A complete visual revision system for research logic, ethics, paradigms, qualitative and quantitative methods, statistical tests, correlation, regression, factor analysis and experimental designs.
Research का लक्ष्य केवल “significant result” पाना नहीं है—सही प्रश्न, उचित design, ईमानदार analysis और सीमाओं सहित defensible conclusion बनाना है।
Try a broader statistical term or method name.
Meaning, purpose, dimensions and scientific cycle
Research is a systematic, empirical, transparent and critical inquiry designed to develop or evaluate knowledge.
Research = व्यवस्थित प्रश्न + प्रमाण + तर्क + जाँच योग्य निष्कर्ष।
Describe → Explain → Predict → Control/Influence; also explore, evaluate, understand lived meaning and support social change.
Clear problem, justified design, valid measures, ethical conduct, appropriate analysis, reproducibility/transparency and bounded claims.
Basic: theory/knowledge. Applied: practical problem. Action: local plan–act–observe–reflect.
Exploratory, descriptive, correlational, explanatory/causal, predictive and evaluative.
Cross-sectional, longitudinal, cohort, prospective/retrospective and time-series.
Quantitative, qualitative or mixed; laboratory, field or natural setting.
Turn an interesting idea into a testable map
Clear, researchable, theoretically or socially significant, feasible and ethical. It identifies population, constructs/variables, relationship and context.
“Stress in students” is a topic. “Does sleep quality predict examination stress among first-year students after controlling workload?” is a research problem.
Manipulated/predictor variable
Study methodMeasured outcome
Recall scoreAny unwanted influence on DV; control by design/statistics when possible.
Varies systematically with IV, creating a rival explanation.
Changes strength/direction of X→Y: when/for whom?
Mechanism through which X relates to Y: how/why?
What the construct means theoretically: “test anxiety = apprehension and arousal in evaluative situations.”
Exact observable procedure: “score on Test Anxiety Inventory” or “heart rate during timed test.”
Does it represent the construct fully and without contamination? Operational clarity supports replication, not automatic validity.
Testable prediction, decision rules and two ways to be wrong
Substantive prediction from theory: variables will relate/differ. Must be clear, testable and falsifiable.
No population effect/difference/association according to the statistical model. Significance testing evaluates evidence against H₀.
Population effect exists. Directional specifies direction (one-tailed); non-directional predicts a difference (two-tailed).
Reject a true H₀: false positive/false alarm. Probability is controlled by chosen alpha, commonly .05.
प्रभाव नहीं था, फिर भी “है” बोल दिया।
Fail to reject a false H₀: false negative/miss. Statistical power = 1 − β.
प्रभाव था, लेकिन study पकड़ नहीं पाई।
| Hypothesis type | Example | Tail |
|---|---|---|
| Directional | Mindfulness group will score lower on stress than control. | One-tailed only with prior justification |
| Non-directional | Groups will differ in stress. | Two-tailed |
| Associative | Sleep quality is related to attention. | No necessary causation |
| Causal | Manipulating sleep duration changes attention. | Requires causal design/control |
| Simple / complex | Two variables / more than two variables | Structure, not tail |
Selection logic, representativeness and sampling error
Each unit has a known non-zero selection probability. Enables design-based estimation/generalization when implementation and coverage are sound.
Simple random · systematic · stratified · cluster · multistage.
Selection probabilities are unknown. Useful for access, specialized cases and qualitative depth, but population generalization is limited.
Convenience · purposive · quota · snowball.
Choose units by lottery/random numbers so every unit has equal known chance. Needs a complete sampling frame.
Chance difference between sample statistic and population parameter; estimated by standard error.
Variability of a statistic across repeated samples. For mean, SE = SD/√n; it usually falls as n rises.
Systematic error from poor coverage, nonresponse, self-selection or flawed recruitment; a large sample does not automatically remove it.
