Design and analyse agricultural experiments without writing code

R. A. Fisher, working at Rothamsted on agricultural field trials in the 1920s, established the three principles that every valid experiment still relies on. They are the criteria the platform uses to judge your data.

Replication. Each treatment is applied to several independent experimental units (plots, pots, animals). Replication is the only way to estimate the experimental error, and it increases precision: the standard error of a treatment mean is s/√r. Measuring the same plot several times is not replication (that is sub-sampling or pseudo-replication). Field trials typically use 3–6 replicates; 4 is the usual minimum.

Randomisation. Treatments are assigned to units by a chance mechanism (lottery, random numbers, software), never by convenience. Randomisation protects against unknown biases (a fertile corner, the border of the field, the order of harvest), makes the errors independent and justifies the F-test. Block 8 will generate randomised layouts for you.

Local control (blocking). Units are grouped so that those within a group are as alike as possible (same soil, slope, moisture, planting date, harvest team). Every treatment then appears in every block, and the block-to-block variation is removed from the error. Blocks should be laid out across the gradient of fertility so that each block is homogeneous inside.

The platform reads tidy (long-format) tables: one row per experimental unit and one column per variable. The first row holds the column names. This is the layout used by R, SAS, SPSS and Excel pivot tables.

• No merged cells. Merged cells keep the value only in the first cell; the others become blanks. Fill every row.
• No title rows, notes or totals inside the table. Put them on another sheet.
• Short headers without spaces or special characters: Yield_t_ha, Height_cm, Block.
• One decimal separator (point or comma, not both) and no thousands separators or units inside the cells (4.6, not 4,6 t/ha).
• Missing plots: leave the cell empty or write NA. Do not write 0 for a missing value.
• Consistent level names: Control and control and Control are three different treatments to a computer.
• Wide tables (treatments or blocks as columns) can be converted to long format with the reshape tool below.

The platform detects whether each column is numeric or categorical and suggests a role; you can always change it.

• Excel: .xlsx, .xlsm, .xlsb, .xls (choose the sheet after loading).
• Open formats: .ods (LibreOffice), .csv, .tsv, .txt (any delimiter: comma, semicolon, tab, pipe), .dat, .prn.
• JSON: an array of objects (one per plot), an array of arrays, or {columns:[…], data:[…]}.
• Clipboard: copy a range in Excel and paste it in the box below.

Files are read locally with the FileReader API; nothing is transmitted.

An ANOVA summarises the whole experiment in one F-test. Exploring first protects you from three classic mistakes: analysing a typing error as if it were a treatment effect, testing means when the variances are wildly different, and reporting a mean for a variable whose distribution has no meaningful centre (skewed counts, bounded scores).

• Location: mean and median. If they differ noticeably, the distribution is skewed or has outliers.
• Spread: standard deviation (SD), interquartile range (IQR) and coefficient of variation (CV).
• Shape: skewness (asymmetry) and kurtosis (weight of the tails) relative to the normal distribution.
• Structure: do the groups differ in level? in spread? do the blocks behave consistently?

• Histogram + density: shape of the whole sample. Compare the orange density with the dashed normal curve. Two humps usually mean two different treatments or blocks, not a problem.
• Box plot: box = middle 50 % (Q1 to Q3), line = median, ◆ = mean, whiskers = most extreme values within 1.5 × IQR, circles = potential outliers. Boxes of very different height signal unequal variances.
• Violin: a smoothed histogram on each side; shows bimodality that a box hides. Needs ≥ 5–6 observations per group to be meaningful.
• Means with error bars: the classic treatment figure. State in the caption what the bars are (SE, SD or CI). Overlapping SE bars do not imply "not significant" — the test decides.
• Strip plot: every plot is shown; the honest picture when replicates are few (3–4), where boxes and violins are misleading.
• Block profiles: one line per block across treatments. Roughly parallel lines mean the treatment ranking is consistent across blocks (additivity, an RCBD assumption). Crossing lines suggest a block × treatment interaction or an outlying plot.
• Interaction plot (two factors): parallel lines = no interaction, the factors act additively; converging or crossing lines = interaction, and the main effects should be interpreted with care.
• Scatter vs. covariate: if the response depends linearly on a variable measured before treatment, ANCOVA (Block 5) will increase precision.

A value flagged by Tukey's rule (beyond 1.5 × IQR) or by |z| > 3 is suspicious, not wrong. Go back to the field book: a decimal shifted, a plot damaged by animals or flooding, a mis-labelled sample. Correct documented errors; declare damaged plots as missing (Block 5 handles missing plots); never delete a value only because it is inconvenient. If in doubt, run the analysis with and without it and report both.

• Q–Q plot: points on the line = normal. An S-shape = heavy or light tails; a curve = skewness; one or two points far off = outliers. The shaded band is a 95 % envelope: a few points outside it are expected.
• Residuals vs fitted: should look like a random cloud around zero. A funnel (wider spread at higher fitted values) = variance grows with the mean → log or square root. A curve = missing term (e.g. a quadratic dose effect) or non-additivity.
• Scale–location: √|residual| against fitted; an increasing trend confirms heteroscedasticity.
• Residuals by treatment: boxes of very different height = unequal variances among treatments.
• Residuals in data order: runs of positive then negative residuals suggest a trend along the field if rows follow the planting order.

Rank-based procedures replace the observations by their ranks and therefore do not need normality; they are the natural choice for ordinal scores, small samples with outliers and heavily skewed measurements.

Rank tests lose little power when the data are actually normal (about 5 % for Kruskal–Wallis vs the F-test) and can gain a lot when they are not. Their hypotheses are about the whole distribution (stochastic dominance), usually summarised as medians.

