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Ch4.R
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Ch4.R
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##############################################################################
######################## Translating Statistics R Code #######################
##############################################################################
##### Note - to run code in R either copy and paste into the R Console window
##### or place cursor anywhere on the line, hold Ctrl and press r
##############################################################################
##################### Chapter 4 - Descriptive Statistics #####################
##############################################################################
##### Skewness
library(e1071)
windows(6,6)
plot(density(rbeta(10000000,5,2)), col = "red", lwd = 2,
xlab = "Negative Skew")
plot(density(rbeta(10000000,2,5)), col = "red", lwd = 2,
xlab = "Positive Skew")
a = rbeta(10000000,5,2)
mean(a); median(a);
skewness(a)
b = rbeta(10000000,2,5)
mean(b); median(b)
skewness(b)
##### Kurtosis
c = rlogis(10000000, location = 0, scale = 2)
plot(density(rlogis(10000000, location = 0, scale = 2)),
col = "red", lwd = 2, xlab = "Positive Kurtosis")
d = sample(seq(-30,30,0.001),10000000, replace = TRUE)
plot(density(d), col = "red", lwd = 2, xlab = "Negative Kurtosis")
kurtosis(c)
kurtosis(d)
##### Transformations
e = c(9.246734, 7.399515, 10.747294, 3.569408, 4.337869, 3.172818,
14.205624, 30.076914, 15.747489, 6.751340, 8.868595, 9.067760,
8.168440, 7.499503, 7.377515, 14.883616, 19.688646, 26.299868,
6.351835, 14.180845, 8.291489, 6.923344, 8.540164, 11.488742,
22.694856, 16.868368, 31.439693, 10.700027, 17.887367,
10.008738, 10.678093, 13.064685, 24.202956, 12.361150,
12.772815, 13.436628, 14.336022, 4.701801, 6.078979, 16.039244,
13.830606, 11.857714, 11.927977, 4.661250, 28.652883, 6.391380,
4.378959, 8.361308, 11.056678, 7.521961)
windows(6,6)
hist(e, xlab = "Temperature (°C)", main = "Weekly UK Temperatures",
ylim = c(0,20))
qqnorm(e); qqline(e)
shapiro.test(e)
e2 = log10(e)
shapiro.test(e2)
hist(e2, xlab = expression("Log Temperature (Log"[10]*" °C)"),
ylim = c(0,20), main = "Weekly UK Log Temperatures")
qqnorm(e2); qqline(e2)
##### Location
### Mode
Children = c(0,1,2,3,4)
Freq = c(5,10,12,2,1)
barplot(xtabs(Freq ~ Children), space = 0, xlab = "Number of Children",
ylab = "Count", main = "Number of Children per Family Sampled")
##### Example 4.1 - Mean
data3 = c(6.61, 7.88, 7.54, 8.08, 8.07, 7.2, 6.81, 6.45, 7.34, 6.27,
6.19, 6.63, 19.98, 7.36, 7.18, 7.86, 7.33, 19.02, 8.03,
8.04, 7.16, 7.14, 7.61, 7.3, 6.75, 6.71, 20.23, 7.67, 6.89,
7.15, 7.52, 8.17, 7.55, 6.8, 19.72, 6.43, 8.05, 6.88, 13.08,
10.16)
median(data3)
data4 = rnorm(40, mean = 7, sd = 0.75)
median(data4)
##### Example 4.2 - Median
mean(data3)
mean(data4)
### Plots
dens = density(data3, adjust = 2)
n = length(dens$y); dx = mean(diff(dens$x))
y.unit = sum(dens$y)*dx; dx = dx / y.unit
x.mean = sum(dens$y*dens$x)*dx
y.mean = dens$y[length(dens$x[dens$x < x.mean])]
y.cs = cumsum(dens$y)
x.med = dens$x[i.med <- length(y.cs[2*y.cs <= y.cs[n]])]
y.med = dens$y[i.med]
windows(6,6)
plot(dens, xlim = c(0,25), xlab = "Skewed Data",
main = "Density Plot of Skewed Data", lwd = 2)
temp = mapply(function(x,y,c) lines(c(x,x), c(0,y), lwd = 2, col = c),
c(x.mean, x.med), c(y.mean, y.med), c("Red", "Blue"))
legend(18,0.35, c("Mean","Median"), lty = c(1,1), lwd = c(2,2),
col = c("red", "blue"))
dens2 = density(data4)
n = length(dens2$y); dx = mean(diff(dens2$x))
y.unit = sum(dens2$y)*dx; dx = dx / y.unit
x.mean = sum(dens2$y*dens2$x)*dx
y.mean = dens2$y[length(dens2$x[dens2$x < x.mean])]
y.cs = cumsum(dens2$y)
x.med = dens2$x[i.med <- length(y.cs[2*y.cs <= y.cs[n]])]
y.med = dens2$y[i.med]
plot(dens2, xlim = c(4.5,9.5), xlab = "Normal Data",
main = "Density Plot of Normal Data", lwd = 2)
temp = mapply(function(x,y,c) lines(c(x,x), c(0,y), lwd = 2, col = c),
c(x.mean, x.med), c(y.mean, y.med), c("Red", "Blue"))
legend(8.5,0.52, c("Mean","Median"), lty = c(1,1), lwd = c(2,2),
col = c("red", "blue"))
