Simple visualization of a 11X5 table (for WordPress 2.9 Features Vote Results)

I guess this is not the number one post I would like to start with on this blog, but I feel the time is right for it (community-wise).

I’ll move on to the subject matter in a moment, but first a short intro: This blog is written by Tal Galili. I am an aspiring statistician who also loves to use R for his work. At the same time I am also a WordPress blogger, writing mainly at www.TalGalili.com where I can use my native language (Hebrew) for self expression.

This combination of statistics and blogging will lead me to sometimes much less statistical, but more Web/Open-Source oriented posts like this one. So for the statisticians in the audience I extend my apologies and invite you to wait for future posts which will be more fully focused on Statistics and R.

And now for the topic at hand. . .

*         *         *         *         *
I have just noticed the nice article published on the wordpress development blog titled “2.9 Features Vote Results“. The post exemplifies a wonderful trend in the WordPress community (led by Jane Wells) having to do with connecting between the core team and the WordPress user community. The way Jane does this is by giving surveys to WordPress users,  which in turn offers the WordPress core team an opportunity to understand the community needs.

In the post “2.9 Features Vote Results“, Jane presented the results of such survey. The post had tables and barplots, but the barplots were only present for the one dimensional variables. In contrast, more elaborate data, such as that of question 2 (asking to rate each of 11 potential features on a scale of 1 to 5), was shown only with a table, such as this:

The table gives the full information (although I would love it if it was easily downloadable, instead of having to type in the numbers) – but its main limitation is that from a quick look, one can not easily get (let alone understand) anything.

For the goal of understanding more of the results with a quick glance, I offer two simple and well-known visualizations for the results.

1) Parallel barplots (click for bigger image)

This plot can be easily implemented in Excel (although I did it in R) and can allow us to compare the different ranking each potential feature received.

For example, this shows us that most answers were usually given rank 4 (“would be nice”) for each feature.

2) Mosaic plot (click for bigger image)

I don’t know if this can be done in Excel, but with R it is just a simple line of code.

(mosaicplot((DataSet.table), las = 1, col = c(“gray”,”gray”,”blue”,3,”dark green”), main = “”))

The advantage of this plot is that it allows us to compare the different features easily, while not only comparing the top rank, but also combining different rankings for easy comparison (for example, comparing how many rank 4 or 5 each feature received).

So for example, the plot shows me that the most ranked with number 5 was the feature “easier embeds” but the most ranked “number 4 or 5″ was the feature “custom image sizes”. The feature “media album” came close to these two, but didn’t top either.

Conclusions from this post:

1. It would be nice (if possible) to publish the full data of the surveys, not just the results.
2. The second question of the survey gives different answer than the first question. But since the difference in percentage seems to be so small compared to the other options, I would guess that all of the top 4 features are more or less in the same level of interest to the community.

p.s. to Jane – why do none of the numbers in this table add up to 3406 (the number of respondants) ?

p.p.s.  to Jane and the Dev team – great work people!

Simple visualization of a 11X5 table (for WordPress 2.9 Features Vote Results)

I guess this is not the number one post I would like to start with on this blog, but I feel the time is right for it (community-wise).

I’ll move on to the subject matter in a moment, but first a short intro: This blog is written by Tal Galili. I am an aspiring statistician who also loves to use R for his work. At the same time I am also a WordPress blogger, writing mainly at www.TalGalili.com where I can use my native language (Hebrew) for self expression.

This combination of statistics and blogging will lead me to sometimes much less statistical, but more Web/Open-Source oriented posts like this one. So for the statisticians in the audience I extend my apologies and invite you to wait for future posts which will be more fully focused on Statistics and R.

And now for the topic at hand. . .

*         *         *         *         *
I have just noticed the nice article published on the wordpress development blog titled “2.9 Features Vote Results“. The post exemplifies a wonderful trend in the WordPress community (led by Jane Wells) having to do with connecting between the core team and the WordPress user community. The way Jane does this is by giving surveys to WordPress users,  which in turn offers the WordPress core team an opportunity to understand the community needs.

In the post “2.9 Features Vote Results“, Jane presented the results of such survey. The post had tables and barplots, but the barplots were only present for the one dimensional variables. In contrast, more elaborate data, such as that of question 2 (asking to rate each of 11 potential features on a scale of 1 to 5), was shown only with a table, such as this:

The table gives the full information (although I would love it if it was easily downloadable, instead of having to type in the numbers) – but its main limitation is that from a quick look, one can not easily get (let alone understand) anything.

