Explore every surface of Bernoullli.
From natural conversational exploration to guided analysis wizards, raw data tables, reproducible R notebooks, and versioned blueprint libraries — see how every part of the workspace connects.
I loaded cowpea_drought.csv (120 observations across 3 cowpea varieties: V1, V2, V3 and 2 water regimes: Drought vs Well-watered; completely randomized design). Next, I fitted a two-way factorial ANOVA model on Plant Height (cm) and evaluated model assumptions.
| Variety | Water_Regime | Plant_Height_cm | Root_Weight_g | Chlorophyll_SPAD |
|---|---|---|---|---|
| V1 | Drought | 42.2 | 6.14 | 38.2 |
| V1 | Well-watered | 50.4 | 8.45 | 44.6 |
| V2 | Drought | 37.8 | 5.82 | 36.1 |
| V2 | Well-watered | 49.3 | 7.90 | 43.8 |
| V3 | Drought | 46.5 | 7.28 | 41.4 |
| V3 | Well-watered | 57.4 | 9.12 | 48.5 |
Two-Way Factorial ANOVA Summary (Illustrative example on simulated data • Unadjusted)
Response: Plant Height (cm) across Variety & Water Regime • Completely Randomized Design (CRD)
| Source | Df | Sum Sq | Mean Sq | F value | p-value | Partial η² | Significance |
|---|---|---|---|---|---|---|---|
| Cowpea Variety (V) | 2 | 412.80 | 206.40 | 18.42 | 1.15e-07 | 0.24 | p < 0.001 *** |
| Water Regime (W) | 1 | 1,284.50 | 1,284.50 | 114.68 | < 2.2e-16 | 0.50 | p < 0.001 *** |
| Variety × Water Regime | 2 | 48.20 | 24.10 | 2.15 | 0.121 | 0.04 | n.s. (not significant) |
| Residuals | 114 | 1,276.80 | 11.20 | — | — | — | — |
Assumption Diagnostics (Plots & tests reported for you to judge)
F(5, 114) = 1.14, p = 0.342. No evidence against equal variances.
W = 0.984, p = 0.281. No evidence of departure from normality (inspect Q-Q plot in the diagnostics panel to judge).
Post-hoc Pairwise Comparisons (Tukey HSD) (Exploratory, unadjusted)
| Factor | Comparison | Mean Difference (cm) | 95% Conf. Interval | p-adj |
|---|---|---|---|---|
| Variety | V3 vs V1 | +5.65 | [+3.87, +7.43] | < 0.0001 *** |
| Variety | V3 vs V2 | +8.40 | [+6.62, +10.18] | < 0.0001 *** |
| Variety | V1 vs V2 | +2.75 | [+0.97, +4.53] | 0.0011 ** |
| Water Regime | Well-watered vs Drought | +10.20 | [+8.99, +11.41] | < 0.0001 *** |
Cowpea Variety Response Means (Plant Height in cm)
| Variety | N | Drought Mean (cm) | Well-watered Mean (cm) | Reduction (cm) | Reduction (%) |
|---|---|---|---|---|---|
| V1 | 40 | 42.2 ± 0.8 | 50.4 ± 0.9 | 8.2 | 16.3% |
| V2 | 40 | 37.8 ± 0.9 | 49.3 ± 0.8 | 11.5 | 23.3% |
| V3 | 40 | 46.5 ± 0.9 | 57.4 ± 1.1 | 10.9 | 19.0% |
Descriptive only (illustrative example on simulated data). The variety × water interaction was not statistically significant (p = 0.121), so differences in drought response between varieties are not statistically supported.
Agronomic Interpretation
- Water regime (p < 0.001, partial η² = 0.50): Drought reduced plant height by 10.2 cm on average (95% CI 8.99 to 11.41) across all varieties.
- Variety (p < 0.001, partial η² = 0.24): All three varieties differed in mean height: V3 > V1 > V2. V3 exceeded V1 by 5.65 cm and V2 by 8.40 cm, and V1 exceeded V2 by 2.75 cm (all Tukey-adjusted p ≤ 0.0011).
- Interaction (p = 0.121): No evidence of a differential drought response between varieties at this sample size (V2 height reduced by 23.3% vs. 16.3% in V1); with 20 plants per cell, a modest interaction could remain undetected.
- Diagnostics: Assumption diagnostics reported, with plots and tests for you to judge. Residual tests gave no evidence against equal variances or normality; inspect the residual plots before relying on results.
Generated Visualizations
Below is the interaction bar plot of Cowpea Plant Height across varieties and watering regimes:
Drought suppression comparison across varieties:
Four-panel ANOVA residual diagnostics:
Deliverables
The ANOVA and group-mean tables were saved as CSVs for downstream reporting:
Methodological Note: Assumption diagnostics reported, with plots and tests for you to judge. Next step is formulating explicit hypothesis tests and running formal post-hoc variance decomposition for publication.
Recommendation: Launch Analysis Mode to configure a publication-grade factorial ANOVA blueprint with comprehensive assumption diagnostics.
I loaded both datasets, checked data types and summary statistics, and generated cross-experimental comparisons and publication figures in the session drawer.
Dataset Comparison at a Glance
| FEATURE | COWPEA DROUGHT EXPERIMENT | MALARIA CASES (2000-2024) |
|---|---|---|
| Type | Experimental / Agronomic | Time series / Epidemiology |
| Key Variables | Variety, Water_Regime, Plant_Height, Root_Weight | Year, Cases_Reported, Region, Rainfall |
| Sample Size | 120 observations (3 varieties, 2 regimes) | 25 annual records (2000–2024; exploratory time series) |
cowpea drought agronomic trial
Blueprints Library
Here is the list of blueprints. Clicking them will create copies of variants for authenticity.
Cowpea Root Architecture Variability under Drought Stress
Gamma Distribution Models for Nigeria Malaria Cases
Ask plain English questions. Get instant visual graphs.
No SQL queries, complex formulas, or code required. Attach your dataset and ask what you want to understand. Bernoullli calculates statistical relationships and streams the answer with transparent reasoning steps, structured statistical tables, and inline distribution plots.
When interpretation matters, transition to Analysis Mode.
Whenever your research requires formal inference rather than casual exploration, Bernoullli recommends launching Analysis Mode. A structured multi-step wizard guides you to select your research objective, evaluate assumption diagnostics, and audit your methodological blueprint before execution.
Track every generated figure, table & session document.
Never lose track of an insight or visualization. The Session Documents drawer catalogs every generated figure, comparison table, downloaded report, and experimental variant created during your session in one structured place — complete with visual thumbnails and one-click access.
Production R code with interactive export & execution.
Behind every analysis lies clean, reproducible R code. Inspect numbered code blocks, package dependencies (car, emmeans, ggplot2), run blocks directly in the cloud sandbox, or export formatted and unformatted scripts in one click.
All generated blueprints are saved to your library to reuse and modify.
Once an analytical blueprint is generated in Analysis Mode, it is automatically saved to your Blueprints Library. Revisit your past analyses anytime, make changes to methodology parameters, create alternative variant copies, or re-execute the approved plan whenever new data arrives.