Research methods and statistics in psychology

Psychology (BA/B.Sc) · Applied psychology · free study notes for exams, placements and interviews

In short

Research methods and statistics is the toolkit that turns questions about behaviour into testable hypotheses, measurable variables and defensible numbers. It covers how a study is designed (experiment, quasi-experiment, correlational, survey, case study, qualitative), how participants are sampled, how data are described and how inferences are drawn using significance tests. It is the single heaviest-weighted unit in UGC NET Paper 2 (Psychology) and in CBCS BA/B.Sc Psychology degrees, and is compulsory in M.A./M.Sc entrance tests (CUET-PG, DU, TISS, NIMHANS, IIT Delhi/Gandhinagar HSS). Employers — market research and UX firms, CSR and development evaluators, HR analytics teams, clinical trial CROs and NGOs — hire psychology graduates mainly for exactly this skill set, tested in placement rounds through SPSS/Excel/R tasks and "which test would you use" questions.

Explained

Science, variables and hypotheses

Research is a systematic, empirical, replicable and self-correcting search for answers; psychology uses the hypothetico-deductive method — theory → hypothesis → operational definition → data → revision.
Variables: *independent* (IV, manipulated), *dependent* (DV, measured), *extraneous* (uncontrolled but influential), *confounding* (an extraneous variable that varies with the IV and ruins the inference), *mediator* (explains how IV affects DV), *moderator* (changes the strength or direction of the effect).
Operational definition: stating a construct in measurable terms — "anxiety = score on Sinha's Comprehensive Anxiety Test" — not the dictionary meaning.
Hypotheses: *research* (directional/non-directional statement), *null* H₀ (no difference/no relationship — the one actually tested), *alternative* H₁. Statistics can reject H₀ or fail to reject it; it never "proves" H₁.
Levels of measurement (Stevens): *nominal* (categories — gender, blood group), *ordinal* (rank — birth order, Likert positions), *interval* (equal intervals, arbitrary zero — IQ, temperature in °C), *ratio* (true zero — reaction time in ms, errors, income in ₹). The level decides the permissible statistic.
Controls: elimination, holding constant, randomisation, matching, counterbalancing (ABBA), statistical control (ANCOVA), and *blinding* (single/double) against experimenter and demand effects.

Research designs

True experiment: manipulated IV + random assignment + control group → the only design supporting causal claims. Types: *independent groups (between-subjects)*, *repeated measures (within-subjects)*, *matched pairs*, *factorial* (e.g. 2 × 3: two IVs, giving main effects and an interaction).
Quasi-experiment: pre-existing groups, no random assignment (gender, school type, caste category, disorder). Non-equivalent control group and interrupted time-series designs fall here.
Pre-experimental: one-shot case study, one-group pretest-posttest — weak, many confounds.
Correlational: measures two or more variables as they occur; shows association and prediction but not causation (third-variable and directionality problems).
Survey/field research: questionnaire, interview (structured, semi-structured, focus group), observation (naturalistic, participant, controlled; with time- or event-sampling and inter-observer agreement).
Developmental designs: *cross-sectional* (quick, confounded by cohort), *longitudinal* (shows change, suffers attrition), *cohort-sequential* (combines both).
Single-subject designs: ABA, ABAB, multiple baseline — standard in behaviour modification and special education.
Qualitative designs: phenomenology, grounded theory (open → axial → selective coding), narrative, ethnography, case study, thematic analysis; judged by credibility, transferability, dependability, confirmability and triangulation, not by p-values. *Mixed methods* combine both strands.
Validity of a design: *internal* (the IV, not something else, caused the change — threats: history, maturation, testing, instrumentation, regression to the mean, selection, attrition) and *external* (generalisability across population, setting, time; ecological validity).

