#In this dataset we are looking at Sales Transactions, from numerous amounts of Sales
#Reps selling numerous Amounts of Products
#The Goal of this is to analyze trasactions within the data to see if there are any
#attempts of Fraud by the salesreps
#Different types of variables
#ID of the sales rep
#Prod - unique identifyer of the product they are selling
#Quant - The Numer of units sold
#Val - The Reported total monetary value of the sale
#Insp - Inspection, if this is OK, Fraud, or Unknown
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.0.5
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
data(sales, package = 'DMwR2')
sales
## # A tibble: 401,146 x 5
## ID Prod Quant Val Insp
## <fct> <fct> <int> <dbl> <fct>
## 1 v1 p1 182 1665 unkn
## 2 v2 p1 3072 8780 unkn
## 3 v3 p1 20393 76990 unkn
## 4 v4 p1 112 1100 unkn
## 5 v3 p1 6164 20260 unkn
## 6 v5 p2 104 1155 unkn
## 7 v6 p2 350 5680 unkn
## 8 v7 p2 200 4010 unkn
## 9 v8 p2 233 2855 unkn
## 10 v9 p2 118 1175 unkn
## # ... with 401,136 more rows
summary(sales)
## ID Prod Quant Val
## v431 : 10159 p1125 : 3923 Min. : 100 Min. : 1005
## v54 : 6017 p3774 : 1824 1st Qu.: 107 1st Qu.: 1345
## v426 : 3902 p1437 : 1720 Median : 168 Median : 2675
## v1679 : 3016 p1917 : 1702 Mean : 8442 Mean : 14617
## v1085 : 3001 p4089 : 1598 3rd Qu.: 738 3rd Qu.: 8680
## v1183 : 2642 p2742 : 1519 Max. :473883883 Max. :4642955
## (Other):372409 (Other):388860 NA's :13842 NA's :1182
## Insp
## ok : 14462
## unkn :385414
## fraud: 1270
##
##
##
##
nlevels(sales$ID)
## [1] 6016
nlevels(sales$Prod)
## [1] 4548
filter(sales, is.na(Quant), is.na(Val))
## # A tibble: 888 x 5
## ID Prod Quant Val Insp
## <fct> <fct> <int> <dbl> <fct>
## 1 v29 p808 NA NA unkn
## 2 v453 p921 NA NA unkn
## 3 v431 p1035 NA NA unkn
## 4 v431 p1 NA NA unkn
## 5 v431 p1 NA NA unkn
## 6 v1039 p1101 NA NA unkn
## 7 v1158 p1101 NA NA unkn
## 8 v1183 p1103 NA NA unkn
## 9 v709 p1125 NA NA ok
## 10 v426 p1190 NA NA unkn
## # ... with 878 more rows
#Number of fraud detection is very low in the inspection column, this is a very small proportion
table(sales$Insp) /nrow(sales) *100
##
## ok unkn fraud
## 3.605171 96.078236 0.316593
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.0.5
ggplot(group_by(sales,ID) %>% summarize(nTrans=n()),aes(x=ID,y=nTrans)) +
geom_bar(stat="identity") +
theme(axis.text.x = element_blank(), axis.ticks.x=element_blank()) +
xlab("Salesmen") + ylab("Nr. of Transactions") +
ggtitle("Nr. of Transactions per Salesman")
ggplot(group_by(sales,Prod) %>% summarize(nTrans=n()),aes(x=Prod,y=nTrans)) +
geom_bar(stat="identity") +
theme(axis.text.x = element_blank(), axis.ticks.x=element_blank()) +
xlab("Product") + ylab("Nr. of Transactions") +
ggtitle("Nr. of Transactions per Product")
#Lets get Unit Price because each transaction sells a different amount of units
sales <- mutate(sales, Uprice = Val/Quant)
summary(sales$Uprice)
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.00 8.46 11.89 20.30 19.11 26460.70 14136
#Some products have very few transactions, 4,548 products, 982 have less than 20 transactions
#Lets get the most expensive and cheapest products
prods <- group_by(sales,Prod)
mpProds <- summarize(prods,medianPrice = median(Uprice, na.rm = TRUE))
bind_cols(mpProds %>% arrange(medianPrice) %>% slice(1:5),
mpProds %>% arrange(desc(medianPrice)) %>% slice(1:5))
