########################################################################
# Nettle1995.R
#
# From "Notes on Probability and Statistics for Analyzing the 
# Sounds of Languages" -- a companion textbook to Peter Ladefoged's
# "Vowels and Consonants: An Introduction to the Sounds of Languages"
# 2nd edition (Blackwell, 2005).
#
# (c) 2007, Grant McGuire, Fangfang Li, Eunjong Kong, & Mary E. Beckman 
# Department of Linguistics, Ohio State University
#
# R code for analyzing the data in Table 1 on p. 362 of Nettle (1995). 
#
# The data for this analysis problem are from:
#    Daniel Nettle (1995). Segmental inventory size, word length, and 
#    communicative efficiency. Linguistics 33, 359-367.  
#
# Note that Nettle based his counts on the descriptions of the segments 
# in the dictionary that he consulted.  Since the tones of Thai are 
# indicated in the orthography in large part by special "consonant" 
# symbols that are prefixed before the syllable-initial consonant, and 
# there are two such symbols (for "high" and "mid" class tones) which 
# contrast with no extra symbol (for "low" class tones), Nettle counted 
# 21 consonants * 3 tone classes = 66 "consonants" plus 9 vowels = 71 
# segments, whereas Maddieson & Precoda counted 21 consonants + 9 vowels 
# = 30 segments.  We have "corrected" the count to the one given in 
# Maddieson & Precoda's UPSID data base plus 9 more, to count long and 
# short vowels separately, since that is how Nettle must be counting the 
# vowels of Nahuatl in order to get the count that he does.  
#
########################################################################
# Part 1 -- Analyzing the data from Table 1 on p. 362 in Nettle (1995).
# 
# Download the file Nettle1995.txt from the course web page, and then 
# set the working directory to the folder where you have put the file. 
setwd('C:/Lx286/dataAnalysisReports/reportNo5')

# Read in the data from the file you downloaded. 
x=read.table("correctedNettle1995.txt", header=T)

names(x)
# [1] "Language"    "NoSegs"      "MeanWordLen" "Dictionary"  "Population"
# [6] "withTone"    "noVows"
# The first four columns are from Nettle (1995), Table 1, on p. 362, the 
# 5th column of the table is the estimated number of speakers, as listed 
# in the Ethnologue database at http://www.ethnologue.com/web.asp
# The 6th column is like column 2, except that we have expanded the 
# numbers for Thai and Mandarin by counting all of the vowels in syllables 
# with distinct tones as different vowels.   That is, we have multipled 
# 9 (short) vowels by 4 tones and 9 (long) vowels by 5 tones, and added 
# these two to the 21 consonants to get 9*4+9*5+21=102 segments altogether.
# For Mandarin, similarly, we have multiplied the number of vowels listed 
# in UPSID by the number of tones and added that to the number of consonants. 
# The last column is the number of vowels.  These numbers are taken from 
# UPSID for Hawaiian, Turkish, German, and Georgian, and from other published 
# sources for Thai, Italian, Hindi, !Xu, and Mandarin.  Note that we are 
# counting the number of vowels when vowels with different tones are deemed 
# to be different vowels. 

# Regress the mean word length against the number of segments.
x.lm1=lm(MeanWordLen ~ NoSegs, data=x)
# Have R print a summary of the results.
summary(x.lm1)
# Residuals:
#     Min      1Q  Median      3Q     Max 
# -2.6030 -0.5072  0.1900  0.4440  1.9032 
# 
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)    
# (Intercept)  7.55411    0.75716   9.977 8.64e-06 ***
# NoSegs      -0.03336    0.01553  -2.148    0.064 .  
# ---
# Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
# 
# Residual standard error: 1.332 on 8 degrees of freedom
# Multiple R-Squared: 0.3657,     Adjusted R-squared: 0.2864 
# F-statistic: 4.613 on 1 and 8 DF,  p-value: 0.064 

# Set up a plotting pretty window for making a scatterplot.
windows(width=4, height=4, pointsize=12)
par(family="serif", oma=rep(0,4), mar=c(3,3,0.1,0.1), mgp=c(1.8,0.5,0),
	type="s")

# Make a scatterplot and label the data points.
plot(x$NoSegs, x$MeanWordLen, xlim=c(0,120), ylim=c(3,9), pch=19,
	xlab="number of segments", ylab="mean word length (number of segments)")
text(x$NoSegs, x$MeanWordLen, x$Language, adj=c(1,0))
# Add a regression curve. 
abline(x.lm1)
# Save the plot in a file to embed into your report.
savePlot("Nettle1995plot", type="jpg")

