Research Methodology and Statistics

Overview

Research begins when a vague curiosity is turned into a testable problem. A problem states a gap in knowledge or a practical need; a hypothesis states an expected relation between variables in a form that evidence could support or refute; an operational definition states exactly how each variable will be observed or manipulated. Sampling then decides whom the findings can speak about: random sampling supports generalisation to a defined population, while purposive or convenience sampling suits exploratory or hard-to-reach groups but limits generalisation. Measurement must be reliable, giving consistent results, and valid, measuring what it claims to measure. Analysis translates data into evidence, and interpretation translates evidence back into theory and practice, with limits stated honestly. Ethics runs through every stage, not as a form signed at the start, but as ongoing responsibility for consent, confidentiality, safety and honest reporting.

Research: meaning, problems, variables, ethics

Research is systematic inquiry designed to produce trustworthy, public knowledge. A good problem is significant, researchable and ethically studyable; it is neither so broad that no study could answer it nor so trivial that the answer matters to no one. Hypotheses may be directional, predicting the direction of a difference or relation, or non-directional, predicting a difference without direction. The null hypothesis states no effect or no difference and is the hypothesis that significance testing actually tests; rejecting it does not prove the research hypothesis true, it shows the data are unlikely under the null, given the test assumptions. Operational definitions are crucial because psychological concepts such as anxiety, attention or intelligence are constructs: they must be tied to observable indicators, whether a questionnaire score, a reaction time or a behavioural count, before they can be studied.

Variables are the vocabulary of design. The independent variable is manipulated or selected by the researcher; the dependent variable is measured as the outcome; extraneous variables are other influences that could affect the outcome; a confounding variable is an extraneous variable that varies systematically with the independent variable, so its effect cannot be separated from the treatment effect. Control means holding extraneous variables constant, balancing them across groups, or measuring them so their influence can be modelled. Ethics requires informed consent from participants who understand the study, its risks and their right to withdraw; protection from harm; confidentiality and, where promised, anonymity; debriefing after deception; special care with children, patients and other vulnerable groups; and honest reporting without fabrication, falsification or plagiarism. Deception is justified only when the study cannot be done otherwise, risk is minimal, and debriefing restores understanding.

Paradigms and methods of research

Quantitative research seeks measurement, comparison and generalisation, using experiments, surveys and structured observation, and it typically tests hypotheses with statistical analysis. Qualitative research seeks meaning, process and context, using interviews, focus groups, observation and case studies, and it typically builds understanding through thematic or narrative analysis. Mixed methods combine both, for example using a survey to map a pattern and interviews to explain it. Neither family is superior in general; the question decides. Counting how many students feel anxious does not explain what anxiety means in their lives, and a moving interview with three students does not establish a population rate.

Specific methods carry specific strengths and weaknesses. The experiment manipulates an independent variable under control and is the strongest design for causal claims, but laboratory artificiality and demand characteristics can threaten ecological validity. The quasi-experiment studies groups that already differ, such as existing classes, and is practical in field settings but weaker on causal inference because random assignment is absent. The survey reaches many people efficiently but depends on honest self-report and careful sampling. Naturalistic observation captures behaviour in context but cannot control variables and risks observer bias. The case study gives depth on a rare or complex instance but generalises weakly. Correlational designs measure relations as they occur, but correlation does not establish causation: a third variable, reverse causation or coincidence may explain the link. Longitudinal designs follow the same people over time and reveal change and order, while cross-sectional designs compare age groups at one time efficiently but confound age with cohort differences.

Statistics: central tendency, dispersion, NPC, tests

Descriptive statistics summarise data. The mean is the arithmetic average and uses every score, but it is pulled by extreme values. The median is the middle score and resists outliers, making it the better centre for skewed distributions. The mode is the most frequent score and is the only centre suitable for nominal data. Dispersion describes spread: the range is simple but driven by extremes; the variance is the average squared deviation from the mean; the standard deviation is its square root and returns spread to the original units, which is why it is the most used measure. A distribution can therefore be described by centre, spread and shape, and reporting a mean without spread, or a difference without an effect size, hides essential information.

The normal probability curve is a symmetrical bell-shaped distribution defined by its mean and standard deviation, with fixed proportions of cases falling within one, two and three standard deviations of the mean. Many statistical tests assume approximate normality, and standard scores convert raw scores to a common scale: a z-score states how many standard deviations a score lies from its mean, allowing comparison across different tests. Inferential statistics generalise from sample to population. A significance test asks whether an observed result is unlikely under the null hypothesis; the p-value is that probability, not the probability that the null is true. Type I error is rejecting a true null, while Type II error is failing to reject a false null. Common tests include the t-test for comparing two means, analysis of variance for comparing several means, chi-square for categorical association, and non-parametric tests such as Mann-Whitney and Wilcoxon when assumptions of normality or interval measurement fail. The examination habit to build is always to ask: what kind of data, how many groups, paired or independent, and are assumptions met?

