Irrigation Trial with a Soil Gradient: Replication or Pseudoreplication?

The main problem is confounding of irrigation with spatial variation and pseudoreplication. Treatments are assigned in strips across rows, so if the strips follow the soil-depth gradient, irrigation is entangled with soil depth, water-holding capacity and possibly row position. The shaded edge row adds another positional effect. Four plots per treatment are not independent replicates if they are contiguous strips; they are subsamples of one strip. The proposed two-way ANOVA without a block term treats all plots as independent, ignores the spatial structure and pools two seasons as if they were independent observations. That inflates the error df and can produce false significance. The clone factor may also be unevenly distributed. The design can describe patterns within this block, but it cannot support a causal claim that deficit irrigation increases Brix without reducing yield. The water authority's interest makes overclaiming a real risk. The minimum fix is to model the spatial structure and to frame the trial as a case study unless true randomisation within blocks exists.

Use a linear mixed-effects model with irrigation, clone and their interaction as fixed effects; include soil depth as a covariate and a spatial block or row/column term as a random effect. If plots are nested within strips, include strip as a random effect and recognise that irrigation is a strip-level treatment, so the denominator df for irrigation should be based on strips, not plots. Include season as a repeated measure or fit a random effect for plot across seasons, and test for a season × irrigation interaction rather than pooling blindly. Check residuals for heteroscedasticity and spatial autocorrelation; if present, use a spatial correlation structure or robust standard errors. Report variance components, effect sizes and 95% CIs. With only two hours of statistician time, pre-specify this model and avoid stepwise selection. If the design cannot support strip-level replication, present the analysis as exploratory and do not use causal language. The model addresses the constraints by separating plot-level noise from treatment effects, but it cannot create randomisation that was not there.

Permit conclusions of the form: 'Within this block and these two seasons, plots under 70% ETc had higher Brix and similar yield to 100% ETc, after accounting for soil depth and spatial position; the estimate is imprecise and the design is not randomised at the strip level.' Permit reporting of effect sizes with confidence intervals and a clear statement that the result is conditional on the site. Prohibit: 'Deficit irrigation increases Brix without reducing yield' as a general claim; '40% ETc is safe' from a single block; and any causal language that ignores the soil-depth confound and the shaded row. Also prohibit pooling the two seasons if a season interaction is present, and prohibit using significance alone to recommend policy. If the water authority wants a recommendation, the dissertation should say that the trial is a pilot and that a replicated randomised block trial across sites is needed. The candidate should also disclose the funder's interest and state that the funder had no role in analysis.