For the goal of understanding more of the results with a quick glance, I offer two simple and well-known visualizations for the results.

1) Parallel barplots (click for bigger image)

This plot can be easily implemented in Excel (although I did it in R) and can allow us to compare the different ranking each potential feature received.

For example, this shows us that most answers were usually given rank 4 (”would be nice”) for each feature.

2) Mosaic plot (click for bigger image)

I don’t know if this can be done in Excel, but with R it is just a simple line of code.

(mosaicplot((DataSet.table), las = 1, col = c(”gray”,”gray”,”blue”,3,”dark green”), main = “”))

The advantage of this plot is that it allows us to compare the different features easily, while not only comparing the top rank, but also combining different rankings for easy comparison (for example, comparing how many rank 4 or 5 each feature received).

So for example, the plot shows me that the most ranked with number 5 was the feature “easier embeds” but the most ranked “number 4 or 5″ was the feature “custom image sizes”. The feature “media album” came close to these two, but didn’t top either.

Conclusions from this post:

1. It would be nice (if possible) to publish the full data of the surveys, not just the results.
2. The second question of the survey gives different answer than the first question. But since the difference in percentage seems to be so small compared to the other options, I would guess that all of the top 4 features are more or less in the same level of interest to the community.

p.s. to Jane – why do none of the numbers in this table add up to 3406 (the number of respondants) ?

p.p.s.  to Jane and the Dev team – great work people!

Kruskal-Wallis one-way analysis of variance

a = c(1, 5, 8, 17, 16)
b = c(2, 16, 5, 7, 4)
c = c(1, 1, 3, 7, 9)
d = c(2, 15, 2, 9, 7)

dati = list(g1=a, g2=b, g3=c, g4=d)

kruskal.test(dati)

        Kruskal-Wallis rank sum test

data:  dati 
Kruskal-Wallis chi-squared = 1.9217, df = 3, p-value = 0.5888

qchisq(0.950, 3)
[1] 7.814728

Analysis of variance: ANOVA, for multiple comparisons

a = c(65, 48, 66, 75, 70, 55)
b = c(64, 44, 70, 70, 68, 59)
c = c(60, 50, 65, 69, 69, 57)
d = c(62, 46, 68, 72, 67, 56)

dati = c(a, b, c, d)

groups = factor(rep(letters[1:4], each = 6))

bartlett.test(dati, groups)

        Bartlett test of homogeneity of variances

data:  dati and groups 
Bartlett's K-squared = 0.4822, df = 3, p-value = 0.9228

qchisq(0.950, 3)
[1] 7.814728

a = c(65, 48, 66, 75, 70, 55)
b = c(64, 44, 70, 70, 68, 59)
c = c(60, 50, 65, 69, 69, 57)
d = c(62, 46, 68, 72, 67, 56)

dati = c(a, b, c, d)

groups = factor(rep(letters[1:4], each = 6))

fligner.test(dati, groups)

        Fligner-Killeen test of homogeneity of variances

data:  dati and groups 
Fligner-Killeen:med chi-squared = 0.1316, df = 3, p-value = 0.9878

fit = lm(formula = dati ~ groups)

anova (fit)

Analysis of Variance Table

Response: dati
          Df  Sum Sq Mean Sq F value Pr(>F)
groups     3    8.46    2.82  0.0327 0.9918
Residuals 20 1726.50   86.33  

qf(0.950, 20, 3)
[1] 8.66019

Comparison of two proportions: parametric (Z-test) and non-parametric (chi-squared) methods

z.prop = function(x1,x2,n1,n2){
  numerator = (x1/n1) - (x2/n2)
  p.common = (x1+x2) / (n1+n2)
  denominator = sqrt(p.common * (1-p.common) * (1/n1 + 1/n2))
  z.prop.ris = numerator / denominator
  return(z.prop.ris)
}

z.prop(30, 65, 74, 103)
[1] -2.969695

prop.test(x = c(30, 65), n = c(74, 103), correct = FALSE)

    2-sample test for equality of proportions without continuity correction

data: c(30, 65) out of c(74, 103)
X-squared = 8.8191, df = 1, p-value = 0.002981
alternative hypothesis: two.sided
95 percent confidence interval:
  -0.37125315 -0.08007196
sample estimates:
prop 1     prop 2
0.4054054  0.6310680

prop.test(x = c(30, 65), n = c(74, 103), correct=TRUE)