Covariates (ANCOVA) are added to any of these models; treatment means are then adjusted to the mean of the covariate. Type III sums of squares are used by default so that unbalanced data and incomplete blocks give adjusted tests; for balanced data Type I and III coincide.

• SS partitions the total variation; MS = SS/df; F = MS(source) / MS(its error). The "tested against" column shows which error each F uses.
• Partial η² = SS(source) / [SS(source) + SS(error)]: proportion of variance attributable to the source; an effect size to accompany the p-value.
• CV % = √MSE / grand mean × 100: precision of the trial, the figure reviewers look for.
• R² of the model: how much of the total variation the design explains (blocks included).
• A significant block effect is not a finding about treatments; it means blocking was worthwhile.
• A significant interaction means the answer to "which level of A is best?" depends on B. Report the cell means and simple effects; the main-effect means alone can be misleading.

Pairwise tests or contrasts? When the factor is quantitative (doses, densities, dates), letters are a poor summary: fit a trend instead. Orthogonal polynomial contrasts partition the treatment SS into linear, quadratic… components; the highest significant one gives the shape of the response, and the fitted equation gives the optimum dose. When treatments have a structure (control vs the rest, organic vs mineral sources), a single planned contrast is more powerful and more informative than all pairwise comparisons.

• The design, the number of replicates and the model, including any covariate and transformation.
• The ANOVA table or, at least, F with its degrees of freedom and p for every treatment factor and interaction; the CV of the trial.
• Tables of means with SE (or the LSD/HSD value) and letters, stating the test and α; back-transformed means when a transformation was used.
• For quantitative factors, the fitted response curve with its equation and R².
• Effect sizes (partial η²) and confidence intervals where possible; p-values alone are increasingly discouraged.

• State what the bar is: SE (precision of the mean; the usual choice), SD (variability of plots) or 95 % CI. Never leave it implicit.
• Letters: "Means with the same letter are not significantly different (Tukey HSD, α = 0.05)". Put the test in the caption, not the title.
• A level with two letters (ab) belongs to both groups; do not "fix" it by hand.
• The Y axis of a bar chart must start at zero; a point plot may zoom in. Say which in the caption if you zoom.
• Units in the axis label: "Grain yield (t ha⁻¹)".
• Colour-blind-safe palettes (Okabe–Ito, Paul Tol) are available; use distinct line styles or markers in addition to colour when the figure may be printed in greyscale.

• Resolution: 300 dpi for colour/halftone, 600–1000 dpi for line art. The export bar shows the pixel size and the printed size in cm for each option.
• Width: single column ≈ 8.5 cm, double column ≈ 17.5 cm (Elsevier, Springer, Wiley are similar). At 300 dpi that is ≈ 1000 and 2100 px; choose "High · 4×" or "Publication · 8×" accordingly.
• Formats: TIFF (with resolution tag, uncompressed here), PNG, or vector (SVG → convert to EPS/PDF in Inkscape if the journal insists). JPG only for photographs.
• Fonts: Arial/Helvetica or Times, 8–12 pt at final size; the "Journal" presets below set this.
• Multi-panel: label panels (a), (b)… in bold at the top-left; keep the same axis scale across panels when they are compared.

• Methods: design, replicates, factors and levels, response and units, transformation, model and error terms, mean-separation test and α, software. The platform drafts this paragraph; edit it to your context.
• Results: the ANOVA (F, df, p, CV), means with SE and letters, trends for quantitative factors, and the interaction tables when relevant.
• Figures: numbered, with self-explanatory captions (what the bars are, which test, α). The report embeds them as vector graphics, so they stay sharp in the PDF and can be extracted.
• Reproducibility: the ZIP package includes the data as loaded, every table as CSV and every figure as SVG plus raster at the chosen resolution — enough for a supplementary-material file.
• The HTML report opens in any browser without internet; "Print → Save as PDF" in the browser produces the PDF (A4 margins are pre-set).

• Randomise with a documented seed: the same seed reproduces the same layout, so the plan can be regenerated and audited. Write the seed in the field book.
• Randomise within the structure of the design: within each block (RCBD), within each row and column (Latin square), main plots within blocks and sub-plots within main plots (split-plot).
• Never "improve" a randomisation by hand to avoid adjacent identical treatments; if a layout is agronomically impossible, change the seed and record why.
• Number the plots in the direction of the field operations (serpentine numbering saves walking) and keep the same numbering for the whole season.

• Long, narrow plots oriented along the fertility gradient are more uniform than square ones; blocks are laid out across the gradient so that each block is homogeneous inside.
• Plot size should be large enough to hold a harvest area free of border effects: border rows and plot ends are discarded (e.g. harvest the central 2 rows × 4 m of a 4-row × 5 m plot).
• Typical field-crop plots: 10–30 m² for cereals, 20–50 m² for maize; pot experiments: one plant or a few plants per pot with more replicates.
• Guard rows around the trial and alleys between blocks reduce interference between neighbouring treatments (fertiliser drift, shading, lodging).

The number of replicates r needed to detect a difference d (as % of the mean) between two treatments, with CV known from previous trials, comes from r ≥ 2 (tα/2 + tβ)² (CV / d)², solved iteratively because the t-values depend on the error degrees of freedom. The calculator below does this and also answers the inverse question: with the replicates I can afford, how small a difference can I detect?

• Aim for at least 10–12 error degrees of freedom; with fewer, F-tests and mean comparisons are weak.
• A difference of 10–15 % of the mean with a CV of 10–15 % typically needs 4–6 replicates in an RCBD.
• Power calculations use the CV; the biggest lever is reducing the CV through plot technique and blocking, not adding replicates.