Conducting and reporting research responsibly
| Ethical issue | Good practice | Important distinction |
|---|---|---|
| Informed consent | Purpose, procedures, risks, benefits, confidentiality, contact and withdrawal; adapt for capacity/age. | Consent is an ongoing process, not a signature alone. |
| Deception | Only when necessary, minimal risk, no feasible alternative, prior ethics review and timely debriefing. | Never deceive about material risks or right to withdraw. |
| Anonymity/confidentiality | Collect minimum data; code, secure, restrict access and state limits. | Anonymous = identity not known/linked; confidential = known but protected. |
| Vulnerable groups | Extra safeguards, accessible assent/consent and avoid coercive incentives. | Protection should not become automatic exclusion. |
| Reporting | Report null results, exclusions, deviations, limitations and conflicts; share responsibly. | Fabrication invents data; falsification manipulates; plagiarism misappropriates. |
| Authorship/data | Credit real contribution, retain secure records, preregister where useful, correct errors. | HARKing and selective reporting distort the evidence record. |
Quantitative, qualitative and mixed-methods logic
Measures variables numerically, tests hypotheses and estimates relations/effects. Often post-positivist; emphasizes standardization, comparison and generalization.
Studies meanings, experiences, processes and context using rich text/visual/observational data. Often constructivist, interpretive or critical.
Integrates quantitative and qualitative strands when one alone is insufficient. Mixing requires an explicit point of integration, not two parallel mini-studies.
Deductive/hypothetico-deductive emphasis; predefined variables, larger samples, statistical analysis, reliability/validity and population inference.
| Mixed design | Sequence | Use |
|---|---|---|
| Sequential explanatory | QUAN → qual | Explain surprising/important numerical results in depth. |
| Sequential exploratory | QUAL → quan | Explore concepts first, then develop/test measures or generalize. |
| Convergent/parallel | QUAN + QUAL | Collect concurrently, compare and integrate complementary evidence. |
| Embedded | One strand nested in another | Answer a secondary/process question inside the primary design. |
Observation, survey, experiment, quasi-experiment and cross-cultural study
Naturalistic/controlled; participant/non-participant; structured/unstructured. Use coding, observer training and inter-rater reliability; watch reactivity and observer bias.
Questionnaire: scalable, standardized, self-report risks. Interview: depth/clarification, interviewer effects and cost. Wording/order/sampling determine quality.
Manipulation + control + random assignment support causal inference. Internal validity improves; artificiality may limit external/ecological validity.
Intervention/exposure without full random assignment: nonequivalent groups, interrupted time series, regression discontinuity. Use design/statistical controls for selection bias.
Research in natural settings; high realism and contextual validity, often less control. Can be observational, experimental or mixed.
Compares processes across cultural groups. Establish translation, construct/measurement equivalence; avoid imposed-etic bias and ecological fallacy.
Different persons/groups measured once. Efficient for prevalence/associations; age differences may be cohort differences.
Same units followed across time. Shows change/order; vulnerable to attrition, testing effects and historical change.
| Validity threat | Meaning | Common defence |
|---|---|---|
| History | External event coincides with treatment | Comparison group, multiple time points |
| Maturation | Natural change over time | Control/comparison and time modelling |
| Selection | Groups differ before treatment | Randomization, matching, covariate/propensity methods |
| Testing/instrumentation | Pretest or measure changes response | Alternate forms, stable calibration, design controls |
| Attrition | Dropout differs systematically | Retention, analyse patterns, appropriate missing-data methods |
Match the approach to the kind of answer you need
Aim: essence/structure of lived experience. In-depth accounts, bracketing/reflexivity and phenomenological analysis.
What is it like?
Aim: generate a process theory grounded in data. Theoretical sampling, constant comparison, coding, memoing and theoretical saturation.
How does the process unfold?
Aim: views produced through facilitated group interaction. Efficient diversity and norm/disagreement data; manage dominance and confidentiality limits.
