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Table 1 Results of hypothesis tests from the mixed model analyses for all response variables

From: Accounting for variation in designing greenhouse experiments with special reference to greenhouses containing plants on conveyor systems

  Day 21 Day 51
  Total area Total area Fresh weight Height Density index
  P b Actionc P b Actionc P b Actionc P b Actionc P b Actionc
Random model change a
Add heterogeneous Locations / Tactics variancesd 0.023 Retain 0.021 Retain 0.061 Retain 0.017 Retain 0.161 Retain
Add columns / Positions ar1, differing for Locations / Tactics 0.416 Omit 0.810 Omit 0.771 Omit 0.015 Omit 0.589 Omit
Drop ColumnsLocations / PositionsTactics deviations 0.347 Omit 0.131 Omit 0.468 Omit 0.245 Omit 0.469 Omit
Drop spl(Columns)Locations/ spl(Positions)Tactics 0.005 Retain 0.262 Retain 0.045 Retain 0.073 Retain 0.464 Retain
Drop position deviations    DNF Omit DNF Omit 0.120 Omit DNF Omit
Drop spl(Position)    DNF Omit DNF Omit DNF Omit DNF Omit
Check heterogeneous Locations / Tactics variancesd 0.038 Retain 0.015 Retain 0.025 Retain 0.007 Retain 0.392 Omit
Check ar1 on Columns / Positions, differing for Locations / Tactics 0.395 Omit 0.839 Omit 0.622 Omit 0.224 Omit 0.467 Omit
Fixed model testing a
lin(Columns)Locations / lin(Positions)Tactics <0.001 NA 0.026 Retain 0.036 NA 0.005 NA 0.012 Retain
lin(Positions)    <0.001 NA <0.001 NA 0.710 NA <0.001 NA
LocationsRows / TacticsLanes 0.210 ns 0.405 ns 0.311 ns 0.311 ns 0.772 ns
Locations / Tactics 0.099 NA <0.001 NA <0.001 NA 0.007 NA <0.001 NA
  1. aThe italicized term before the slash is for Day 21 and the one after the slash is for Day 51.
  2. bDNF indicates that the parameters in the changed model “Did Not Fit”, either because of a lack of convergence or because the estimates for one or more parameters was zero; on occasion terms with a P-value between 0.05 and 0.10 are retained on the grounds that there is some indication that the terms are required.
  3. cNA indicates that testing was not applicable because, for this term, (i) its factors are a subset of those for a significant fixed term or (ii) it has the same factors as a higher-order term that is significant; ns indicates not significant.
  4. dA significance level of 0.25 is used for this hypothesis test in order to decrease the chance of a Type I error and to err on the side of allowing for heterogeneous variances if there is some evidence for them.