Fig. 1.

Main steps of power analysis.

 


Fig. 2.

Probability (power) of detecting a statistically significant (α = 0.05) treatment effect in total C concentration from the Long-Term Ecological Research experiment (randomized complete block design [RCBD] with 30 samples: six replicate plots and five subsamples per plot) as a function of relative differences between no-till (NT) and conventional tillage (CT) treatments for surface, middle, and deep soil layers (based on data from Syswerda et al. 2011). The numbers above each bar represent the number of subsamples that need to be taken in each of six replicated plots of this RCBD experiment to detect the hypothesized differences between CT and NT treatments with 90% probability (power) at α = 0.05.

 


Fig. 3.

Probability (power) of detecting statistically significant (α = 0.05) treatment effects from the 11 Major Land Resources Area sites sampled by Blanco-Canqui and Lal (2008), a set of 11 completely randomized design experiments with three replications, as a function of relative differences between conventional tillage (CT) and no-till (NT) treatments for three soil depths. The graph shows the average power values calculated based on the analyses conducted for each of the 11 experiments. Vertical lines within bars represent standard deviations.

 


Fig. 4.

Probability of getting statistically significant (α = 0.05) results in analyses of soil C concentrations at the 50- to 60-cm depth if there were a 200% (4×) difference in soil C concentrations between the conventional tillage (CT) and no-till (NT) treatments of Blanco-Canqui and Lal (2008) The data are from the 11 Major Land Resources Area sites reported (completely randomized design [CRD] with three replications). Numbers above the bars represent the number of replications needed in a CRD analysis conducted separately at each site to detect the hypothesized 200% (4×) difference with 90% probability (power) (α = 0.05).

 


Fig. 5.

Probability of detecting a statistically significant (α = 0.05) treatment effect in total C stocks from the Long-Term Ecological Research experiment (randomized complete block design [RCBD] with six replications and five subsamples per replicated plot) if the difference between no-till (NT) and conventional tillage (CT) treatments was 50% of the grand average in each layer (data from Syswerda et al., 2011). Layer-only analysis refers to the statistical analyses conducted separately for each layer in which the 50% difference occurred. Whole-profile analysis refers to statistical analyses conducted using calculated whole-profile C stocks. The numbers above the bars represent the number of subsamples needed in each of six replicated plots of this RCBD experiment to detect the hypothesized difference in C stocks with 90% probability (α = 0.05).