Aim: how people organize identity/events as stories. Attend to plot, sequence, audience, turning points and social context.
Aim: intensive study of a bounded case using multiple sources. Intrinsic, instrumental or collective; analytic rather than simple statistical generalization.
Aim: culture-sharing group’s practices and meanings. Prolonged field engagement, participant observation, field notes and reflexivity.
Flexible method to develop patterns/themes across data. Familiarize → code → construct/review/name themes → report with analytic evidence.
Credibility, transferability, dependability, confirmability; triangulation, negative cases, member reflection, audit trail and researcher reflexivity.
Best when the question asks for the structure and meaning of a lived experience, such as living with chronic pain.
Two questions every distribution must answer
ΣX/N. Uses every score; algebraically powerful, but sensitive to outliers/skew. Best for interval/ratio data with roughly symmetric distribution.
Middle ordered score (50th percentile). Resistant to extremes; good for ordinal or skewed distributions/open-ended classes.
Most frequent category/value. Only centre usable for nominal data; may be multiple or absent.
Max − Min. Fast but uses only two scores and is unstable.
IQR = Q₃−Q₁; QD = IQR/2. Resistant middle-50% spread.
Average squared deviation from mean; sample s² = Σ(X−X̄)²/(n−1).
√variance; typical distance from mean in original score units.
| Scale | Permitted summary | Example |
|---|---|---|
| Nominal | Mode, frequency/proportion | Therapy type |
| Ordinal | Median, percentiles, IQR; ranks | Class rank, Likert category |
| Interval | Mean, SD, correlation; no true zero | IQ, Celsius |
| Ratio | All arithmetic; meaningful ratios | Reaction time, errors |
Areas, standard scores, skewness and kurtosis
Approx. 68.26% within ±1 SD, 95.44% within ±2, and 99.73% within ±3.
z = (X−μ)/σ. Positive = above mean; negative = below. Converts different scales into SD units.
Symmetric, unimodal, total area 1, tails asymptotic; curve determined by μ and σ.
| Shape | Meaning | Recall |
|---|---|---|
| Positive skew | Long right tail; usually Mean > Median > Mode | Tail pulls mean right |
| Negative skew | Long left tail; usually Mean < Median < Mode | Tail pulls mean left |
| Leptokurtic | Greater tail weight/sharper peak than normal | Lepto = lofty |
| Platykurtic | Lighter tails/flatter peak | Platy = plateau |
| Mesokurtic | Normal-reference kurtosis | Meso = middle |
Interactive decision support for syllabus tests
Compare means of two independent groups when continuous outcome and assumptions are reasonable.
| Design | Parametric | Non-parametric counterpart |
|---|---|---|
| 2 independent groups | Independent t-test | Mann–Whitney U |
| 2 related conditions | Paired t-test | Wilcoxon signed-rank; Sign test if only direction |
| 3+ independent groups | One-way ANOVA | Kruskal–Wallis H |
| 3+ related conditions | Repeated-measures ANOVA | Friedman test |
| Categorical association | — | Chi-square; Phi for 2×2 strength |
One-sample, independent and paired comparisons
Is sample mean different from a known/hypothesized μ?
t = (X̄−μ₀)/(s/√n); df = n−1.
Compare means of two unrelated groups. Classical pooled test assumes homogeneity; Welch t handles unequal variances better.
Compute each pair’s difference D, then test mean difference against zero. Pairing removes stable between-person variation.
| Test | Unit of analysis | Core assumptions |
|---|---|---|
| One-sample t | Scores compared to μ₀ | Independent observations; difference from μ approximately normal for small n |
| Independent t | Two independent group means | Independent observations, continuous outcome, approximate normal residuals; pooled version adds equal variances |
| Paired t | Within-pair difference scores | Pairs independent of other pairs; difference scores approximately normal |
Five high-frequency NET/JRF tests
Two related conditions; counts direction of non-zero differences. Ignores magnitude; tests median-type change under conditions.