Sampling and measurement quality

Population vs sample; parameter vs statistic. Sampling error is the natural difference between a sample statistic and the parameter; sampling *bias* is systematic and is the real danger.
Probability sampling: simple random, systematic (every kᵗʰ), stratified (proportionate/disproportionate — used when caste, gender or urban-rural strata matter), cluster, multi-stage (used in NFHS, NSSO-style surveys).
Non-probability sampling: purposive, quota, convenience, snowball (for hidden groups — substance users, sexual minorities). Most Indian student dissertations use convenience sampling — state it as a limitation.
Reliability (consistency): test-retest (temporal), parallel/alternate forms, split-half (corrected by Spearman-Brown), internal consistency (Cronbach's α; ≥ 0.70 acceptable, ≥ 0.80 good), inter-rater (Cohen's κ, ICC).
Validity (does it measure the construct): face, content (expert judgement, content validity ratio), criterion — *concurrent* and *predictive*, construct — *convergent* and *discriminant*, plus factorial validity via factor analysis.
Relationship: reliability is necessary but not sufficient for validity; a test's validity coefficient cannot exceed the square root of its reliability.
Standardisation and norms: uniform administration and scoring, with age/grade norms, percentiles, z-scores, T-scores (M = 50, SD = 10), stanines, sten and IQ (M = 100, SD = 15).
Item analysis: difficulty index (p), discrimination index (d), distractor analysis; modern tests use item response theory (item characteristic curves, difficulty/discrimination parameters) and check item bias / DIF — important in multilingual India.
Psychometric practice in India: translation plus back-translation and cultural adaptation are mandatory before using a Western test; Indian-developed tools include Bhatia's Battery of Performance Tests, Malin's Intelligence Scale for Indian Children (MISIC), Raven's SPM Indian norms, Seguin Form Board, Vineland Social Maturity Scale (Indian adaptation), NIMHANS Neuropsychological Battery, Sinha's Comprehensive Anxiety Test and the Kuppuswamy socio-economic status scale (income slabs revised for inflation each year).

Descriptive statistics

Frequency distributions: class intervals, histogram, frequency polygon, ogive (cumulative), stem-and-leaf, box plot.
Central tendency: *mean* (interval/ratio, affected by outliers), *median* (ordinal and skewed data, robust), *mode* (nominal, only measure for categories). Mean = median = mode in a symmetric distribution.
Variability: range, quartile deviation (semi-interquartile range), average deviation, standard deviation (most used), variance, coefficient of variation (relative, unit-free, in %).
Shape: *skewness* (positive = long right tail = a few very high scores; negative = long left tail) and *kurtosis* (leptokurtic = peaked, platykurtic = flat, mesokurtic = normal).
Normal probability curve (NPC): bell-shaped, symmetric, unimodal, asymptotic; mean = median = mode; total area = 1. ≈68.26% of cases within ±1σ, ≈95.44% within ±2σ, ≈99.73% within ±3σ; 95% of cases within ±1.96σ. Applications: converting raw scores to standard scores, fixing grades, computing percentiles, test standardisation.
Standard scores: z = (X − M)/σ makes scores from different tests comparable; derived scores (T, stanine, IQ) are linear transformations of z.

