Quantitative Research Methods India: Every Formula, Verified in DuckDB

Descriptive statistics are the foundation of quantitative research methods India, and Poseidon treats them as typed, deterministic computations. For a number_rating column, mean, median, standard deviation, variance, range, quartiles and IQR are computed via DuckDB aggregates, not by asking an LLM to summarise. For categorical multiple_choice, frequency tables show absolute, relative and valid percent with correct denominator after skip-logic correction via routing edges. Contingency tables (crosstabs) are built with GROUP BY on the Demographic Axis Node — city tier, age, NCCS — so 'purchase channel by city tier' is a true cross-tab, not a pivot you must build. Visualisation choices follow data shape: histogram for continuous numeric, boxplot for distribution, bar for frequency, scatter and line for trends. All are formula-driven from the column's declared storage format and valid formulas, so a likert_5pt is never averaged as if it were revenue, and a multi_select is never counted as if it were single-choice.

Why does typing matter? Because without it, Indian survey data breaks generic tools. A multi_select stored as 'Feature A;Feature B' must be unnested via UNNEST(string_split(col, ';')) to count selections; a ranking stored as ordered semicolon list must use Borda count Σ(n − rank_position) for aggregate priority; an NPS integer 0-10 must use (Promoters minus Detractors)/Total ×100 with configurable cut points per scale bounds, not a mean of 0-10. Poseidon's Survey Knowledge Graph encodes these as Column to Formula edges with confidence EXTRACTED when type directly declares the mapping, INFERRED when fuzzy matched, AMBIGUOUS when multiple formulas fit. That is quantitative research methods India that respects questionnaire design. For a Chennai team asking 'average Likert by income,' the graph ensures top-2-box and top-3-box are offered as valid options alongside mean, because Likert scales support both interpretations; for Kochi, the same.

The payoff is that you can ask descriptives in English and get the correct descriptive, verified. 'What is average rating for delivery speed in Tier 2?' returns mean with n and 95% Wilson score confidence interval for proportions where appropriate, not just a number. 'How many respondents chose each payment mode overall?' correctly reports multi-frequency where percentages may exceed 100, with note that denominator is selections. Built by Jupiter Meta Labs in Bangalore, Hercules Works delivers this via Poseidon's parallel sub-agents: Data Profiler provides per-column null rate and top values, Column Selector walks the graph, and Code Generator assembles the SQL template for the valid formula. No manual choice, no Excel error. From Free ₹0/month with 10 AI chats to Pro at ₹30,000/quarter, quantitative research methods India on Hercules starts with descriptives done right, so every inferential test that follows stands on solid ground — and is three-layer verified at 99.1% before you see it.

Inferential statistics let you move from 'what we saw' to 'what we can claim,' and quantitative research methods India on Hercules makes that move responsible. Poseidon supports one-sample, independent-samples and paired-samples t-tests, Mann-Whitney U and Wilcoxon signed-rank for non-parametric alternatives, binomial and chi-square tests for independence, distribution and homogeneity, one-way and Welch's ANOVA plus two-way ANOVA (between/repeated) and repeated-measures ANOVA, with post-hoc corrections via Bonferroni, Tukey and Scheffé, plus Kruskal-Wallis for non-parametric multi-group comparison. You never choose from that menu manually. Ask 'is Tier 1 satisfaction significantly higher than Tier 2?' and the graph maps the likert_5pt column to the t-test family, Column Selector identifies the city_tier axis, and the pipeline checks assumptions before picking Welch versus Student or Mann-Whitney for non-normal Likert. The test executes as a SQL template — deterministic, not prompt-driven — and returns p-value with Wilson or Fisher z confidence interval as appropriate.

For Indian data, assumption checks are not pedantry; they are protection. A Mumbai BFSI brand comparing NPS by age band cannot run ANOVA if variances differ; Welch's correction is needed. A Pune pricing study comparing 'too expensive' proportions cannot run chi-square if expected counts are under five; Fisher is safer. Poseidon's Quality Checker flags small n, cardinality and variance issues from profiler stats, and the graph's confidence tags signal when mapping is INFERRED and needs caution. That is quantitative research methods India that teaches while it tests: results include 'p equals 0.03 at n Tier 1=412, n Tier 2=389, Welch's t' plus business implication via the 'So What' rule, not just stars. For a founder like Karthik in Delhi testing 'does ad recall drive purchase intent?' chi-square for independence is chosen with correct table orientation, and the narrative warns if correlation is not causation — a safeguard the Self-Critique layer also enforces at 0-10 scoring.