    2-sample test for equality of proportions with continuity correction

data: c(30, 65) out of c(74, 103)
X-squared = 7.9349, df = 1, p-value = 0.004849
alternative hypothesis: two.sided
95 percent confidence interval:
  -0.38286428 -0.06846083
sample estimates:
prop 1     prop 2
0.4054054  0.6310680

qchisq(0.950, 1)
[1] 3.841459

Wilcoxon signed rank test

a <- c(214, 159, 169, 202, 103, 119, 200, 109, 132, 142, 194, 104, 219, 119, 234)
b <- c(159, 135, 141, 101, 102, 168, 62, 167, 174, 159, 66, 118, 181, 171, 112)

wilcox.test(a,b, paired=TRUE)

Wilcoxon signed rank test

data: a and b
V = 80, p-value = 0.2769
alternative hypothesis: true location shift is not equal to 0

a <- c(214, 159, 169, 202, 103, 119, 200, 109, 132, 142, 194, 104, 219, 119, 234)
b <- c(159, 135, 141, 101, 102, 168, 62, 167, 174, 159, 66, 118, 181, 171, 112)

 diff <- c(a - b) #calculating the vector containing the differences
 diff <- diff[ diff!=0 ] #delete all differences equal to zero
 diff.rank <- rank(abs(diff)) #check the ranks of the differences, taken in absolute
 diff.rank.sign <- diff.rank * sign(diff) #check the sign to the ranks, recalling the signs of the values of the differences
 ranks.pos <- sum(diff.rank.sign[diff.rank.sign > 0]) #calculating the sum of ranks assigned to the differences as a positive, ie greater than zero
 ranks.neg <- -sum(diff.rank.sign[diff.rank.sign < 0]) #calculating the sum of ranks assigned to the differences as a negative, ie less than zero
 ranks.pos #it is the value V of the wilcoxon signed rank test
[1] 80
 ranks.neg
[1] 40

I know it’s been so long…

Corpus Linguistics with R, Day 2

R Lesson 2

text<-c("This is a first example sentence.", "And this is a second example sentence.")

# gsub replaces stuff in strings

> gsub ("second", "third", text)
SEARCH-REPLACE-SUBJECT
[1] "This is a first example sentence."
[2] "And this is a third example sentence."
> gsub ("n", "X", text)
[1] "This is a first example seXteXce."
[2] "AXd this is a secoXd example seXteXce."
> gsub ("is", "was", text)
[1] "Thwas was a first example sentence."
[2] "And thwas was a second example sentence."

---

Perl-style regex

^ beginning of str, e.g. "^x", ***OR*** NOT inside of []
$ end of str, e.g. "x$"
. any other char
\ escape char - TWO ("\\") needed
[] character classes, e.g. [aeiou] vowels, [a-h] is same as [abcdefgh]
{MIN,MAX} number of immediately preceding unit (chacter)

examples
lo+l

> grep("analy[sz]e", c("analyze", "analyse", "moo"), perl=T, value=T)
[1] "analyze" "analyse"

> grep("(first|second)", text, perl=T, value=T)
[1] "This is a first example sentence."
[2] "And this is a second example sentence."
> grep("(first|lalala)", text, perl=T, value=T)
[1] "This is a first example sentence."
>

> grep("ab{2}", z, perl=T, value=T)
[1] "aabbccdd"
> grep("(ab){2}", z, perl=T, value=T)
[1] "ababcdcd"
>
>
> gsub("a (first|second)", "another", text, perl=T)
[1] "This is another example sentence."
[2] "And this is another example sentence."
>
>
>
>
> gsub("[abcdefgh]", "X", text, perl=T)
[1] "TXis is X Xirst XxXmplX sXntXnXX."
[2] "AnX tXis is X sXXonX XxXmplX sXntXnXX."