Inferential statistics and hypothesis testing

Sampling distribution and standard error: repeated sample means form a near-normal distribution (central limit theorem) with SE = σ/√n; SE falls as n rises, so precision improves with sample size.
Steps of hypothesis testing: (1) state H₀ and H₁; (2) fix α (0.05 or 0.01) and one- vs two-tailed; (3) choose the test and check assumptions; (4) compute the statistic and df; (5) compare with the critical value (or p with α); (6) decide and interpret in psychological terms.
Errors: *Type I* (α) = rejecting a true H₀ (false positive); *Type II* (β) = retaining a false H₀. Power = 1 − β; raised by larger n, larger effect, higher α, lower error variance, within-subjects designs. Power ≥ 0.80 is the convention; G*Power is the usual free tool.
Parametric tests (assume normality, interval data, homogeneity of variance, independence): *z-test* (σ known or large n), *t-test* — one-sample, independent-samples (equal/unequal variance, Levene's test), paired/correlated; ANOVA — one-way, two-way (main effects + interaction), repeated measures, mixed; ANCOVA; MANOVA. ANOVA uses the F ratio = MS between/MS within; a significant F is followed by post-hoc tests (Tukey HSD, Scheffé, Bonferroni).
Non-parametric tests (ordinal/nominal data or violated assumptions): chi-square (goodness of fit, independence), Mann-Whitney U (two independent groups), Wilcoxon signed-rank (two related), Kruskal-Wallis H (k independent), Friedman (k related), sign test, Spearman's rho, Kendall's tau. Less powerful when parametric assumptions do hold.
Effect size and estimation: Cohen's d (0.2 small, 0.5 medium, 0.8 large), η² and partial η², r² (variance explained), odds ratio; confidence intervals are now reported alongside p because p alone says nothing about magnitude. The replication debate (p-hacking, HARKing, pre-registration) is examined in recent UGC NET papers.
Correlation: Pearson r (interval, linear), Spearman rho (ranks), point-biserial, biserial, phi (two dichotomies), tetrachoric, partial and multiple correlation. r ranges −1 to +1; it is not a percentage and is unaffected by linear transformations. Causation needs covariation, temporal order and elimination of alternatives.
Regression: simple linear (Y′ = a + bX), multiple regression (predictors, β weights, R², multicollinearity), logistic regression for binary outcomes. Factor analysis (EFA — extraction, eigenvalues > 1, scree plot, varimax rotation; CFA within structural equation modelling) reduces many items to latent factors — the method behind the Big Five and most trait theories.
Software: SPSS and JAMOVI/JASP in Indian university labs, R and Python (pandas, statsmodels) in analytics jobs, Excel for basic work; SPSS output reading is a common placement task.

Ethics, reporting and Indian regulation

Core principles: informed consent (written, in a language the participant understands), assent plus parental consent for minors, voluntary participation and right to withdraw, confidentiality and anonymity, no deception unless scientifically necessary, debriefing, protection from harm, and no fabrication, falsification or plagiarism.
Indian framework: ICMR National Ethical Guidelines for Biomedical and Health Research Involving Human Participants (2017) govern research with human participants, including social and behavioural research; approval by an Institutional Ethics Committee (IEC) registered with CDSCO/DHR is required; the New Drugs and Clinical Trials Rules, 2019 apply to trials. Clinical trials are registered with the Clinical Trials Registry – India (CTRI) run by ICMR-NIMS.
Data protection: the Digital Personal Data Protection Act, 2023 governs digital personal data — notice, consent, purpose limitation and data-minimisation duties apply to online surveys and participant databases; its rules were notified in 2025 with phased compliance timelines, so check current deadlines before citing one.
Practice regulation: the Rehabilitation Council of India Act, 1992 governs registration of clinical psychologists (CRR) and the training route (M.Phil/now the postgraduate professional programme in clinical psychology); the National Commission for Allied and Healthcare Professions Act, 2021 sets up councils covering psychology-related allied professions, and its rollout is still in progress. The Mental Healthcare Act, 2017 requires capacity-based consent and confidentiality in any research with persons with mental illness.
Reporting: APA style (7th edition) — title, abstract, introduction with literature review and rationale, method (participants, tools, design, procedure), results (tables, figures, exact statistics with df, p, effect size, CI), discussion, limitations, references. Standard inline form: *t*(58) = 2.41, *p* = .019, *d* = 0.63. UGC-CARE listed journals matter for Indian publication credit.