Two related conditions; ranks absolute differences and restores signs. Uses magnitude order; assumes symmetric difference distribution for location interpretation.
Two independent groups; compares rank distributions. Median interpretation requires similarly shaped distributions.
Three or more independent groups; ANOVA on ranks in spirit. Significant H needs post-hoc pair comparisons.
Three or more related conditions/blocks; ranks conditions within each person/block. Significant result needs post-hoc tests.
| Test | Data/design | Key information retained |
|---|---|---|
| Sign | Paired; at least ordinal direction | Sign only |
| Wilcoxon signed-rank | Paired ordinal/continuous | Direction + rank magnitude |
| Mann–Whitney | 2 independent samples | Ranks across groups |
| Kruskal–Wallis | 3+ independent samples | Pooled ranks |
| Friedman | 3+ related samples | Within-block ranks |
Can the study find the effect, and how large is it?
Probability of rejecting H₀ when a specified true effect exists. A priori power chooses sample size; post-hoc “observed power” adds little beyond p/effect estimates.
Magnitude in standardized or interpretable units. Report with confidence interval; conventions are rough context-dependent guides.
Large n can make tiny effects significant; small studies can miss meaningful effects. Evaluate precision, practical meaning and design quality.
| Effect family | Use | Common guide (context matters) |
|---|---|---|
| Cohen d | Standardized mean difference | .20 small, .50 medium, .80 large |
| r / rank r | Association or standardized test effect | .10 small, .30 medium, .50 large |
| η² / partial η² | Variance proportion in ANOVA framework | Partial η² differs from η²; state which |
| ω² | Less biased population variance estimate | Often preferred for generalization |
| Cramér’s V / Phi | Categorical association | Interpret using table size/context |
Direction, strength, form and control
Two continuous variables; strength/direction of linear association. Sensitive to outliers and restriction of range.
Rank-order correlation; ordinal data or monotonic relationship. Pearson correlation of ranks.
Association of X and Y after statistically controlling one or more Z variables from both.
Correlation between observed Y and its best linear prediction from a set of predictors; non-negative (0 to 1).
Z may create or alter X–Y association. Partial correlation adjusts measured Z but does not guarantee causal control.
A strong curved relation can yield low Pearson r. Always inspect the scatterplot.
Measurement unreliability and restricted range can reduce observed r.
The four coefficients students often swap
One genuinely dichotomous variable (e.g., treatment/control) and one continuous variable. Mathematically equivalent to Pearson r with 0/1 coding.
| Coefficient | Variable 1 | Variable 2 | Example |
|---|---|---|---|
| Point-biserial | True dichotomy | Continuous | Therapy group vs symptom score |
| Biserial | Artificial dichotomy from assumed continuous variable | Continuous | Pass/fail cut on ability vs performance |
| Phi (φ) | True dichotomy | True dichotomy | Treatment/control × improved/not |
| Tetrachoric | Artificial dichotomy from latent continuous | Artificial dichotomy from latent continuous | Two yes/no items assumed thresholds on traits |
From one line to a team of predictors
Predicted Y when all X = 0; interpretation depends on meaningful zero/range.
Expected change in Y for one-unit X increase; in multiple regression, holding other predictors constant.
Observed Y − predicted Ŷ. Residual diagnostics reveal nonlinearity, heteroscedasticity and outliers.
Variance in Y explained by predictor set; adjusted R² penalizes adding predictors.
| Assumption/issue | Meaning | Check/response |
|---|---|---|
| Linearity | Mean Y is linear in predictors | Scatter/residual plots; transformation/nonlinear terms |
| Independence | Errors not correlated | Design; time/cluster models if violated |
| Homoscedasticity | Residual variance roughly constant | Residual plot; robust SE/appropriate model |
| Normal residuals | For small-sample tests/CIs, residuals approximately normal | Q–Q plot; robust/bootstrap options |
| Multicollinearity | Predictors excessively overlap | VIF/tolerance; theory-based selection/composites |
| Influential cases | Observation strongly changes fit | Leverage/Cook’s distance; verify and report sensitivity |
Change in Y SDs per 1 SD X, holding others constant; aids within-model comparison, not causal priority.
