# Analysis of variance in simple designs Perform analysis of variance and other important complementary analyzes. The function are easy to use. Performs analysis in various simples designs, with balanced and unbalanced data. Too performs analysis the kruskal-Wallis and Friedman (designs 14 and 15). ```r ea1(data, design = 1, alpha = 0.05, list = FALSE, p.adjust=1, plot=2) ``` ## Arguments - `data`: data is a data.frame see how the input data in the examples - `design`: 1 = completely randomized design 2 = randomized block design 3 = latin square design 4 = several latin squares 5 = analysis with a covariate (completely randomized design) 6 = analysis with a covariate (randomized block design) 7 = incomplete blocks type I and II 8 = incomplete blocks type III or augmented blocks 9 = incomplete blocks type III in animal experiments 10 = lattice (intra-block analysis) 11 = lattice (inter-block analysis) 12 = switchback design 13 = switchback design in blocks 14 = Kruskal-Wallis rank sum test 15 = Friedman rank sum test - `alpha`: significance level for multiple comparisons - `list`: FALSE = a single response variable TRUE = multivariable response - `p.adjust`: 1="none"; 2="holm"; 3="hochberg"; 4="hommel"; 5="bonferroni"; 6="BH", 7="BY"; 8="fdr"; for more details see function "p.adjust" - `plot`: 1 = box plot for residuals; 2 = standardized residuals vs sequence data; 3 = standardized residuals vs theoretical quantiles ## Details The response variable must be numeric. Other variables can be numeric or factors. ## Returns Returns analysis of variance, means (adjusted means), multiple comparison test (tukey, snk, duncan, t and scott knott) and residual analysis. Too returns analysis the kruskal-Wallis and Friedman (designs 14 and 15). ## References CRUZ, C.D. and CARNEIRO, P.C.S. Modelos biometricos aplicados ao melhoramento genetico. 2nd Edition. Vicosa, UFV, v.2, 2006. 585p. KAPS, M. and LAMBERSON, W. R. Biostatistics for Animal Science: an introductory text. 2nd Edition. CABI Publishing, Wallingford, Oxfordshire, UK, 2009. 504p. SAMPAIO, I. B. M. Estatistica aplicada a experimentacao animal. 3nd Edition. Belo Horizonte: Editora FEPMVZ, Fundacao de Ensino e Pesquisa em Medicina Veterinaria e Zootecnia, 2010. 264p. SANDERS W.L. and GAYNOR, P.J. Analysis of switchback data using Statistical Analysis System, Inc. Software. Journal of Dairy Science, 70.2186-2191. 1987. PIMENTEL-GOMES, F. and GARCIA C.H. Estatistica aplicada a experimentos agronomicos e florestais: exposicao com exemplos e orientacoes para uso de aplicativos. Editora Fealq, v.11, 2002. 309p. ## Author(s) Emmanuel Arnhold ## See Also ea2, ec ## Examples ```r # Kaps and Lamberson(2009) data(data1) data(data2) data(data3) data(data4) # analysis in completely randomized design r1<-ea1(data1, design=1) names(r1) r1 # analysis in randomized block design r2<-ea1(data2, design=2) # analysis in latin square design r3<-ea1(data3, design=3) # analysis in several latin squares design r4<-ea1(data4, design=4) r1[1] r2[1] r3[1] r4[1] # analysis in unbalanced randomized block design response<-ifelse(data2$Gain>850, NA, data2$Gain) ndata<-data.frame(data2[-3],response) ndata r5<-ea1(ndata, design=2 ) r5 # multivariable response (list argument = TRUE) t<-c('a','a','a','b','b','b','c','c','c') r1<-c(10,12,12.8,4,6,8,14,15,16) r2<-c(102,105,106,125,123,124,99,95,96) r3<-c(560,589,590,658,678,629,369,389,378) d<-data.frame(t,r1,r2,r3) results=ea1(d, design=1, list=TRUE) names(results) results results[1][[1]] names(results[1][[1]]) # analysis with a covariate # Kaps and Lamberson (2009) data(data10) # analysis in completely randomized design r6<-ea1(data10[-3], design=5) r6 # incomplete blocks type I and II # Pimentel Gomes and Garcia (2002) data(data11) data(data12) r7<-ea1(data11,design=7) r8<-ea1(data12,design=7) r7;r8 # incomplete blocks type III or augmented blocks # Cruz and Carneiro (2006) data(data13) r9<-ea1(data13, design=8) r9 # incomplete blocks type III in animal experiments # Sampaio (2010) data(data14) r10<-ea1(data14, design=9) r10 # lattice # Pimentel Gomes and Garcia (2002) data(data15) r11<-ea1(data15, design=10) # intra-block analysis r12<-ea1(data15, design=11) # inter-block analysis r11 r12 # switchback design # Sampaio (2010) data(data16) r13<-ea1(data16, design=12) r13 # switchback design in blocks # Sanders and Gaynor (1987) data(data17) r14<-ea1(data17, design=13) r14 #Kruskal-Wallis Rank Sum Test r15<-ea1(data1, design=14) r15 #Friedman Rank Sum Test r16<-ea1(data2, design=15) r16 # Graeco-Latin Square #latin letters treatment=c("A","B","C","D","E","B","C","D","E","A","C", "D","E","A","B","D","E","A","B","C","E","A","B","C","D") ##blocked factors #greek letters block=c(1,2,3,4,5,3,4,5,1,2,5,1,2,3,4,2,3,4,5,1,4,5,1,2,3) # rowns rows=rep(1:5,5) #coluns columns=rep(1:5, each=5) #variable response=c(-1,-8,-7,1,-3,-5,-1,13,6,5,-6,5,1,1,-5,-1,2,2,-2,4,-1,11,-4,-3,6) # table data=data.frame(treatment, block, rows, columns, response) r16=ea1(data, design=16) r16 ### Repetitions of Graeco-Latin Square #latin letters treatment=c("A","B","C","D","E","B","C","D","E", "A","C","D","E","A","B","D","E","A","B","C","E","A","B","C","D", "A","B","C","D","E","B","C","D","E","A","C","D", "E","A","B","D","E","A","B","C","E","A","B","C","D") #squares squares=rep(1:2,25) ##blocked factors #greek letters block=c(1,2,3,4,5,3,4,5,1,2,5,1,2,3,4,2,3,4,5,1,4,5,1,2,3, 1,2,3,4,5,3,4,5,1,2,5,1,2,3,4,2,3,4,5,1,4,5,1,2,3) # rowns rows=c(rep(1:5,5),rep(1:5,5)) #coluns columns=c(rep(1:5, each=5),rep(1:5, each=5)) #variable response=c(-1,-8,-7,1,-3,-5,-1,13,6,5,-6,5,1,1,-5,-1,2,2,-2,4,-1,11,-4,-3,6, -2,-9,-8,1,-2,-5,-1,9,6,5,-5,2,3,1,-7,-1,2,4,-1,2,-2,15,-5,-1,7) # table data=data.frame(treatment, squares, block, rows, columns, response) r17=ea1(data, design=17) r17 ```

ea1 function