Research Methodology and Statistics in Psychology

Research, hypotheses and variables. Kerlinger defines scientific research as systematic, controlled, empirical and critical investigation of hypothesised relations among phenomena; its purposes are exploratory, descriptive, explanatory and predictive, and its dimensions include basic versus applied and cross-sectional versus longitudinal. A research problem should be clear, researchable and significant, ideally a question about how variables relate. A hypothesis is a testable statement of a relation between variables: null H0 versus alternative H1, directional (one-tailed) or not (two-tailed). Rejecting a true H0 is a Type I error (α); retaining a false H0 is a Type II error (β). Variables are independent (manipulated), dependent (measured), extraneous or confounding, moderator (alters the strength of a relation) and mediator (carries the effect). An operational definition states a concept as the operations that measure it.

Sampling. Probability designs give every unit a known chance: simple random, systematic (every kth unit), stratified, cluster and multistage. Non-probability designs: convenience, purposive, quota and snowball (hidden populations). The standard error of the mean, σ/√n, falls as n rises.

Ethics in conducting and reporting. The Nuremberg Code (1947), the Declaration of Helsinki (1964) and the Belmont Report (1979: respect for persons, beneficence, justice) underlie the APA Ethics Code. Duties: informed consent, freedom to withdraw, minimal risk, confidentiality, deception only when unavoidable and always followed by debriefing, and ethics-committee review. Milgram's obedience studies and Zimbardo's prison study (1971) are the classic controversies. Reporting forbids fabrication, falsification and plagiarism, and requires honest authorship and data sharing.

Paradigms and quantitative methods. Quantitative research is deductive and statistical; qualitative research is inductive, seeks meaning in context and is judged by trustworthiness (Lincoln and Guba); mixed methods combine them (Creswell: convergent, explanatory sequential, exploratory sequential). Observation is naturalistic or controlled, participant or not; reactivity (the Hawthorne effect) threatens it. Surveys use interviews (structured to unstructured) or questionnaires. An experiment manipulates the IV with random assignment; a quasi-experiment lacks random assignment (Campbell and Stanley, 1963). Field studies trade control for realism. Cross-cultural studies guard against bias with back-translation and separate emic (culture-specific) from etic (universal) constructs.

Qualitative methods. Phenomenology describes lived experience by bracketing presuppositions (Smith's IPA). Grounded theory (Glaser and Strauss, 1967) builds theory from data by constant comparison and theoretical sampling to saturation, with open, axial and selective coding (Strauss and Corbin). Focus groups use about six to ten people and a moderator. Narrative research analyses life stories; case studies probe one unit in depth; ethnography is prolonged participant observation yielding Geertz's thick description.

Central tendency, dispersion and the normal curve. Use the mean for interval data, the median for ordinal or skewed data, the mode for nominal; for moderate skew, mode ≈ 3 median − 2 mean. Dispersion: range, quartile deviation (Q3 − Q1)/2, SD, and CV = SD/mean × 100. The normal probability curve is symmetric (mean = median = mode), asymptotic, with inflection points at ±1σ; ±1σ holds 68.26%, ±2σ 95.44%, ±3σ 99.73%, while ±1.96σ and ±2.58σ bound 95% and 99%. In positive skew, mean > median > mode. Garrett's kurtosis Ku = Q/(P90 − P10) is 0.263 for the normal curve; above it is platykurtic, below leptokurtic.

Parametric and non-parametric tests; power; effect size. Parametric tests assume interval data, normality and equal variances. The t-test compares two means: independent (df = n1 + n2 − 2) or paired (df = n − 1). Non-parametric counterparts: the sign test uses only the direction of paired differences; the Wilcoxon signed-rank test uses direction and ranked size (paired t); Mann-Whitney U compares two independent groups (independent t); Kruskal-Wallis H, three or more independent groups (one-way ANOVA); Friedman, three or more related conditions (repeated-measures ANOVA). Power = 1 − β, rising with n, α and effect size; 0.80 is Cohen's convention. Cohen's d = (M1 − M2)/SD: 0.2 small, 0.5 medium, 0.8 large; η² = SSbetween/SStotal.

Correlation. Pearson's r suits linear interval data, and r² is shared variance; Spearman's rho = 1 − 6Σd²/[n(n² − 1)] suits ranks. Partial correlation removes a third variable from both: r12.3 = (r12 − r13 × r23)/√[(1 − r13²)(1 − r23²)]. Multiple correlation R1.23 links one variable to the best weighted combination of others and runs 0 to 1. Biserial: continuous × artificially dichotomised; point-biserial: continuous × genuine dichotomy; tetrachoric: both artificially dichotomised, normal underneath; phi: both genuine dichotomies, φ = √(χ²/N).

Regression and factor analysis. Simple regression Y′ = a + bX by least squares, with b = r(SY/SX), a = Ȳ − bX̄ and standard error of estimate SY√(1 − r²). Multiple regression adds predictors; beta weights compare them, R² is variance explained, and multicollinearity distorts weights. Factor analysis assumes linear relations, an adequate sample, KMO adequacy and a significant Bartlett's test. Methods: principal components (Hotelling), principal axis, Thurstone's centroid, maximum likelihood; keep factors with eigenvalue > 1 (Kaiser) or above the scree elbow (Cattell). Rotation seeks Thurstone's simple structure: orthogonal (varimax) keeps factors uncorrelated, oblique (oblimin, promax) lets them correlate. Interpret a factor by naming what its high loadings (about .30 or .40 and above) share. Communality h² is a variable's sum of squared loadings across factors; an eigenvalue sums a factor's squared loadings.

Experimental designs. One-way ANOVA: F = MSbetween/MSwithin, df k − 1 and N − k; post hoc tests (Tukey, Scheffé) locate differences. Factorial ANOVA adds interaction. Randomized block designs remove block variance from error. Repeated-measures designs test everyone in every condition, need counterbalancing and assume sphericity. A Latin square puts each treatment once in every row and column, controlling two nuisance variables. Cohort studies follow a group sharing a characteristic over time; time-series designs measure repeatedly around an intervention. MANOVA handles several DVs (Wilks' lambda); ANCOVA adjusts the DV for a covariate such as a pretest. Single-subject designs (ABAB reversal, multiple baseline) compare treatment with baseline A.