• |r| 0.1 (small), 0.3 (medium), 0.5 (large).
• Cohen's d 0.2 (small), 0.5 (medium), 0.8 (large).