########################################################################
# Part 2 -- Seeing the effect of factoring in tone contrasts for the two 
# languages with lexical tone.
# 
# Do the same sequence of commands to make a scatterplot and apply a 
# regression model, but this time using the number of segments in the 
# column "withTone" as the independent variable. 

x.lm2=lm(MeanWordLen ~ withTone, data=x)
summary(x.lm2)
# Residuals:
#     Min      1Q  Median      3Q     Max 
# -0.9509 -0.5571 -0.2236  0.4874  1.4448 
# 
# Coefficients:
#              Estimate Std. Error t value Pr(>|t|)    
# (Intercept)  8.170675   0.468530  17.439 1.19e-07 ***
# withTone    -0.040239   0.007985  -5.039  0.00100 ** 
# ---
# Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
# 
# Residual standard error: 0.8189 on 8 degrees of freedom
# Multiple R-Squared: 0.7604,     Adjusted R-squared: 0.7305 
# F-statistic: 25.39 on 1 and 8 DF,  p-value: 0.001003 

plot(x$withTone, x$MeanWordLen, xlim=c(0,120), ylim=c(3,9), pch=19,
	xlab="number of segments, counting tone contrasts", 
	ylab="mean word length (number of segments)")
text(x$withTone, x$MeanWordLen, x$Language, adj=c(1,0))
# Add a regression curve. 
abline(x.lm2)
# Save the plot in a file to embed into your report.
savePlot("Nettle1995withTone", type="jpg")

########################################################################
# Part 3 -- Modeling the relationship if there were minimum redundancy 
# in the system, after adjusting for Peter Ladefoged's implicit claim 
# about the constraints from syllable structure on p. 4 of his book.

# Calculate the number of consonants by subtracting the number of 
# vowels from the number of segments, using the first value (the one 
# that doesn't include tone) for the number of segments. 
x$noCons=x$withTone-x$noVows

# Add a placeholder variable for the mean length of words as estimated 
# by the model that will be described in the next comment.  
x$meanWordModeled=0

# Assume a lexicon of 45,000 words, as in Nagy & Anderson's (1984) 
# estimate of the number of words an American high school senior knows.
# Calculate average length of words one would get if each language were 
# maximally efficient in using segments to get the shortest possible 
# words, given the following constraints: (1) the only possible syllable 
# types are V and CV and (2) V can only occur at the beginning of a 
# word, so that there are no V.V sequences.  That is, the language 
# should use up the shortest words first, before going on to use the 
# next shortest template.  
noWords=45000

# Loop through the list of languages, filling in the meanWordModelled 
# estimate after calculating the lengths of words in a 45,000 word 
# lexicon that follows the above constraints.  
for (i in 1:dim(x)[1]) {
	# Set up variables for the number of vowels and the number of 
	# consonants in the current language.  
	V=x$noVows[i]
	C=x$noCons[i]
	# Set up a variable to hold all of the "word lengths" in the 
	# hypothetical lexicon and fill in the number of segments in 
	# all of the monosyllabic words that are just a vowel. 
	words=rep(0,V)
	# Fill in the number of segments in all of the monosyllabic words 
	# that are a CV syllable. 
	w1=V+1
	w2=w1+C*V
	words[w1:w2]=2
	# Fill in the number of segments in all of the disyllabic words 
	# that are VCV. 
	w1=w2
	w2=w1+V*C*V
	words[w1:w2]=3
	# Fill in the number of segments in all of the disyllabic words 
	# that are CVCV. 
	w1=w2
	w2=w1+C*V*C*V
	words[w1:w2]=4
	# Fill in the number of segments in all of the trisyllabic words 
	# that are VCVCV, for languages where still need more words.
	if (w2 < noWords) {
		w1=w2
		w2=w1+V*C*V*C*V
		words[w1:w2]=5
		if  (w2 < noWords) {
			# Fill in the number of segments in all of the 
			# trisyllabic words that are CVCVCV, if still need .... 
			w1=w2
			w2=w1+C*V*C*V*C*V
			words[w1:w2]=6
		}
	}
	print(paste(x$Language[i],length(words)))
	# Calculate the mean value for the first 45,000 words.
	x$meanWordModeled[i]=mean(words[1:noWords])
}

# Add the model points and a regression curve for it.
points(x$withTone, x$meanWordModeled, pch=20, col="grey40")
abline(lm(meanWordModeled ~ withTone, data=x), col="grey40")
legend("topright","model", pch=20, col="grey40", lty=1)

savePlot("Nettle1995withToneWithModel", type="jpg")