Correlational analysis and regression

Correlation measures the strength and direction of a linear relation between two variables. The Pearson product-moment correlation ranges from minus one to plus one: positive values mean scores rise together, negative values mean one rises as the other falls, and values near zero mean no linear relation. Its square, the coefficient of determination, states the proportion of variance in one variable accounted for linearly by the other. Spearman rank correlation is used when data are ordinal or when the relation is monotonic but not linear, because it correlates ranks rather than raw scores. Point-biserial correlation handles one dichotomous and one continuous variable, and other coefficients exist for other data combinations. A scatterplot should always be inspected before interpreting a correlation, because outliers, restricted range and non-linear patterns can distort or hide a relation, and a strong correlation in a restricted sample may vanish in a wider one.

Regression goes beyond describing a relation to predicting one variable from another. Simple linear regression fits the line that minimises squared prediction errors, giving a slope that states the expected change in the outcome for a one-unit change in the predictor, and an intercept that states the predicted outcome when the predictor is zero. Multiple regression extends this to several predictors, showing each predictor's contribution while controlling for the others, and it raises new concerns: multicollinearity when predictors overlap heavily, overfitting when too many predictors chase a small sample, and the temptation to read prediction as causation. Regression is powerful for selection, forecasting and identifying predictors, but a regression coefficient is not a causal effect unless the design supports causal interpretation. Always report the correlation, the regression equation, the proportion of variance explained, and the limits of generalisation beyond the sampled range.

Factor analysis

Factor analysis is a family of techniques for discovering whether many observed variables can be explained by fewer underlying dimensions called factors. Suppose a battery of tests includes vocabulary, comprehension, arithmetic, spatial rotation, memory span and reasoning items. If scores on some tests move together across people, factor analysis asks whether a common factor, such as verbal ability or general reasoning, accounts for that pattern. Exploratory factor analysis discovers the factor structure without imposing it in advance; confirmatory factor analysis tests a pre-specified structure against data. The factor loading is the correlation between a variable and a factor, and high loadings mark the variables that define a factor. Eigenvalues summarise how much variance each factor explains, and the common practice of retaining factors with eigenvalues above one is a guideline, not a law, and must be checked against the scree plot and interpretability.

Rotation clarifies factor structure by redistributing loadings so each variable loads highly on few factors. Orthogonal rotation keeps factors uncorrelated, while oblique rotation allows factors to correlate, which is often more realistic for psychological abilities and traits. Factor analysis is invaluable for test construction, for testing theories of intelligence and personality, and for reducing many measures to manageable dimensions. Its limits are equally important: factors are mathematical summaries, and naming a factor does not prove a real psychological entity exists; different extraction and rotation choices can yield different solutions; large samples are needed for stability; and factor structure in one population need not replicate in another. A factor should therefore be validated against theory, replication and external criteria before it is treated as a discovered trait or ability.

Experimental designs

Experimental design is the architecture that lets a researcher attribute an outcome to a treatment rather than to chance, maturation or selection. The simplest designs compare an experimental group with a control group after random assignment, which balances known and unknown extraneous variables on average. Pre-test post-test designs add a baseline measure, allowing change to be assessed, but pre-testing itself can sensitise participants. Post-test only designs avoid that sensitisation and are clean when randomisation is sound. Within-subjects or repeated-measures designs expose each participant to all conditions, controlling individual differences powerfully, but they introduce order effects, practice and fatigue, which counterbalancing addresses by varying condition order across participants. Between-subjects designs avoid carryover but need larger samples to overcome individual differences.

Factorial designs manipulate two or more independent variables at once, revealing main effects of each variable and interaction effects where the effect of one variable depends on the level of another. Interactions are often the most interesting finding: a teaching method may help high-ability students and hinder low-ability ones, a pattern invisible in main effects alone. Threats to internal validity include history, maturation, testing, instrumentation, selection bias, attrition and regression to the mean. Threats to external validity include artificial settings, unrepresentative samples and reactive arrangements. Single-subject designs, with baseline and intervention phases for one participant, suit clinical and applied work where group averaging would hide individual change. The design lesson is cumulative: randomisation, control groups, counterbalancing and replication are not rituals; each blocks a specific alternative explanation, and a design is strong to the extent that its blocks match the plausible rivals for its claim.

Choosing a test

Designs and their main threat