) and fixed costs (implements, tractors,

pickup trucks, land lease, etc.). Following Bestor (2011) and Munkvold et al. (2001), the probability of tebuconazole treatments resulting in a yield difference larger than the estimated yield difference needed to offset the cost of tebuconazole was calculated from the observed yield difference between the treated and untreated plots and their observed standard deviation which was calculated from a pooled variance. That is, the probability that net returns from a tebuconazole treatment will SCH 900776 supplier at least break even, PT[R  n > (1 + 0) ∗ (C  f + C  a)]; be at least 25% greater than the investment on tebuconazole, PT[R  n > (1 + 0.25) ∗ (C  f + C  a)]; and be at least 50% larger than the investment on tebuconazole PT[R  n > (1 + 0.50) ∗ (C  f + C  a)] are estimated as equation(4) PT=1−Prob t[β0−(Yf−Yc)Sp(1nt+1nc)1/2,dfe],where β  0 is the yield difference needed to offset the cost of tebuconazole application (kg/ha), Sp2=((nt−1)S12+(nc−1)S22)/((nt−1)+(nc−1)) is a pool variance ( Box and Tiao, 1973), S12 is the variance of the observed yield from the treated plot, S22 is the variance of the observed yield from the untreated plot, nt is the number of observations

in the treated plot, nc is the number of observations in the control plot, and dfe is the number of degrees of freedom which is calculated using nt and nc. The yield difference needed to offset the cost of tebuconazole application is computed as equation(5)

β0=(1+ERn)(Cf+Ca)P,where ERn = 0, 0.25, or Trametinib Amino acid 0.50, when breaking even, achieving net returns 25% greater, or achieving net returns 50% greater than the tebuconazole investment respectively. Equations (3), (4) and (5) are used to conduct a probability analysis based on Bayesian inference. Bayesian inference approaches have been used in the management of fungal diseases (Esker and Conley, 2012, Bestor, 2011, De Bruin et al., 2010, Wiik and Rosenqvist, 2010, Munkvold et al., 2001 and Tari, 1996), in the management of insects (Foster et al., 1986), ecological studies (Cullinan et al., 1997), genetics (George et al., 2000 and Zhivitovsky, 1999), and in human and veterinary epidemiology (Knorr and Rasser, 2000 and Richardson and Gilks, 1993). Table 3 reports the OLS regression coefficients from equation (1). Overall average wheat yields in 2011 and 2012 were statistically different at the 5% significance level. In fact, at the 5% probability level, wheat yields in 2012 were typically 1118.25 kg/ha greater than in 2011, regardless of the location, cultivar, and treatment. This statistical difference in yield may be attributed to the presence of a disease in the Howe location in 2011 as discussed below, but it could also be partially attributed to the 56.