# qmlDay3_part2.R
#
# R code and notes for second part of third 1.5 hour session of week-long 
# course in quantitative methods in linguistics, given at the "mini-institute" 
# after the LSA Summer Meeting, 14-18 July 2008 ... continued
# 
# (c) 2008, Mary E. Beckman, Cynthia Clopper, Shari Speer (Ohio State 
#           University, Department of Linguistics)
# 

# Assumes that you've already read in data sets, etc., using code in 
# qmlDay3_part1.R file.

# Plot the distribution of F1 values in the Hillenbrand et al. dataset. 
hist(hill$F1, freq=FALSE, main="", 
	xlab="Hillenbrand et al. (1995) vowels, F1 frequency (Hz)")
# Plot the distribution of F1 values in the Hillenbrand et al. dataset, 
# differentiating low vowels from non-low vowels. 
brks=seq(300,1400,100)
x=subset(hill, vowel=="ae" | vowel=="ah" | vowel=="aw")
y=subset(hill, vowel!="ae" & vowel!="ah" & vowel!="aw")
hist(y$F1, breaks=brks, freq=FALSE, ylim=c(0,0.0035), main="", col="gray40",
	xlab="Hillenbrand et al. (1995) vowels, F1 frequency (Hz)")
hist(x$F1, breaks=brks, freq=FALSE, density=10, add=T)

# Use t-test to confirm that low vowels have significantly different 
# mean F1 from mid and high vowels. 
t.test(x$F1,y$F1)

# Plot the distribution of F1 values in the high and mid lax front vowels 
# in the Hillenbrand et al. dataset. 
brks=seq(300,1100,50)
x=subset(hill, vowel=="ih")
y=subset(hill, vowel=="eh")
hist(y$F1, breaks=brks, freq=FALSE, ylim=c(0,0.007), main="", col="gray40",
	xlab="Hillenbrand et al. (1995) [E] and [I] F1 frequency (Hz)")
hist(x$F1, breaks=brks, freq=FALSE, density=10, add=T)
legend("topright",c("head","hid"),col=c("gray40","black"),density=c(0,10))

# Use t-test to ask whether that mid vowel has significantly different 
# mean F1 from high vowel. 
t.test(x$F1,y$F1)

# Now do the same thing for the tense and lax high front vowels. 
brks=seq(300,600,50)
x=subset(hill, vowel=="ih")
y=subset(hill, vowel=="iy")
hist(y$F1, breaks=brks, freq=FALSE, ylim=c(0,0.007), main="", col="gray40",
	xlab="Hillenbrand et al. (1995) [i] and [I] F1 frequency (Hz)")
hist(x$F1, breaks=brks, freq=FALSE, density=10, add=T)
legend("topright",c("heed","hid"),fill=c("gray40","black"),density=c(0,10))

# Use t-test to ask whether that mid vowel has significantly different 
# mean F1 from high vowel. 
t.test(x$F1,y$F1)
# Yes, it is significantly different, but how informative is that, given 
# the overlap?

# Take advantage of fact that the F4 should not vary systematically with 
# front vowel height, to look at relationship.
t.test(x$F4,y$F4)
brks4=seq(2500,6000,500)
hist(y$F4, breaks=brks4, freq=FALSE, ylim=c(0,0.0012), main="", col="gray40",
	xlab="Hillenbrand et al. (1995) [E] and [I] F4 frequency (Hz)")
hist(x$F4, breaks=brks4, freq=FALSE, density=10, add=T)
# Let's make a scatterplot.
plot(y$F4, y$F1, xlim=c(brks4[1], brks4[8]), ylim=c(brks[1],brks[7]), 
	pch=19, xlab="F4 (Hz)",ylab="F1 (Hz)")
points(x$F4, x$F1, col="gray40")
legend("topright",c("i","I"),pch=c(19,1),col=c("black","gray40"))

brks2=seq(1800,3550,250)
hist(y$F2, breaks=brks2, freq=FALSE, ylim=c(0,0.0012), main="", col="gray40",
	xlab="Hillenbrand et al. (1995) [i] and [I] F2 frequency (Hz)")
hist(x$F2, breaks=brks2, freq=FALSE, density=10, add=T)
# Let's make a scatterplot.
plot(y$F2, y$F1, xlim=c(brks2[1], brks2[8]), ylim=c(brks[1],brks[7]), 
	pch=19, xlab="F2 (Hz)",ylab="F1 (Hz)")
points(x$F2, x$F1, col="gray40")
legend("topright",c("i","I"),pch=c(19,1),col=c("black","gray40"))

# Calculate covariance.
cov(x$F1,x$F2)
cov(y$F1,y$F2)
cov(y$F1,y$F4,use="pairwise.complete.obs")

# Calculate correlations.
cor(x$F1,x$F2)
cor(y$F1,y$F2)
cor(x$F1,x$F4,use="pairwise.complete.obs")
cor(y$F1,y$F4,use="pairwise.complete.obs")

# Test hypothesis that the correlation is significantly different from 0.
cor.test(x$F1,x$F2)
cor.test(y$F1,y$F2)
cor.test(x$F1,x$F4)
cor.test(y$F1,y$F4)