1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
# Student - Newman - Keuls Test
#
# Author: FrankKonietschke
###############################################################################
snk <- function(formula,data,alpha, MSE=NULL, df=NULL, silent = FALSE){
dat <- model.frame(formula, data)
if (ncol(dat) != 2) {
stop("Specify one response and only one class variable in the formula")
}
if (is.numeric(dat[, 1]) == FALSE) {
stop("Response variable must be numeric")
}
response <- dat[, 1]
group <- as.factor(dat[, 2])
fl <- levels(group)
a <-nlevels(group)
N <- length(response)
samples <- split(response,group)
n <- sapply(samples,"length")
mm <- sapply(samples,"mean")
vv <- sapply(samples,"var")
if (is.null(MSE)){
MSE <- sum((n-1)*vv)/(N-a)
}
if (is.null(df)){
df <- N-a
}
nc <- a*(a-1)/2
order.h1 <- data.frame(Sample=fl, Size=n, Means=mm,Variance=vv)
ordered <- order.h1[order(order.h1$Means,decreasing=FALSE), ]
rownames(ordered) <- 1:a
#---------------- Compute helping indices ----------#
i <- 1:(a-1)
h1 <- list()
for(s in 1:(a-1)){
h1[[s]]<- i[1:s]
}
vi <- unlist(h1)
j <- a:2
h2 <-list()
for (s in 1:(a-1)){
h2[[s]] <- j[s:1]
}
vj <- unlist(h2)
h3 <- list()
h4 <- list()
for (s in 1:(a-1)){
h3[[s]] <- rep(j[s],s)
h4[[s]] <- rep(i[s],s)
}
Nmean <- unlist(h3)
Step <- unlist(h4)
#--------Compute the Mean Differences---------#
mean.difference <- sapply(1:nc,function(arg){
i <- vi[arg]
j <- vj[arg]
(ordered$Means[j]-ordered$Means[i])
})
mean.difference <- round(mean.difference, 4)
# ------- Compute the test statistics --------#
T <- sapply(1:nc,function(arg){
i<-vi[arg]
j<-vj[arg]
(ordered$Means[j]-ordered$Means[i])/sqrt(MSE/2*(1/ordered$Size[i] + 1/ordered$Size[j]))
})
T <- round(T, 4)
# ----- Compute now the critical value -----#
quantiles <- qtukey(1-alpha,Nmean,df)
pvalues <- ptukey(T,Nmean,df,lower.tail=FALSE)
#---- Calculate the rejected Hypotheses ------#
Rejected1 <- (pvalues<alpha)
#------------ Names for the Output -----------#
names.ordered <- sapply(1:nc, function(arg){
i <- vi[arg]
j <- vj[arg]
paste(ordered$Sample[j], "-", ordered$Sample[i], sep="")
})
# ------ Compute now the rejected statistics-----#
for (s in 1:nc){
if (Rejected1[s]==FALSE){
Under1 <- (vj[s]>=vj)
Under2 <- (vi[s]<=vi)
Under3 <- Under1 * Under2
Under4 <- which(Under3==1)
Rejected1[Under4] <- FALSE
}
}
#-----Prepare the pValues for the Output----#
Out1 <- (pvalues < alpha)
Out2 <- (Rejected1 == FALSE)
Out3 <- Out1 * Out2
Out4 <- (Out3 == 1)
pvalues <- round(pvalues,4)
pvalues[Out4] <- paste(">",alpha)
variances.output <- data.frame(Overall=MSE, df=df)
Comparison <- data.frame(Comparison=names.ordered,Diff=mean.difference, Statistic=T, Adj.P=pvalues, Rejected=Rejected1, Layer = Step)
if (! silent)
{
cat("#----Student-Newman-Keuls (1927; 1939; 1952) rejective Multiple Test Procedure \n\n")
cat("#----Attention: The SNK test controls the FWER only in the WEAK sense \n\n")
}
result <- list(Ordered.Means = ordered, Variances=variances.output,
SNK = Comparison)
return(result)
}
snk.wrapper <- function(model, data, alpha, silent=FALSE) {
result <- snk(formula=formula(model),
data,
alpha = alpha)
difference <- result$SNK$Diff#, result$SNK$Statistic, result$SNK$Layer)
diffm<-cbind(difference,rep(NA,length(difference)),rep(NA,length(difference)))
diffm<-matrix(diffm,nrow=length(difference))
rownames(diffm)<-result$SNK$Comparison
return(list(adjPValues=result$SNK$Adj.P,rejected=result$SNK$Rejected,statistics=result$SNK$Statistic,
confIntervals= diffm,errorControl = new(Class='ErrorControl',type="FWER",alpha=alpha)))
}
mutoss.snk <- function() { return(new(Class="MutossMethod",
label="Student-Newman-Keuls Test",
errorControl="FWER.weak",
callFunction="snk.wrapper",
output=c("adjPValues", "rejected", "confIntervals", "errorControl"),
info="<h2>Student - Newman - Keuls rejective test procedure.\
The procedure controls the FWER in the WEAK sense. </h2>\n\n\
<p> The Newman-Keuls procedure is based on a stepwise or \
layer approach to significance testing. Sample means are \
ordered from the smallest to the largest. The largest \
difference, which involves means that are r = p steps apart, \
is tested first at alpha level of significance; if significant, \
means that are r = p - 1 steps apart are tested at \alpha level \
of significance and so on.\
</p>\n\
<h3>Reference:</h3>\
<ul>\
<li>Keuls M (1952). \"<i> The use of the studentized range in \
connection with an analysis of variance
</i>\" Euphytica 1 37, 112-122. </li>\n\
</ul>",
parameters=list(
data=list(type="data.frame"),
model=list(type="ANY"),
alpha=list(type="numeric")
)
)) }
|
