> kruskal.test(Yield~fTrt) Kruskal-Wallis rank sum test data: Yield by fTrt Kruskal-Wallis chi-squared = 12.6894, df = 4, p-value = 0.01290 > > amoeba1.aov <- aov(Yield~fTrt) > > summary(amoeba1.aov) Df Sum Sq Mean Sq F value Pr(>F) fTrt 4 19666 4916.4 5.0444 0.001911 ** Residuals 45 43858 974.6 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > > # Obtain Tukey's Comparisons among levels of treatment > > TukeyHSD(amoeba1.aov, "fTrt") Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = Yield ~ fTrt) $fTrt diff lwr upr p adj H-None -42.9 -82.57118 -3.228817 0.0281550 F-None -49.5 -89.17118 -9.828817 0.0078618 HF-None -29.9 -69.57118 9.771183 0.2208842 FH-None -56.1 -95.77118 -16.428817 0.0019658 F-H -6.6 -46.27118 33.071183 0.9894377 HF-H 13.0 -26.67118 52.671183 0.8832844 FH-H -13.2 -52.87118 26.471183 0.8774716 HF-F 19.6 -20.07118 59.271183 0.6284290 FH-F -6.6 -46.27118 33.071183 0.9894377 FH-HF -26.2 -65.87118 13.471183 0.3444453 > > # Obtain Bonferroni's Comparisons among levels of treatment (does not use MSE from ANOVA and not pooled df) > > pairwise.t.test(Yield, fTrt, p.adj="bonf") Pairwise comparisons using t tests with pooled SD data: Yield and fTrt None H F HF H 0.0360 - - - F 0.0093 1.0000 - - HF 0.3768 1.0000 1.0000 - FH 0.0022 1.0000 1.0000 0.6707 P value adjustment method: bonferroni > > # Histogram of Residuals and Plot Residuals versus Time order > > hist(residuals(amoeba1.aov), breaks=seq(-75,75,15)) > > plot(residuals(amoeba1.aov), type="o") > > # Bartlett's test for equal variances > > bartlett.test(Yield~fTrt) Bartlett test of homogeneity of variances data: Yield by fTrt Bartlett's K-squared = 8.2024, df = 4, p-value = 0.08444 > >