What it does
After harvest, every plot of a trial has a yield. The question is whether the treatments really differ, or whether the differences are just plot-to-plot noise. This calculator runs the analysis of variance (ANOVA) used for field trials and then compares the treatment means:
- ANOVA table: degrees of freedom, sums of squares, mean squares, the F value and its p-value for treatments, and for blocks, rows and columns where the design has them.
- CV %: the coefficient of variation, the square root of the error mean square as a percentage of the grand mean. It tells you how precise the trial was.
- LSD: the least significant difference at 5 % or 1 %, LSD = t × √(2 × error mean square ÷ replicates), with t from Student’s distribution on the error degrees of freedom. Two means further apart than the LSD differ significantly.
- Letters: means that share a letter are not significantly different. The highest mean’s group is “a”.
Designs
- Randomised complete block (RCBD): needs a block column, and every treatment exactly once in every block.
- Completely randomised (CRD): no blocks. Replication can be unequal; then the LSD is worked out for each pair of treatments.
- Latin square: needs a row column and a column column, with each treatment once in every row and every column.
The tool checks the layout and says plainly what is wrong (a missing plot, a treatment twice in a block). It does not estimate missing plots.
How to use it
- Paste your data, one plot per line, or press Open a file for a CSV or Excel sheet. A header row is recognised and the columns are picked from their names; change them with the column menus if needed.
- Pick the design and the significance level.
- Protected LSD (on by default) separates means only when the treatment F test is significant, which keeps the overall error rate in check. Turn it off to always compare all pairs.
- Download the means and ANOVA as a CSV, or the full report as an image, PDF or Word file.
Worked example
Press Use the example: five made-up varieties in four blocks, yields in t/ha. As an RCBD the page shows F = 86.77, p < 0.001 for treatments. The grand mean is 4.445, the error mean square is 0.0149 on 12 degrees of freedom, so the CV is 2.7 % and the LSD at 5 % is 2.179 × √(2 × 0.0149 ÷ 4) = 0.188. Variety B (5.225) gets “a”, D (4.775) “b”, A (4.300) and E (4.175) share “c”, and C (3.750) is “d”.
Change the design to CRD and the block differences go into the error: the CV rises to 7.5 %, the LSD to 0.500, and the groups overlap (A is “bc”, D is “ab”). That is why blocking pays.
FAQ
Which yield unit? Any. The results are in the same unit as your data.
What is a good CV? For yield trials, under about 10 % is good and 10 to 20 % is acceptable; higher usually points to typing errors or a very uneven field.
Should I use LSD or Tukey? The LSD is the usual choice for planned comparisons and small sets of treatments. With many treatments it finds more differences by chance; use the 1 % level or a stricter test then.
Is my data uploaded? No. Everything runs in your browser and works offline.
Where the numbers come from
- Sums of squares, F tests, CV % and Fisher's least significant difference are standard methods, as in Gomez and Gomez, Statistical Procedures for Agricultural Research (2nd ed.), chapters 2 and 5. Letters by the insert-and-absorb algorithm of Piepho (2004), Journal of Computational and Graphical Statistics 13: 456-466.
- Checked against statsmodels (anova_lm) and scipy (t quantiles) on the example (as RCBD and CRD), a 4 × 4 Latin square and an unbalanced CRD: every sum of squares, F, p-value, CV and LSD.
- The example yields are made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.