Crucially, Poseidon never invents the math. Each inferential method is a named primitive with a SQL template, validated against ground truth and verified per answer via Numerical Claim Verifier within 0.5 tolerance and Output Validator for range checks. A service firm in Ahmedabad asking 'did CSAT improve after the fix?' gets a paired t-test if same respondents are tracked, independent if cohorts differ — the questionnaire version from survey_chats.survey_version supplies that context via the Knowledge Graph. With DuckDB-on-Parquet at 10-20× faster than Pandas and semantic cache at 78% hit, repeated significance hunts like weekly NPS tracker comparisons return under 200 ms verified. From Free to Pro, quantitative research methods India on Hercules gives you inferential power without inferential risk — the right test, the right template, the right verification, narrated in business language with evidence (p, CI, n) after implication, as Kantar would present it but in seconds, not weeks.

Correlation and regression connect causes to outcomes, and quantitative research methods India on Hercules spans the full spectrum formula-driven. Poseidon supports Pearson, Spearman and point-biserial plus partial correlation; simple linear, multiple linear and logistic (binary and multinomial) regression; Lasso and Ridge penalised regression; and coefficients of determination R squared, adjusted R squared and pseudo R squared variants with odds ratios and hazard ratios where applicable. Ask 'what drives NPS among Tier 2 mothers?' and the pipeline maps Likert and interval columns to regression family, selects predictors via Survey Knowledge Graph's column relevance, and runs driver analysis with Shapley value decomposition so you see which attribute moves NPS most, not just p-values. Ask 'are satisfaction and repeat purchase correlated?' and Pearson is used for interval, Spearman for ordinal Likert, with Fisher z confidence interval — the graph ensures the correct correlation for the column type, not a one-size-fits-all.

The India-specific strength is dimensionality without confusion. A Bangalore wearables startup priced via Van Westendorp while also collecting Likert attribute ratings — regression must handle Hindi, Tamil and English open-ends separately via theme scores, and must handle multi_select correctly by unnesting before predictor creation. Poseidon does both automatically, with language-aware theme nodes from Open-Ended Intelligence. For a Delhi ecommerce brand, 'does discount sensitivity predict churn?' routes to logistic regression with churn as binary, returns odds ratios and pseudo R squared, and checks sample-size adequacy before claiming significance. For an Indore manufacturer, 'forecast demand from attribute scores' uses Lasso/Ridge to avoid overfit on correlated Likerts, with cross-validated penalty. Each regression is a template with validated SQL, not an LLM writing Python that may forget standardisation via z-score where needed.

Verification keeps regression honest. Numerical Claim Verifier re-computes R squared and coefficients via fresh DuckDB SQL, Output Validator checks that pseudo R squared is within [0,1] and that odds ratios are positive, and Self-Critique flags causal language where only correlation exists — e.g., 'higher satisfaction causes repeat' is rewritten to 'higher satisfaction is associated with repeat (r=0.34, p<0.01, n=612).' That is quantitative research methods India that respects evidence. Combined with streaming SSE progress (you see 'Generating SQL...Verifying numbers...') and persistence via chat_turns.stream_logs, long regressions that take up to 60-90 seconds remain observable and recoverable. Built by Jupiter Meta Labs in Bangalore and trusted from Kochi to Jaipur, Hercules Works turns correlation and regression from a statistics degree into a sentence you can act on, with price points from Free ₹0/month to Pro ₹30,000/quarter and SuperJ's 20M Indians as the fuel.

Segmentation and dimensionality reduction reveal hidden structure, and quantitative research methods India on Hercules treats them as first-class, not add-ons. Poseidon supports K-means clustering with elbow method, hierarchical clustering with single/complete/average linkage, factor analysis with Varimax/Promax rotation, and Principal Component Analysis with Kaiser criterion and scree plot — all as deterministic templates on Parquet. Ask 'what segments exist in our category based on attitude battery?' and Data Profiler plus Column Selector identify the battery of numeric attitudinal items, then K-means or hierarchical segments them, with the Analytics Planner suggesting the technique if not specified. Factor analysis reduces correlated Likerts to latent factors like 'value-seeking' versus 'status-seeking,' PCA condenses them for modelling, and CHAID-style lightweight decision-tree segmentation offers an alternative where chi-square splits are intuitive. This is quantitative research methods India that finds groups, not just cuts by age or city handed to it.