## New names:
## * Prod -> Prod...1
## * medianPrice -> medianPrice...2
## * Prod -> Prod...3
## * medianPrice -> medianPrice...4
## # A tibble: 5 x 4
## Prod...1 medianPrice...2 Prod...3 medianPrice...4
## <fct> <dbl> <fct> <dbl>
## 1 p560 0.0169 p3689 9204.
## 2 p559 0.0188 p2453 456.
## 3 p4195 0.0303 p2452 329.
## 4 p601 0.0552 p2456 305.
## 5 p563 0.0558 p2459 284.
#THe distributiion of unit prices for the cheapest and most expensive products.
#We use log scale to avoid the valuyes of the cheapest product becoming indistringuishable
library(ggplot2)
library(forcats)
## Warning: package 'forcats' was built under R version 4.0.5
ggplot(filter(sales,Prod %in% c('p3689', 'p560')), aes(x=fct_drop(Prod), y=Uprice)) +
geom_boxplot() + scale_y_log10() +
xlab('') + ylab('log10(UnitPrice)')
## Warning: Removed 1 rows containing non-finite values (stat_boxplot).
#Sales people who bring more (less) money to the company
ids <- group_by(sales, ID)
tvIDs <- summarize(ids, totalVal = sum(Val, na.rm = TRUE))
bind_cols(tvIDs %>% arrange(totalVal) %>% slice(1:5),
tvIDs %>% arrange(desc(totalVal)) %>% slice(1:5))
## New names:
## * ID -> ID...1
## * totalVal -> totalVal...2
## * ID -> ID...3
## * totalVal -> totalVal...4
## # A tibble: 5 x 4
## ID...1 totalVal...2 ID...3 totalVal...4
## <fct> <dbl> <fct> <dbl>
## 1 v3355 1050 v431 211489170
## 2 v6069 1080 v54 139322315
## 3 v5876 1115 v19 71983200
## 4 v6058 1115 v4520 64398195
## 5 v4515 1125 v955 63182215
#Top 100 people on this account for almost 40% of income of the company while the bottom
#2,000 out of the 6,016 generate less than 2% of the income
arrange(tvIDs,desc(totalVal)) %>% slice(1:100) %>%
summarize(t100=sum(totalVal)) /
(summarize(tvIDs,sum(totalVal))) * 100
## t100
## 1 38.33277
arrange(tvIDs,totalVal) %>% slice(1:2000) %>%
summarize(b2000=sum(totalVal)) /
(summarize(tvIDs,sum(totalVal))) * 100
## b2000
## 1 1.988716
#Carrying out a similiar analysis in terms of the qwuanitity that is sold for each product
prods <- group_by(sales,Prod)
qtProds <- summarize(prods, totalQty = sum(Quant, na.rm = TRUE))
bind_cols(qtProds %>% arrange(desc(totalQty)) %>% slice(1:5),
qtProds %>% arrange(totalQty) %>% slice(1:5))
## New names:
## * Prod -> Prod...1
## * totalQty -> totalQty...2
## * Prod -> Prod...3
## * totalQty -> totalQty...4
## # A tibble: 5 x 4
## Prod...1 totalQty...2 Prod...3 totalQty...4
## <fct> <int> <fct> <int>
## 1 p2516 535301953 p2442 0
## 2 p3599 474050752 p2443 0
## 3 p314 367166615 p1653 108
## 4 p569 107686551 p4101 202
## 5 p319 86818285 p3678 405
arrange(qtProds,desc(totalQty)) %>% slice(1:100) %>%
summarize(t100=sum(as.numeric(totalQty))) /
(summarize(qtProds,sum(as.numeric(totalQty)))) * 100
## t100
## 1 74.63478
arrange(qtProds,totalQty) %>% slice(1:4000) %>%