> grep("forg[eo]t(s|ting|ten)?_v", a.corpus.file, perl=T, value=T)
all forms of forget

*? lazy matching e.g.
gregexpr("s.*?s", text[1], perl=T)

> gregexpr("s.*?s", text[1], perl=T)
[[1]]
[1] 4 14
attr(,"match.length")
[1] 4 12

# note: things that are matched are consumed and can then not be found again in the same passtext

> gsub("(19|20)[0-9]{2}", "YEAR", text)
[1] "They killed 250 people in YEAR." "No, it was in YEAR."
> #replaces only 19xx and 20xx

---

> textfile<-scan(file.choose(), what="char", sep="\n")
Enter file name: corp_gpl_short.txt
Read 9 items
> textfile<-tolower(textfile)
> textfile
[1] "the licenses for most software are designed to take away your"
[2] "freedom to share and change it. by contrast, the gnu general public"
[3] "license is intended to guarantee your freedom to share and change free"
[4] "software--to make sure the software is free for all its users. this"
[5] "general public license applies to most of the free software"
[6] "foundation's software and to any other program whose authors commit to"
[7] "using it. (some other free software foundation software is covered by"
[8] "the gnu library general public license instead.) you can apply it to"
[9] "your programs, too."
> unlist(strsplit(textfile, "//W"))
[1] "the licenses for most software are designed to take away your"
[2] "freedom to share and change it. by contrast, the gnu general public"
[3] "license is intended to guarantee your freedom to share and change free"
[4] "software--to make sure the software is free for all its users. this"
[5] "general public license applies to most of the free software"
[6] "foundation's software and to any other program whose authors commit to"
[7] "using it. (some other free software foundation software is covered by"
[8] "the gnu library general public license instead.) you can apply it to"
[9] "your programs, too."
> text_split<-unlist(strsplit(textfile, "//W"))
> text_split
[1] "the licenses for most software are designed to take away your"
[2] "freedom to share and change it. by contrast, the gnu general public"
[3] "license is intended to guarantee your freedom to share and change free"
[4] "software--to make sure the software is free for all its users. this"
[5] "general public license applies to most of the free software"
[6] "foundation's software and to any other program whose authors commit to"
[7] "using it. (some other free software foundation software is covered by"
[8] "the gnu library general public license instead.) you can apply it to"
[9] "your programs, too."
>
> text_split<-unlist(strsplit(textfile, "//W"))
> text_split
[1] "the licenses for most software are designed to take away your"
[2] "freedom to share and change it. by contrast, the gnu general public"
[3] "license is intended to guarantee your freedom to share and change free"
[4] "software--to make sure the software is free for all its users. this"
[5] "general public license applies to most of the free software"
[6] "foundation's software and to any other program whose authors commit to"
[7] "using it. (some other free software foundation software is covered by"
[8] "the gnu library general public license instead.) you can apply it to"
[9] "your programs, too."
> text_split<-unlist(strsplit(textfile, "\\W"))

> textfile<-scan(file.choose(), what="char", sep="\n")
Enter file name: corp_gpl_short.txt
Read 9 items
> textfile<-tolower(textfile)
> textfile
[1] "the licenses for most software are designed to take away your"
[2] "freedom to share and change it. by contrast, the gnu general public"
[3] "license is intended to guarantee your freedom to share and change free"
[4] "software--to make sure the software is free for all its users. this"
[5] "general public license applies to most of the free software"
[6] "foundation's software and to any other program whose authors commit to"
[7] "using it. (some other free software foundation software is covered by"
[8] "the gnu library general public license instead.) you can apply it to"
[9] "your programs, too."
> unlist(strsplit(textfile, "//W"))
[1] "the licenses for most software are designed to take away your"
[2] "freedom to share and change it. by contrast, the gnu general public"
[3] "license is intended to guarantee your freedom to share and change free"
[4] "software--to make sure the software is free for all its users. this"
[5] "general public license applies to most of the free software"
[6] "foundation's software and to any other program whose authors commit to"
[7] "using it. (some other free software foundation software is covered by"
[8] "the gnu library general public license instead.) you can apply it to"
[9] "your programs, too."