Key points

Operational definition – restating a construct as something measurable; without it a hypothesis cannot be tested.
Null hypothesis – the "no effect" statement that is actually tested; it is rejected or retained, never proved.
Random assignment vs random selection – assignment protects internal validity; selection protects external validity.
Confounding variable – varies along with the IV, making the cause ambiguous; the main threat to experiments.
Levels of measurement – nominal, ordinal, interval, ratio; they determine which statistic is legitimate.
Reliability vs validity – consistency vs measuring the right thing; a reliable test can still be invalid.
Cronbach's α – internal consistency index; ≥ 0.70 is the usual acceptability cut-off.
Standard error – SD of a sampling distribution, σ/√n; halving it needs four times the sample.
Type I vs Type II error – false positive (α) vs false negative (β); lowering α raises β unless n rises.
Power – 1 − β, probability of detecting a real effect; target ≥ 0.80.
NPC areas – ±1σ ≈ 68.26%, ±2σ ≈ 95.44%, ±3σ ≈ 99.73%, ±1.96σ = 95%.
z-score – (X − M)/σ; makes scores from different tests comparable.
t-test vs ANOVA – two means vs three or more means; ANOVA avoids inflated Type I error from multiple t-tests.
F ratio – between-group variance ÷ within-group variance; a large F suggests real group differences.
Chi-square – non-parametric test for frequencies; needs expected frequency ≥ 5 in most cells.
Correlation ≠ causation – r shows covariation only; third variables and reverse direction remain possible.
Effect size – magnitude independent of n (d, η², r²); must be reported with p in APA 7th edition.
Indian ethics route – ICMR 2017 guidelines, IEC approval, informed consent; DPDP Act, 2023 for digital personal data.

Formulas and examples

Mean (ungrouped): M = ΣX / N — ΣX = sum of scores, N = number of scores; unit = unit of the score
Median (grouped): Md = L + [(N/2 − cf)/f] × i — L = lower limit of median class, cf = cumulative frequency below it, f = frequency of that class, i = class width
Standard deviation (sample): s = √[Σ(X − M)² / (N − 1)] — use N for a population (σ); unit = score unit
Coefficient of variation: CV = (s / M) × 100 (%)
z-score: z = (X − M) / σ (dimensionless); T = 50 + 10z; IQ = 100 + 15z
Standard error of mean: SE = σ / √N (or s/√N)
One-sample t: t = (M − μ) / (s/√N), df = N − 1
Independent-samples t: t = (M₁ − M₂) / √[s²pooled(1/n₁ + 1/n₂)], df = n₁ + n₂ − 2, where s²pooled = [(n₁−1)s₁² + (n₂−1)s₂²] / (n₁+n₂−2)
Paired t: t = D̄ / (s_D/√N), df = N − 1, where D̄ = mean of difference scores
Pearson r = Σ(X−Mx)(Y−My) / [(N−1) sx sy] (equivalently Σzxzy / N)
Spearman rho = 1 − [6Σd²] / [N(N² − 1)] — d = difference in ranks
Regression: Y′ = a + bX, where b = r (sy/sx), a = My − b·Mx
Chi-square: χ² = Σ[(O − E)² / E], df = (rows − 1)(columns − 1); E = (row total × column total)/grand total
One-way ANOVA: F = MS_between / MS_within; MS = SS/df; df_between = k − 1, df_within = N − k
Cohen's d = (M₁ − M₂) / s_pooled; η² = SS_between / SS_total
Spearman-Brown: r_full = 2r_half / (1 + r_half)
95% CI for a mean = M ± 1.96 × SE (large N; use t·SE for small N)

Example 1 — mean, SD, CV and z-score. Scores of 8 students on a 50-item memory test: 32, 28, 40, 36, 24, 30, 38, 32.

ΣX = 32+28+40+36+24+30+38+32 = 260 → M = 260/8 = 32.5
Deviations: −0.5, −4.5, 7.5, 3.5, −8.5, −2.5, 5.5, −0.5; squares: 0.25, 20.25, 56.25, 12.25, 72.25, 6.25, 30.25, 0.25 → Σ = 198
s = √(198/7) = √28.286 = 5.32; CV = (5.32/32.5) × 100 = 16.4%
Student scoring 40: z = (40 − 32.5)/5.32 = +1.41, i.e. T-score = 50 + 14.1 = 64.1, well above average.