summarize(b4000=sum(as.numeric(totalQty))) /
(summarize(qtProds,sum(as.numeric(totalQty)))) * 100
## b4000
## 1 8.944681
#Anything out in boxplot.stats is considered an outlier
nouts <- function (x) length(boxplot.stats(x)$out)
noutsProds <- summarise(prods, nOut = nouts(Uprice))
arrange(noutsProds, desc(nOut))
## # A tibble: 4,548 x 2
## Prod nOut
## <fct> <int>
## 1 p1125 376
## 2 p1437 181
## 3 p2273 165
## 4 p1917 156
## 5 p1918 156
## 6 p4089 137
## 7 p538 129
## 8 p3774 125
## 9 p2742 120
## 10 p3338 117
## # ... with 4,538 more rows
#Around 29,000 of our transactions are outliers which is 7% of our data
sum(noutsProds$nOut)
## [1] 29446
sum(noutsProds$nOut) / nrow(sales) *100
## [1] 7.34047
#Our main concern are transactions that have both the missing value of Quant and Val.
#THis below will look at transactions with unknowns on both Val and Quant
prop.naQandV <- function(q,v) 100*sum(is.na(q) & is.na(v)) / length(q)
summarise(ids, nProbs = prop.naQandV(Quant,Val)) %>% arrange(desc(nProbs))
## # A tibble: 6,016 x 2
## ID nProbs
## <fct> <dbl>
## 1 v1237 13.8
## 2 v4254 9.52
## 3 v4038 8.33
## 4 v5248 8.33
## 5 v3666 6.67
## 6 v4433 6.25
## 7 v4170 5.56
## 8 v4926 5.56
## 9 v4664 5.49
## 10 v4642 4.76
## # ... with 6,006 more rows
#Looking at respect to the products
summarise(prods, nProbs = prop.naQandV(Quant,Val)) %>% arrange(desc(nProbs))
## # A tibble: 4,548 x 2
## Prod nProbs
## <fct> <dbl>
## 1 p2689 39.3
## 2 p2675 35.4
## 3 p4061 25
## 4 p2780 22.7
## 5 p4351 18.2
## 6 p2686 16.7
## 7 p2707 14.3
## 8 p2690 14.1
## 9 p2691 12.9
## 10 p2670 12.8
## # ... with 4,538 more rows
#The option of removing all transactions wiht unknown values on both quantity and the value
#is the best option we have
sales <- filter(sales, !(is.na(Quant) & is.na(Val)))
#Analyze the remaining reporta with unkown values in either quanity or value of transaction
prop.nas <- function(x) 100*sum(is.na(x)) / length(x)
summarise(prods, propNA.Q = prop.nas(Quant)) %>% arrange(desc(propNA.Q))
## # A tibble: 4,548 x 2
## Prod propNA.Q
## <fct> <dbl>
## 1 p2442 100
## 2 p2443 100
## 3 p1653 90.9
## 4 p4101 85.7
## 5 p4243 68.4
## 6 p903 66.7
## 7 p3678 66.7
## 8 p4061 66.7
## 9 p3955 64.3
## 10 p4313 63.6
## # ... with 4,538 more rows
#Looking into two products (p2442 and p2443 that have all of their transactions with
#unknown values of the quantity)
filter(sales, Prod %in% c('p2242', 'p2443')) %>%
group_by(Insp) %>% count()
## # A tibble: 3 x 2
## # Groups: Insp [3]
## Insp n
## <fct> <int>
## 1 ok 1
## 2 unkn 32
## 3 fraud 2
#We will delete them
sales <- droplevels(filter(sales, !(Prod %in% c('p2242', 'p2443'))))
#Are there sales people with all transactions with an unknown quality
summarise(ids, propNA.Q = prop.nas(Quant)) %>% arrange(desc(propNA.Q))