> text_split<-unlist(strsplit(textfile, "//W+"))
> text_split
[1] "the licenses for most software are designed to take away your"
[2] "freedom to share and change it. by contrast, the gnu general public"
[3] "license is intended to guarantee your freedom to share and change free"
[4] "software--to make sure the software is free for all its users. this"
[5] "general public license applies to most of the free software"
[6] "foundation's software and to any other program whose authors commit to"
[7] "using it. (some other free software foundation software is covered by"
[8] "the gnu library general public license instead.) you can apply it to"
[9] "your programs, too."
> sort(table(text_split), decreasing=T)
text_split
to software the free and general
9 9 7 5 4 3 3
is it license public your by change
3 3 3 3 3 2 2
for foundation freedom gnu most other share
2 2 2 2 2 2 2
all any applies apply are authors away
1 1 1 1 1 1 1
can commit contrast covered designed guarantee instead
1 1 1 1 1 1 1
intended its library licenses make of program
1 1 1 1 1 1 1
programs s some sure take this too
1 1 1 1 1 1 1
users using whose you
1 1 1 1
>

> text_freqs
text_split
to software the free and general is
9 7 5 4 3 3 3
it license public your by change for
3 3 3 3 2 2 2
foundation freedom gnu most other share all
2 2 2 2 2 2 1
any applies apply are authors away can
1 1 1 1 1 1 1
commit contrast covered designed guarantee instead intended
1 1 1 1 1 1 1
its library licenses make of program programs
1 1 1 1 1 1 1
s some sure take this too users
1 1 1 1 1 1 1
using whose you
1 1 1
> text_freqs[text_freqs>1]
text_split
to software the free and general is
9 7 5 4 3 3 3
it license public your by change for
3 3 3 3 2 2 2
foundation freedom gnu most other share
2 2 2 2 2 2
>

> !(text_split %in% stop_list)
[1] FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[13] TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE
[25] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
[37] TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[49] TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
[61] TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[73] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
[85] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
> text_stopremoved<-text_split[!(text_split %in% stop_list)]
> text_stopremoved
[1] "licenses" "for" "most" "software" "are"
[6] "designed" "to" "take" "away" "your"
[11] "freedom" "to" "share" "change" "it"
[16] "by" "contrast" "gnu" "general" "public"
[21] "license" "is" "intended" "to" "guarantee"
[26] "your" "freedom" "to" "share" "change"
[31] "free" "software" "to" "make" "sure"
[36] "software" "is" "free" "for" "all"
[41] "its" "users" "this" "general" "public"
[46] "license" "applies" "to" "most" "free"
[51] "software" "foundation" "s" "software" "to"
[56] "any" "other" "program" "whose" "authors"
[61] "commit" "to" "using" "it" "some"
[66] "other" "free" "software" "foundation" "software"
[71] "is" "covered" "by" "gnu" "library"
[76] "general" "public" "license" "instead" "you"
[81] "can" "apply" "it" "to" "your"
[86] "programs" "too"
>

# LOAD an R file
source("something.r")

Corpus Linguistics with R, Day 1

(This post documents the first day of a class on R that I took at ESU C&T. I is posted here purely for my own use.)


R Lesson 1

> 2+3; 2/3; 2^3
[1] 5
[1] 0.6666667
[1] 8

---

Fundamentals - Functions

> log(x=1000, base=10)
[1] 3

---

(Formals describes the syntax of other functions)

formals(sample)

---

Variables

( <- allows you to save something in a data structure (variable) )
> a<-2+3
> a
[1] 5

# is for comments

whitespace doesn't matter

---
# Pick files
file.choose()

# Get working dir
getwd()

# Set working dir
setwd("..")

# Save
> save(VARIABLE_NAME, file=file.choose())
Fehler in save(test, file = file.choose()) : Objekt ‘test’ nicht gefunden
> save.image("FILE_NAME")

---

> setwd("/home/cornelius/Code/samples/Brown_95perc")
> getwd()
[1] "/home/cornelius/Code/samples/Brown_95perc"
> dir()

> my_array <- c(1,2,3,4)
> my_array
[1] 1 2 3 4
> my_array <- c("lalala", "lululu", "bla")
> my_array2 <- c(1,2,3,4)
> c(my_array, my_array2)
[1] "lalala" "lululu" "bla" "1" "2" "3" "4"
>

# it is possible to add something to ALL values in a vector, i.e.
my_array2 + 10

# c (conc) makes a list
stuff1<-c(1,2,3,4,5)

---

# sequence starts at 1 (first arg), goes on for 5 (second arg), increments by 1 (third arg)
seq(1, 5, 1)

---

# put a file into a corpus vector
# what=real|char sep=seperator
> my_corpus<-scan(file=file.choose(), what="char", sep="\n")

# unique elements in my array
unique(array)

# count elements in an array
table(array)

# sort elements in an array
sort(table(array))

---
# this tells me the position of the elements in my text that aren't "this"
> values<-which(my_little_corpus!="this")
> values
[1] 2 3 4 5 6 7 8 9 11 12 13 14

# this will produce TRUE|FALSE for my condition (is this element "this")
> values<-my_little_corpus!="this"
> values
[1] FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
[13] TRUE TRUE

# this will return the array without "this"
> values<-my_little_corpus[my_little_corpus!="this"]
> values
[1] "is" "just" "a" "little" "example" "bla" "bla"
[8] "bla" "is" "the" "third" "line"

...