Example 2 — independent-samples t-test. Mindfulness training (n₁ = 16, M₁ = 42, s₁ = 6) vs control (n₂ = 16, M₂ = 36, s₂ = 5) on a well-being scale; α = .05, two-tailed.

s²pooled = [(15 × 36) + (15 × 25)]/30 = (540 + 375)/30 = 915/30 = 30.5
SE of difference = √[30.5 × (1/16 + 1/16)] = √(30.5 × 0.125) = √3.8125 = 1.953
t = (42 − 36)/1.953 = 3.07, df = 30. Critical t = 2.042 → 3.07 > 2.042, so H₀ is rejected, p < .05.
Cohen's d = 6/√30.5 = 6/5.523 = 1.09 — a large effect. Report: *t*(30) = 3.07, *p* < .05, *d* = 1.09.

Example 3 — chi-square test of independence. 200 final-year students, stream by preference for a campus job.

Observed	Prefers campus job	Prefers higher study	Row total
Arts (n = 100)	70	30	100
Science (n = 100)	50	50	100
Column total	120	80	200

Expected = row × column / 200 → all four cells: 100×120/200 = 60, 100×80/200 = 40.
χ² = (70−60)²/60 + (30−40)²/40 + (50−60)²/60 + (50−40)²/40 = 100/60 + 100/40 + 100/60 + 100/40 = 1.667 + 2.5 + 1.667 + 2.5 = 8.33
df = (2−1)(2−1) = 1; critical χ² at .05 = 3.84, at .01 = 6.63 → significant at the .01 level. Stream and job preference are associated.

Example 4 — one-way ANOVA. Three teaching methods, n = 5 each (N = 15). Group means: A = 10, B = 14, C = 18; grand mean = 14. SS_within is given as 120.

SS_between = 5[(10−14)² + (14−14)² + (18−14)²] = 5[16 + 0 + 16] = 160
df_between = 3 − 1 = 2 → MS_between = 160/2 = 80; df_within = 15 − 3 = 12 → MS_within = 120/12 = 10
F = 80/10 = 8.00; critical F(2,12) at .05 = 3.89 → significant. η² = 160/(160+120) = 160/280 = 0.571, i.e. 57% of score variance is linked to method. Follow with Tukey HSD to find which pairs differ.

Example 5 — correlation, regression and NPC. For 30 students, stress (X: Mx = 40, sx = 8) and sleep hours (Y: My = 6, sy = 1.2) correlate r = −0.60.

r² = 0.36 → 36% of the variance in sleep is shared with stress; 64% unexplained.
b = r(sy/sx) = −0.60 × (1.2/8) = −0.09; a = 6 − (−0.09 × 40) = 6 + 3.6 = 9.6 → Y′ = 9.6 − 0.09X.
Predicted sleep at X = 50: Y′ = 9.6 − 4.5 = 5.1 hours.
NPC use: if stress is normally distributed, a score of 56 gives z = (56 − 40)/8 = +2.0, so about 97.7% of students score below it — the top 2.28% band.

Situation	Parametric test	Non-parametric equivalent
One sample vs known mean	One-sample t / z	Sign test
Two independent groups	Independent t	Mann-Whitney U
Two related measures	Paired t	Wilcoxon signed-rank
Three+ independent groups	One-way ANOVA	Kruskal-Wallis H
Three+ related measures	Repeated-measures ANOVA	Friedman test
Association, two continuous	Pearson r	Spearman rho
Association, two categories	—	Chi-square / phi