## # A tibble: 6,016 x 2
## ID propNA.Q
## <fct> <dbl>
## 1 v2925 100
## 2 v4356 100
## 3 v5537 100
## 4 v5836 100
## 5 v6044 100
## 6 v6058 100
## 7 v6065 100
## 8 v2923 90
## 9 v4368 88.9
## 10 v2920 85.7
## # ... with 6,006 more rows
#Carrying out similiar analysis for the value column
summarise(prods, propNA.V = prop.nas(Val)) %>% arrange(desc(propNA.V))
## # A tibble: 4,548 x 2
## Prod propNA.V
## <fct> <dbl>
## 1 p2689 39.3
## 2 p2675 35.4
## 3 p1110 25
## 4 p4061 25
## 5 p2780 22.7
## 6 p4351 18.2
## 7 p4491 18.2
## 8 p2707 17.9
## 9 p1462 17.8
## 10 p1022 17.6
## # ... with 4,538 more rows
#Now with respect to the sales person
summarise(ids, propNA.V = prop.nas(Val)) %>% arrange(desc(propNA.V))
## # A tibble: 6,016 x 2
## ID propNA.V
## <fct> <dbl>
## 1 v5647 37.5
## 2 v74 22.2
## 3 v5946 20
## 4 v5290 15.4
## 5 v4022 14.0
## 6 v1237 13.8
## 7 v4472 12.5
## 8 v975 9.57
## 9 v4254 9.52
## 10 v2814 9.09
## # ... with 6,006 more rows
#Proportions are not too high, At this stage we have removed all reports that had insufficient
#information, for remaining NA values, we will start by obtaining typical unit price
#for each product. We will use the edian unit price of the transactions as typical price
#of respective products
tPrice <- filter(sales, Insp != 'fraud') %>%
group_by(Prod) %>%
summarise(medianPrice = median(Uprice, nana.rm = TRUE))
#We now have a typical unit price for each product, we can use it to calculate any of the two
#possibly missing values. We can do this because we currently do not have transactions with both missing values
noQuantMedPrices <- filter(sales, is.na(Quant)) %>%
inner_join(tPrice) %>%
select(medianPrice)
## Joining, by = "Prod"
noValMedPrice <- filter(sales, is.na(Val)) %>%
inner_join(tPrice) %>%
select(medianPrice)
## Joining, by = "Prod"
noQuant <- which(is.na(sales$Quant))
noVal <- which(is.na(sales$Val))
sales[noQuant, 'Quant'] <- ceiling(sales[noQuant, 'Val'] / noQuantMedPrices)
sales[noVal, 'Val'] <- sales[noVal,'Quant'] *noValMedPrice
sales$Uprice <- sales$Val / sales$Quant
ms <- filter(sales, Insp != 'fraud') %>%
group_by(Prod) %>%
summarize(median = median(Uprice, na.rm = TRUE),
iqr = IQR(Uprice, na.rm = TRUE),
nTrans = n(),
fewTrans = ifelse(nTrans>20, FALSE,TRUE))
ms
## # A tibble: 4,546 x 5
## Prod median iqr nTrans fewTrans
## <fct> <dbl> <dbl> <int> <lgl>
## 1 p1 11.4 10.4 196 FALSE
## 2 p2 10.9 5.61 81 FALSE
## 3 p3 10 5.73 31 FALSE
## 4 p4 9.91 6.00 111 FALSE
## 5 p5 11 8.30 161 FALSE
## 6 p6 13.3 6.97 63 FALSE
## 7 p7 4.85 0.547 52 FALSE
## 8 p8 3.85 0.728 11 TRUE
## 9 p9 1.94 0.343 38 FALSE
## 10 p10 42.2 33.0 38 FALSE
## # ... with 4,536 more rows
ggplot(ms,aes(x=median,y=iqr, color = fewTrans)) +
geom_point() +
xlab('Median') + ylab('IQR')
