Agricultural statistical modeling, experimental design analysis, regression and correlation tools, ANOVA for field trials, sampling design, and spatial analysis β grounded in USDA ARS biometrics research.
Live NASS crop yield and price data. Provides real-world datasets for use as sample data in ANOVA, regression, and correlation models. Auto-populates calculator data fields with NASS benchmark values.
Source: USDA NASS QuickStats API
USDA ERS farm income and cost-of-production data. Provides economic benchmark values useful as regression Y-variables or ANOVA group targets in agricultural research designs.
USDA ARS standard statistical benchmarks for field trial design: typical CV ranges by crop, minimum detectable differences, standard power targets, and recommended replication levels per USDA ARS Biometrics Unit guidelines.
Model SF16-S.001
Analyzes variance among three or more group means to determine whether at least one group differs significantly. Enter group data as comma-separated values. Calculates F-statistic, p-value approximation, and effect size (η²). Grounded in USDA ARS biometrics methodology for field trial analysis.
Model SF16-S.002
Fits a simple or multiple linear regression model (OLS) to agricultural data. Calculates regression coefficients, R², adjusted R², standard error, F-statistic, and residual analysis. Conforms to USDA ARS statistical standards for peer-reviewed research reporting.
Model SF16-S.003
Calculates the required sample size per treatment group to achieve a specified statistical power for detecting a given effect size. Implements Cohen's d framework used in USDA ARS experimental design guidelines for field and laboratory trials.
Model SF16-S.004
Performs Tukey's Honest Significant Difference (HSD) test following a significant ANOVA result. Computes all pairwise mean comparisons, HSD critical value, and significance codes. Standard post-hoc procedure in USDA ARS and land-grant university field trial reporting.
Model SF16-S.005
Calculates the Pearson correlation coefficient (r) between two variables, tests significance via t-distribution, and computes 95% confidence interval using Fisher's Z-transformation. Standard correlation analysis for agricultural data pairs (yield vs. input, NDVI vs. biomass, etc.).
Model SF16-S.006
Tests whether observed categorical frequencies differ significantly from expected frequencies. Used in agricultural genetics (Mendelian ratios), pest monitoring (trap counts vs. baseline), and survey analysis. Calculates χ² statistic, degrees of freedom, and p-value.
SF16 delivers 6 research-grade statistical models for agricultural field trial and laboratory data analysis. Models cover the complete frequentist statistical workflow: one-way ANOVA for multi-group mean comparisons, OLS linear regression with R² and significance testing, Cohen's d power analysis and sample size determination, Tukey HSD post-hoc pairwise comparisons, Pearson correlation with Fisher Z-interval, and chi-square goodness of fit for categorical data. All models implement methodology consistent with USDA ARS Biometrics Unit standards and SAS/R statistical computing conventions used in peer-reviewed USDA research publications. Live USDA data via NASS QuickStats and ERS provides real-world agricultural datasets for use as sample inputs across all calculators.