Clustering Indian consumers is where the Survey Knowledge Graph earns its keep. Raw demographics — age, NCCS — are weak predictors compared to latent segments like 'value-aspirers' or 'trust-first mothers' that emerge from clustering of embeddings and behaviours across SuperJ's 20M responses. Poseidon discovers these via community detection style logic and then anchors them with demographic correlates so you can target them via SuperJ quotas or media plans. For a Chennai FMCG brand, K-means on a 12-item battery produced three segments where 'durability' was not one theme but two — 'lasts long' (functional) versus 'does not break trust' (emotional) — with language-specific drivers visible via Tamil versus Hindi theme nodes. Hierarchical clustering showed that at distance threshold 0.6, 'paisa vasool' and 'family approval' co-located, hinting at a combined message. All segments carry n, mean scores and validation via silhouette, reported with implication-first narrative.

Reliability and agreement checks keep segmentation credible. Poseidon offers Cronbach Alpha for scale internal consistency, Cohen's Kappa (weighted) and Fleiss' Kappa for inter-rater agreement, Kendall's Tau and Kendall's W for rank concordance, and Intraclass Correlation for test-retest, plus Z-score standardisation and sample-size/power analysis to plan the next wave. You see alpha equals 0.83 for your CSAT scale with n=612, not just 'the scale is reliable.' Those checks run before the narrative claims a segment is real, and Output Validator ensures alpha is within [0,1]. For a Lucknow political tracker or a Hyderabad healthcare study, that reliability story is the difference between a segment you bet a campaign on and one you note as exploratory. With DuckDB columnar execution and colourblind-safe chart advisor visuals (heatmap for cross-tab, horizontal bar for clusters), quantitative research methods India on Hercules makes segmentation both statistically sound and visually clear — horas, not weeks.

Specialised market-research and advanced methods complete the library for quantitative research methods India where Indian decisions live. Poseidon supports NPS as (Promoters minus Detractors)/Total ×100 with configurable cut points, top-2-box/top-3-box for CSAT/Likert, Borda count Σ(n − rank_position) for ranking, MaxDiff/Best-Worst preference scores, Van Westendorp Price Sensitivity Meter (too cheap/cheap/expensive/too expensive), Gabor-Granger price elasticity, brand awareness funnel (awareness→recall→consideration→preference→loyalty), conjoint/importance × performance matrix, driver analysis via Shapley, CHAID-style segmentation, K-means on attitudinal batteries, Just-About-Right (JAR) for product optimisation and post-stratification weighting for representativeness. Also supported: confidence intervals via Wilson score for proportions and Fisher z for correlations, survival analysis (Kaplan-Meier, Cox regression, log-rank test) for churn timing, and mediation/moderation to test whether 'trust mediates price to purchase.' All are named primitives with SQL templates, not prompt inventions.

Why list so many? Because real Indian business questions cross methods. A Jaipur pricing question — 'what price maximises purchase at 60% intent for Tier 2?' — needs Gabor-Granger plus Wilson CI, not just a mean. An Ahmedabad concept test — 'which of six concepts wins among value-aspirers?' — needs Borda plus driver Shapley plus weighted n. An Indore In-Home Use Test — 'is attribute intensity just right?' — needs JAR with correct cut points per scale bounds from the Question Node. Poseidon's Analytics Planner adds such derived tasks automatically when the Research Brief hints at pricing or concept goals, so quantitative research methods India arrives before you ask by name. Each method is chosen via column type to valid formula mapping from the graph — a multiple_choice cannot trigger a t-test, a numeric rating can — so the method matches the data, not the wording.

Verification and narrative tie the library together. Every specialised computation is re-derived via fresh DuckDB SQL at 0.5 tolerance, checked structurally (NPS in [-100,100], top-box within [0,100]), and scored by Self-Critique 0-10 for unsupported claims. Results are streamed with 0-100% progress and persisted, cached at 78% hit with schema-hash invalidation, and delivered via hercules.works/ai with the SuperJ panel's 20M verified Indians at 60-90%+ rates as the source. Whether you run Van Westendorp for an edtech plan in Delhi or survival analysis for churn in Mumbai, quantitative research methods India on Hercules gives you the named method, the correct formula, the verified number and the business implication — formula-driven, not prompt-driven — at Free ₹0/month, Starter ₹1,119/month (₹895 annual) and Pro ₹30,000/quarter (₹24,000 annual), trusted by Unilever, Kantar and SBI Mutual Fund for decisions that must be paisa vasool and provably correct.