## Warning: Removed 1 rows containing missing values (geom_point).
ggplot(ms,aes(x=median,y=iqr, color = fewTrans)) +
geom_point() +
scale_y_log10() + scale_x_log10() +
xlab('log(Median)') + ylab('log(IQR)')
## Warning: Transformation introduced infinite values in continuous y-axis
## Removed 1 rows containing missing values (geom_point).
#We will use a non paramentric test to compare distributions of unit prices
#Kolmoorov_Sminorv test used to test the validitiy of the null hypothesis, both come from the same distribution
#If two distributiuons are similiar are calculated from statistic, the distance should be small
#For each product with few transactions, we have searcheded for the product with the most similiar media and IQR
ms <- mutate(ms, smedian = scale(median), siqr = scale(iqr))
smalls <- which(ms$fewTrans)
nsmalls <- as.character(ms$Prod[smalls])
similar <- matrix(data = NA, length(smalls),7,dimnames = list(nsmalls,
c('RowSimProd,', 'ks.stat',
'ks.p', 'medP', 'iqrP', 'medS',
'iqrS')))
xprods <- tapply(sales$Uprice, sales$Prod, list)
for(i in seq_along(smalls)) {
d <- scale(ms[,c("smedian","siqr")],
c(ms$smedian[smalls[i]],ms$siqr[smalls[i]]),
FALSE)
d <- sqrt(drop(d^2 %*% rep(1, ncol(d))))
stat <- ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]])
similar[i, ] <- c(order(d)[2], stat$statistic, stat$p.value,
ms$median[smalls[i]],ms$iqr[smalls[i]],
ms$median[order(d)[2]],ms$iqr[order(d)[2]])
}
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): p-value will be
## approximate in the presence of ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): p-value will be
## approximate in the presence of ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): p-value will be
## approximate in the presence of ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): p-value will be
## approximate in the presence of ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): p-value will be
## approximate in the presence of ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
## Warning in ks.test(xprods[[nsmalls[i]]], xprods[[order(d)[2]]]): cannot compute
## exact p-value with ties
head(similar)
## RowSimProd, ks.stat ks.p medP iqrP medS iqrS
## p8 2564 0.3286713 0.5404426 3.850211 0.7282168 3.889186 0.6903691
## p18 213 0.2568922 0.2581586 5.187266 8.0359968 5.274884 7.8207052
## p38 1044 0.3650794 0.1130832 5.490758 6.4162095 5.651818 6.2436224
## p39 2655 0.3701299 0.3675215 7.986486 1.4229755 7.904192 1.3410302
## p40 3971 0.3333333 0.1389203 9.674797 1.6104511 9.668854 1.5109890
## p47 1387 0.3125000 0.4854058 2.504092 2.5625835 2.413498 2.6402087
bind_rows(filter(ms,Prod==rownames(similar)[1]),
ms[similar[1,1],])
## # A tibble: 2 x 7
## Prod median iqr nTrans fewTrans smedian[,1] siqr[,1]
## <fct> <dbl> <dbl> <int> <lgl> <dbl> <dbl>
## 1 p8 3.85 0.728 11 TRUE -0.0813 -0.0719
## 2 p2566 3.89 0.690 13 TRUE -0.0810 -0.0721
nrow(similar[similar[,'ks.p'] >= 0.9, ])
## [1] 145
sum(similar[,'ks.p'] >= .9)
## [1] 145
#Precision and Recall curves are visual representations of the performance of a model
#n Terms of position and recall statistics
#These working points can be given by different cut off limits
#ROCR is a package that contains several functions that are very useful for evaluating binary classifiers
#Plot can give us different performances curves
library(ROCR)
## Warning: package 'ROCR' was built under R version 4.0.5
data("ROCR.simple")
pred <- prediction(ROCR.simple$predictions, ROCR.simple$labels)
perf <- performance(pred,'prec', 'rec')
plot(perf)
PRcurve <- function(preds, trues,...) {
require(ROCR, quietly = TRUE)
pd <- prediction(preds, trues)
pf <- performance(pd,'prec','rec')
pf@y.values <- lapply(pf@y.values, function(x) rev(cummax(rev(x))))
plot(pf, ...)
