In MATHSTATSOU/Intro2R: Introduction to R

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "ws#>",
  warning = FALSE,
  message = FALSE
)

# directory to Lab
dirdl <- system.file("Lab2",package = "Intro2R")

# create rmd link

library(Intro2R)
dir(dirdl)

Introduction

r rmdfile("Lab 2","MATH4753Laboratory2.docx","Lab2") will cement a number of R skills and theory related to the following:

1. The empirical rule
2. The Chebyshev rule
3. Transformation of data to z values
4. Location of outliers using z values

R skills

For the empirical rule you will need to be able to calculate means and standard deviations.

You can make z values in a number of different ways.

Z, Method 1

Suppose we wish to make Z values from the DDT variable in the ddt data frame.

d <- ddt$DDT
z <- (d-mean(d))/sd(d)
head(z)

Z, Method 2

We can use a built in function called scale()

zmat<-scale(ddt$DDT) # scale makes a matrix of z values
z<-zmat[,1] # take the column to form a vector
head(z)

Verify Chebyshev and Empirical rules

To show how many data values lie within k standard deviations of the mean you will need to count the number of values in an interval

Making intervals

mn <- mean(ddt$DDT)
sdd <- sd(ddt$DDT)
mp<-c(-1,1)
k<-2

mn+mp*k*sdd

Values within k standard deviations of the mean

We can subset the data frame with abs(z)<2 and then pull off the DDT column. The function length adds up the number of values in the vector

ddl2<-ddt[abs(z)<2,"DDT"]
length(ddl2)/length(ddt$DDT)*100

98.6% of the DDT lies within 2 standard deviations of the mean.

Dotplot in ggplot

The dotplot is a simple device, we can set bins of a certain size (I will use 1/5 sd(LENGTH)) to break the continuous data into discrete levels.

In addition we will use the cut() function to create labels corresponding to regions of LENGTH that are distant from the mean by integral standard deviations.

See the code below:

library(ggplot2)
library(dplyr)
mn <- mean(ddt$LENGTH)
sdd <- sd(ddt$LENGTH)
ddt <- ddt %>% mutate( z = (LENGTH-mn)/sdd, 
                       Far = ifelse(abs(z)> 3, "Outlier", 
                                    ifelse(abs(z)>=2 & abs(z)<=3, 
                                           "Posiible Out.", "MAIN")))
g <- ggplot(ddt, aes(x = LENGTH)) + geom_dotplot(aes(fill = Far),binwidth = 1/5*sdd)
g <- g + geom_density(aes(y = ..count..))
g <- g + labs(title = "LENGTH data categorized by outlier status using z")
g

Or we could just cut the LENGTH variable as below:

library(ggplot2)
library(dplyr)
mn <- mean(ddt$LENGTH)
sdd <- sd(ddt$LENGTH)
ddt <- ddt %>% mutate( Lcut = cut(LENGTH, c(min(LENGTH)-1, 
                                            seq(mn-3*sdd, mn+3*sdd, by = sdd), max(LENGTH)),
                                  labels = c("Outlier","Possible Out","Main","Main", "Main","Main", "Possible Out", "Outlier")))
g <- ggplot(ddt, aes(x = LENGTH)) + geom_dotplot(aes(fill = Lcut),binwidth = 1/5*sdd)
g <- g + geom_density(aes(y = ..count..))
g <- g + labs(title = "LENGTH data categorized by outlier status")
g

Instructions

You will need the following files

dir(dirdl)

Make sure you place them all in Lab2.

r rmdfile("EPAGAS", "EPAGAS.XLS","Lab2")

r rmdfile("Lab2.R", "Lab2.R", "Lab2")

r rmdfile("Lab document","MATH4753Laboratory2.docx","Lab2")

MATHSTATSOU/Intro2R documentation built on Feb. 20, 2025, 6:18 a.m.