Where it is used

Market and consumer research: Nielsen, Kantar, Ipsos, IMRB-style agencies and in-house insights teams in HUL, ITC and Flipkart use sampling design, questionnaire construction, factor analysis and conjoint/regression modelling; psychology graduates enter as research executives.
UX and behavioural research: Zoho, Zomato, Swiggy, Razorpay, PhonePe and design studios run usability studies, A/B tests and eye-tracking with within-subjects designs and significance testing.
Assessment and HR analytics: psychometric firms (Mettl/Mercer, AON, SHL India, Thomas Assessments), DRDO's DIPR and the Services Selection Boards build and validate tests — item analysis, reliability, norming and adverse-impact checks.
Clinical, health and trial research: NIMHANS, AIIMS, PGIMER and CROs need IEC-approved protocols, CTRI registration, randomisation, blinding and outcome analysis for psychotherapy and neuropsychology studies.
Development and policy evaluation: J-PAL South Asia, IFMR/LEAD, Pratham ASER, UNICEF and state SCERTs run randomised controlled trials and large multi-stage surveys on learning, nutrition and mental health.
Academia and teaching: UGC NET/JRF, Ph.D. course work, dissertation guidance, SPSS/R workshops, and UGC-CARE journal publication for college and university posts.

Interview questions

Q: Why do we test the null hypothesis rather than the research hypothesis? A: The null makes an exact, falsifiable prediction (no difference), so a sampling distribution can be built for it; we can only show the data are improbable under it, which is indirect support for H₁.
Q: Difference between random selection and random assignment? A: Random selection draws participants from the population and protects external validity; random assignment allocates them to conditions and protects internal validity by equating groups.
Q: When would you use a non-parametric test? A: With nominal or ordinal data, small samples, markedly skewed distributions or heterogeneous variances — assumptions of parametric tests being violated.
Q: A study reports p = .04 with n = 2,000. Is the finding important? A: It is statistically significant but possibly trivial; with large n even tiny differences reach significance, so judge the effect size and confidence interval, not p alone.
Q: Can a test be reliable but not valid? A: Yes — a consistently mis-scored or wrong-construct test (a reading test used as an intelligence test) gives stable but meaningless scores; validity cannot exceed the square root of reliability.
Q: What does a correlation of −0.60 mean? A: A moderate-to-strong inverse linear relationship; as one variable rises the other tends to fall, and 36% of the variance is shared — but no causal direction is implied.
Q: Why is ANOVA preferred to multiple t-tests? A: Each t-test carries its own α, so three comparisons inflate the family-wise Type I error to about 14%; ANOVA tests all means in one F test at the stated α.
Q: How do you increase statistical power? A: Increase sample size, use a within-subjects or matched design, reduce measurement error, use a one-tailed test when justified, or accept a higher α.
Q: What is a confounding variable, with an example? A: An extraneous variable that changes with the IV — if the training group is also the younger group, age confounds the result; randomisation or statistical control removes it.
Q: Which ethical clearance is needed for a human-participant study in India? A: Approval from a registered Institutional Ethics Committee following the ICMR National Ethical Guidelines (2017), with written informed consent; clinical trials also need CTRI registration, and digital personal data falls under the DPDP Act, 2023.
Q: How would you adapt a Western personality test for use in Kerala? A: Translate and back-translate, check cultural appropriateness of items, pilot it, re-establish reliability and validity, test for item bias, and build fresh local norms.
Q: What is the difference between a mediator and a moderator? A: A mediator is the mechanism through which the IV affects the DV (stress → poor sleep → low performance); a moderator changes the strength or direction of that effect (social support weakening the stress effect).

Common mistakes

Writing the null hypothesis as a difference, or saying results "prove" the hypothesis instead of rejecting/retaining H₀.
Computing a mean on nominal or ordinal data (average of Likert categories, mean of roll-number codes) and ignoring levels of measurement.
Using N instead of N − 1 in sample SD, or forgetting to square deviations before summing.
Treating correlation as causation in discussion sections — the most penalised error in dissertation vivas.
Picking a test by habit rather than by design: running independent t on repeated measures data, or ANOVA on a 2 × 2 frequency table that needs chi-square.
Using chi-square with expected frequencies below 5, or on percentages rather than raw frequencies.
Reporting only p, with no df, effect size or confidence interval, and omitting sampling limitations and ethics approval from the method section.