}
PRcurve(ROCR.simple$predictions, ROCR.simple$labels)
#Lift charts provide a different perspective of the model predictions.
# X axis is the rate of positive predictions, which is the probability that model
#predicts a positive class
#This estimated by the proportion of positive class predictions dived by the total number
#of test cases, Y axis is the value of recall divded by the value of RPP
pred <- prediction(ROCR.simple$predictions, ROCR.simple$labels)
perf <- performance(pred, "lift", "rpp")
plot(perf, main = "Lift Chart")
#SHows the recall values in terms of the inspection effort that is captured by the RPP
#Cumulative Recall Chart
CRchart <- function(preds, trues, ...) {
require(ROCR, quietly = T)
pd <- prediction(preds, trues)
pf <- performance(pd, "rec", "rpp")
plot(pf, ...)
}
CRchart(ROCR.simple$predictions, ROCR.simple$labels,
main='Cumulative Recall Chart')
#Normalized Distance to Typical Price
avgNDTP <- function(toInsp,train,stats) {
if (missing(train) && missing(stats))
stop('Provide either the training data or the product stats')
if (missing(stats)) {
stats <- as.matrix(filter(train,Insp != 'fraud') %>%
group_by(Prod) %>%
summarise(median=median(Uprice),iqr=IQR(Uprice)) %>%
select(median,iqr))
rownames(stats) <- levels(train$Prod)
stats[which(stats[,'iqr']==0),'iqr'] <- stats[which(stats[,'iqr']==0),'median']
}
return(mean(abs(toInsp$Uprice-stats[toInsp$Prod,'median']) /
stats[toInsp$Prod,'iqr']))
}
#Random Stratified Sample
evalOutlierRanking <- function(testSet,rankOrder,Threshold,statsProds,...)
{
ordTS <- testSet[rankOrder,]
N <- nrow(testSet)
nF <- if (Threshold < 1) as.integer(Threshold*N) else Threshold
cm <- table(c(rep('fraud',nF),rep('ok',N-nF)),ordTS$Insp)
prec <- cm['fraud','fraud']/sum(cm['fraud',])
rec <- cm['fraud','fraud']/sum(cm[,'fraud'])
AVGndtp <- avgNDTP(ordTS[1:nF,],stats=statsProds)
return(c(Precision=prec,Recall=rec,avgNDTP=AVGndtp))
}
#Unsupervised Approaches
#NDTP is a unitless metric and can mix together the values for the different products
#To get a scaled ranking for each product
#Gives a ranking order and score for potential outliers
BPrule.wf <- function(form,train,test,...) {
require(dplyr, quietly=TRUE)
ms <- as.matrix(filter(train,Insp != 'fraud') %>%
group_by(Prod) %>%
summarise(median=median(Uprice),iqr=IQR(Uprice)) %>%
select(median,iqr))
rownames(ms) <- levels(train$Prod)
ms[which(ms[,'iqr']==0),'iqr'] <- ms[which(ms[,'iqr']==0),'median']
ORscore <- abs(test$Uprice-ms[test$Prod,'median']) /
ms[test$Prod,'iqr']
rankOrder <- order(ORscore,decreasing=TRUE)
res <- list(testSet=test,rankOrder=rankOrder,
probs=matrix(c(ORscore,ifelse(test$Insp=='fraud',1,0)),
ncol=2))
res
}