> cc<-c("banana", "bagel")
> cc == "banana"; cc!="banana" #
[1] TRUE FALSE
[1] FALSE TRUE
> "banana" %in% cc
[1] TRUE
> c("bagel", "banana") %in% cc
[1] TRUE TRUE
> match ("banana", cc)
[1] 1
> match (c("bagel","banana"), cc)
[1] 2 1

# match looks for a list of tokens and returns their position in the datastructure

---
> cat(bb, sep="\n", file=scan(what="char"), append=F)
# write the contents of bb to a file, ask the user for file

moo<-scan(what="char")
# read something the user types into a var

# Clear Mem
> rm(list=ls(all=T))
>

---

# create vector1 (ordered)
vec1<-c("a","b","c","d","e","f,",g","h","i","j")

# oder
# > letters[1:10]
# [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"

# create vector2 (random)
# > vector2<-sample(vector1)

---

length()
# number of elements

nchar()
# number of characters

> aa<-"know"
> nchar(aa)
[1] 4
> aa<-c("I","do","not","know")
> nchar(aa)
[1] 1 2 3 4
> lala<-c("cat","gnu","hippopotamus")
> lala
[1] "cat" "gnu" "hippopotamus"
> nchar(lala)
[1] 3 3 12

> substr("hippopotamus", 0, 5)
[1] "hippo"
>

# like explode() / implode()
paste (string, sep="my_seperator", collapse="stuff to put in")

---

# percentages
x/sum(x)

barplot (1,2,3)

Read in corpus data and build a list of words frequencies
1) scan file
2) strsplit by " "
3) unlist to make vector
4) make a table with freqs
5) sort
6) output

#search for strings
grep("needle", haystack)

> grep("is", text, value=T)
[1] "This is a first example sentence."
[2] "And this is a second example sentence."
> grep("And", text, value=T)
[1] "And this is a second example sentence."
> grep("sentence", text, value=T)
[1] "This is a first example sentence."
[2] "And this is a second example sentence."
>

gregexpr
# alternative to grep, returns a list of vectors

> mat<-gregexpr("e", text)
> mat
[[1]]
[1] 17 23 26 29 32
attr(,"match.length")
[1] 1 1 1 1 1

[[2]]
[1] 16 22 28 31 34 37
attr(,"match.length")
[1] 1 1 1 1 1 1

> unlist(mat)
[1] 17 23 26 29 32 16 22 28 31 34 37
> mat<-gregexpr("sentence", text)
> sapply (mat, c)
[1] 25 30


Wilcoxon-Mann-Whitney rank sum test (or test U)

a = c(6, 8, 2, 4, 4, 5)
b = c(7, 10, 4, 3, 5, 6)

wilcox.test(a,b, correct=FALSE)

Wilcoxon rank sum test

data: a and b
W = 14, p-value = 0.5174
alternative hypothesis: true location shift is not equal to 0

a = c(6, 8, 2, 4, 4, 5)
b = c(7, 10, 4, 3, 5, 6)

wilcox.test(b,a, correct=FALSE)

Wilcoxon rank sum test

data: b and a
W = 22, p-value = 0.5174
alternative hypothesis: true location shift is not equal to 0

sum.rank.a = sum(rank(c(a,b))[1:6]) #sum of ranks assigned to the group a
 W = sum.rank.a – (length(a)*(length(a)+1)) / 2
 W
[1] 14

sum.rank.b = sum(rank(c(a,b))[7:12]) #sum of ranks assigned to the group b
 W = sum.rank.b – (length(b)*(length(b)+1)) / 2 
 W
[1] 22

sum(rank(c(a,b))[1:6]) #sum of ranks assigned to the group a
[1] 35
sum(rank(c(a,b))[7:12]) #sum of ranks assigned to the group b
[1] 43

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