##### Example 4.3 - Group means
Temp = c(72, 70, 71, 70, 90, 88, 87, 83, 75, 89, 91, 79, 93, 74, 86,
84, 86, 90, 92, 75, 74, 87, 83, 81, 90, 50, 61, 59, 51, 55,
58, 52, 52, 56, 55, 52, 61, 54, 56, 59, 57, 53, 72, 67, 83,
76, 80, 65, 85, 77, 83, 71, 84, 78, 74, 65, 72, 75, 79, 76,
69, 78, 71, 74, 65, 69, 66, 76, 70, 79, 66, 69)
Groups = c(rep("A", 25), rep("B", 17), rep("C", 30))
data5 = data.frame(Temp, Groups)
tapply(data5$Temp, data5$Groups, mean)
mean(data5$Temp)
##### Example 4.4 - Weighted means
data5$Scores = data5$Temp
tapply(data5$Scores, data5$Groups, mean)
mean(c(82.4, 55.35294, 73.8))
tapply(data5$Scores, data5$Groups, length)
25/(25+17+30); 17/(25+17+30); 30/(25+17+30)
(0.3472222*82.4) + (0.2361111*55.35294) + (0.4166667*73.8)
mean(data5$Scores)
##### Spread
### Standard Deviation
f = qnorm(p = seq(0.01,0.99,0.01), mean = 20, sd = 1)
g = qnorm(p = seq(0.01,0.99,0.01), mean = 20, sd = 2)
h = qnorm(p = seq(0.01,0.99,0.01), mean = 20, sd = 3)
i = qnorm(p = seq(0.01,0.99,0.01), mean = 20, sd = 5)
windows(6,6)
plot(density(f), ylim = c(0.0,0.4), xlim = c(0,40), lwd = 2,
xlab = "Time (mins)", main = "Time to Complete a Task
(Changing the Variation in the Data)")
lines(density(g), col="red", lwd=2)
lines(density(h), col="blue", lwd=2)
lines(density(i), col="darkgreen", lwd=2)
legend(27,0.41, c("SD = 1","SD = 2","SD = 3","SD = 5"),
title = c("Standard Deviation"), lty = c(1,1),
lwd = c(2,2), col = c("black", "red", "blue", "darkgreen"))
##### Example 4.5 - Range
range(data3)
max(data3) - min(data3)
range(data4)
max(data4) - min(data4)
##### Example 4.6 - Quantiles and Percentiles
quantile(data3, prob = seq(0, 1, length = 6))
quantile(data4, prob = seq(0, 1, length = 6))
quantile(data3); quantile(data4)
quantile(data3, prob = c(0.95, 0.99))
quantile(data4, prob = c(0.95, 0.99))
### IQR and SIQR
IQR(data3); IQR(data3)/2
IQR(data4); IQR(data4)/2
##### Example 4.7 - MAD
x = c(1, 4, 3, 5, 6, 2, 4, 2, 3, 4)
mad(x, constant = 1)
mad(data3, constant = 1)
mad(data4, constant = 1)
##### Example 4.8 - MAD
abs(x - median(x)) / mad(x, constant = 1)
x2 = c(10, 4, 3, 5, 6, 2, 4, 2, 3, 4)
abs(x2 - median(x2)) / mad(x2, constant = 1)
##### Example 4.9 - MAD and AAD
MADs = mad(data3, constant = 1); MADs
AADs = mean(abs(data3 - mean(data3))); AADs
MADn = mad(data4, constant = 1); MADn
AADn = mean(abs(data4 - mean(data4))); AADn
abs(data3 - median(data3))/ MADs
abs(data3 - mean(data3))/ AADs
abs(data4 - median(data4))/ MADn
abs(data4 - mean(data4))/ AADs
##### Example 4.10 - CV
mean(data3); mean(data4)
sd(data3); sd(data4)
(sd(data3) / mean(data3))*100; (sd(data4) / mean(data4))*100
##### Discrete data
cars = rep(c("Red", "Black", "Blue", "White", "Silver","Green"),
c(30,34,32,20,29,5))
Cars = data.frame(cars)
tab = xtabs(~ Cars$cars); tab2 = as.data.frame(tab)
tab2$Percentage = round(tab2$Freq/150*100, 1); tab2
library(ggplot2)
windows(6,6)
ggplot(Cars, aes(x = factor(cars), fill = factor(cars))) +
geom_bar(colour = "black", width = 1) + theme_bw() +
scale_fill_manual(name = "Car Color", values = c("black",
"dodgerblue3","forestgreen","firebrick3","grey","white")) +
xlab("Car Color") + ylab("Count of Cars\n") +
guides(fill = FALSE) +
ggtitle(expression(bold("Count of Cars by Color"))) +
scale_y_continuous(limits = c(0,35), breaks = seq(0,35, by = 5))+
theme(axis.text.x = element_text(size = 10, colour = "grey10",
face = "italic")) +
geom_text(aes(y = ((..count..)/sum(..count..)),
label = scales::percent((..count..)/sum(..count..))),
stat = "count", vjust = -0.5, col = "lightblue2")
##### Example 4.11 - Contingency tables
gender = rep(c("M","F"), each = 25)
smokes = sample(c(0,1), 50, replace = TRUE)
data6 = data.frame(gender, smokes)
xtabs( ~ gender + smokes, data = data6)
##### Correlation - one example
x = c(10.0, 8.5, 16.8, 11.2, 17.8, 5.4, 21.6, 9.6, 14, 13.5, 19.7,
20.2, 6.9, 16.7, 15.6, 18.9, 21.7, 20.6, 14.7, 12.3, 6.9, 19.4,
5.2)
y = c(-12.5, -11.1, -22.3, -15.4, -25.3, -8.4, -32.6, -16.5, -15.3,
-16.8, -27.1, -25.1, -9.3, -19.8, -17.6, -23.1, -31.2, -29,
-18.8, -13, -8.1, -20.7, -6.5)
corrd = data.frame(x,y)
cor(corrd$x, corrd$y)
plot(corrd$y ~ corrd$x, xlab = "X", ylab = "Y",
xlim = c(4,22), ylim = c(-35,-5),
main = "Strong Negative Correlation of -0.95")