<p>RCBD: Power Calculation [ST&D 241]</p><p>(ST&D 207) Percent oil in flax seed harvested from plants inoculated with rust disease at different stages.</p><p>2 Treatment Block 1 Block 2 Block 3 Block 4 Mean τi Seedling 34.4 35.9 36.0 34.1 35.100 0.188 Early bloom 33.3 31.9 34.9 37.1 34.300 1.521 Late bloom 34.4 34.0 34.5 33.1 34.000 2.351 Full bloom 36.8 36.6 37.0 36.4 36.700 1.361 Ripening 36.3 34.9 35.9 37.2 36.075 0.293 Control 36.4 37.3 37.7 36.7 37.025 2.225 Mean 35.267 35.100 36.000 35.767 35.533 Σ = 7.940 2 βi 0.071 0.188 0.218 0.054 Σ = 0.531</p><p>Source df SS MS F Treatment 5 31.758 6.352 4.790 Block 3 3.187 1.062 0.801 Error 15 19.888 1.326 </p><p>To calculate the power of an RCBD, use Pearson and Hartley's power function charts (1953, Biometrika 38:112-130). To begin, calculate :</p><p> r  2 4  7.940     i     2.00 MSE t 1.326  6 </p><p>Looking in the power charts for dft = 5, dfe = 15, and  = 0.05, we find a power of ~ 90%.</p><p>Power analysis in SAS is also straightforward:</p><p>1 Data Flax; Do Trtmt = 1 to 6; Do Block = 1 to 4; Input Oil @@; Output; End; End; Cards; 34.4 35.9 36.0 34.1 33.3 31.9 34.9 37.1 34.4 34.0 34.5 33.1 36.8 36.6 37.0 36.4 36.3 34.9 35.9 37.2 36.4 37.3 37.7 36.7 ; Proc GLM Data = Flax; Class Trtmt Block; Model Oil = Trtmt Block;</p><p>Proc GLMPower Data = Flax; Class Trtmt Block; Model Oil = Trtmt Block; Power Stddev = 1.151472  The Root MSE from ANOVA table Alpha = 0.05  Specify the alpha ntotal = 24  Specify n, the number of EUs in the experiment Power = .;  A period here tells SAS to calculate the power Run; Quit;</p><p>The output:</p><p>Fixed Scenario Elements</p><p>Dependent Variable Oil Alpha 0.05 Error Standard Deviation 1.151472 Total Sample Size 24 Error Degrees of Freedom 15</p><p>Computed Power</p><p>Test Index Source DF Power</p><p>1 Trtmt 5 0.904</p><p>2</p>