Researcher enters blocks by theory to test incremental ΔR²; differs from automated stepwise selection.
Good prediction may rely on proxies/confounds; causal claim requires design and assumptions beyond regression.
Assumptions, extraction, rotation and interpretation
Meaningful intercorrelations, adequate sample, no severe multicollinearity/singularity. KMO assesses sampling adequacy; significant Bartlett rejects identity correlation matrix.
PCA explains total variance with components (data reduction); common factor methods such as PAF/ML model shared variance/latent factors.
Use theory, scree plot, parallel analysis, interpretability and replication. Eigenvalue >1 alone often overextracts.
Maximizes variance of squared loadings within factors, seeking variables that load high or low on each. Factors remain uncorrelated.
| Term | Meaning |
|---|---|
| Factor loading | Association of variable with factor; magnitude and pattern guide meaning. |
| Communality h² | Proportion of a variable’s variance explained by retained common factors. |
| Orthogonal rotation | Factors constrained uncorrelated: Varimax, Quartimax, Equamax. |
| Oblique rotation | Factors may correlate: Direct Oblimin, Promax; often realistic in psychology. |
| Cross-loading | Variable loads meaningfully on more than one factor, weakening simple structure. |
ANOVA family, blocks, time, cohorts and single-case logic
One factor with 3+ levels; F = MSbetween/MSwithin. Significant omnibus F needs planned contrasts/post-hoc tests.
Two or more factors; tests each main effect and interaction. Interaction means one factor’s effect depends on another.
Group similar units into blocks on nuisance variable, then randomize treatments within blocks; reduces error variance.
Same participants in all conditions; controls individual differences. Risks order/carryover; counterbalance. Sphericity matters for 3+ levels.
Each treatment appears once in each row and column; controls two blocking variables. Assumes no important interactions with blocks.
Group sharing exposure/time characteristic followed or reconstructed. Prospective/retrospective; estimates incidence and temporal association, not randomization.
Many observations before/after intervention. Interrupted series tests level/slope change while accounting for pre-existing trend/autocorrelation.
Compares adjusted group means while modelling covariate(s). Assumes linear covariate–outcome relation and homogeneous regression slopes.
Tests group effects on a set of correlated DVs jointly; may control familywise error and reveal multivariate pattern. Follow-up analyses needed.
Includes between-subject and within-subject factors; tests group, time/condition and their interaction.
Repeated measurement within individual; baseline and intervention phases demonstrate functional control through replication.
Nonequivalent groups, interrupted time series and related designs estimate intervention effects without full randomization.
| Single-case design | Logic | Caution |
|---|---|---|
| AB | Baseline then intervention | Weak causal evidence; no replication |
| ABA / ABAB | Withdraw/reintroduce intervention to replicate effect | Withdrawal may be unethical/impossible or carryover persists |
| Multiple baseline | Stagger intervention across behaviours, settings or persons | Requires independent baselines and clear staggered change |
| Changing criterion | Stepwise performance criteria; behaviour tracks each shift | Best for gradually changing reversible behaviour |
Independent observations, approximately normal residuals and homogeneity of variance; repeated measures adds sphericity.
A covariate measured after treatment or affected by treatment can bias interpretation; covariate adjustment does not create randomization.
Needs adequate sample, multivariate assumptions and conceptually related DVs; more outcomes do not automatically mean better analysis.
NET/JRF-style checks; answer before reading feedback
Problem → variables → hypothesis → sample → ethics → method/paradigm.
Describe → inspect curve → choose test → estimate effect/power.
Correlation → special r → regression → factor structure → experimental design.
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