1 Executive Summary

  • The aim of this report is to analyse the data available from the 2016 Queensland Shark Control Program. To understand the number of sharks caught and the differences between the sharks and climate in which they were caught.
  • The main discoveries are that shark species are caught in their known migratory habitats, and that over the past 15 years the size of tiger sharks caught in this program is not statistically different.

2 Full Report

2.1 Initial Data Analysis (IDA)

  • The data came from the Queensland Shark Control Program which is a program implemented by the Department of Agriculture and Fisheries of the Queensland Government. The program aims to “reduce the risk of shark bites in Queensland coastal waters” (Shark Control Program, 2022) by gathering data from sharks caught in secured nets and drums at eleven popular beach areas along the QLD coast (Pushaw, 2015).

  • The data is valid because it comes directly from the organisation that initiated the program and collects the data.

  • Possible issues include the potential effect on the profits of businesses or organisations that deal directly with shark populations. These many offshoots use the data to inform their business activity.

  • Potential stakeholders include but are not limited to, tourism, commercial and recreational fishing, and conservation organisations. Due to the fact that profits are at stake, it is not impossible for data to be misrepresented in order to reduce risk of loss of revenue. This may be done by inflating or deflating species and population numbers.

  • Each row represents the circumstances surrounding one shark being caught in a net or drum. Each row is dedicated to one individual shark caught in the year 2016.

  • Each column represents the variables surrounding the individual shark being caught. This includes its species, the date of the catch, the area in which the shark is caught, the specific location within the area in which the shark is caught, the longitude and latitude of the shark when caught, the length of the shark, the water temperature when the shark is caught, the month in which the shark is caught, and the day of the week.

  • The key variables are the species of shark caught, the date and location in which it is caught, the water temperature, and the size of the shark. From these variables one can investigate various questions about the current climate. The species of shark can indicate the population levels and possible conservation status risks of a species. The date and location can indicate a change in migratory patterns or effects of climate change that has caused habitats to shift. The water temperature can indicate a rise or fall in temperature during migratory periods. The size of the shark can indicate nutrition levels, change in lifespan, or increased habitat competition for a species.

#Read in dataset
sharks<-read.csv("/Users/brynnarollins/Desktop/MATH 1005/Assessments/Project 2/sharks.csv", header=TRUE)
  • Dimensions of the data set. 532 observations of 10 variables.
#Dimensions of the dataset
dim(sharks)
## [1] 532  10
  • Data classification
#Classification of the variables
sharks$Date=as.Date(sharks$Date, format="%Y-%m-%d")
sharks$Water.Temp..C.=as.numeric(sharks$Water.Temp..C.)
str(sharks)
## 'data.frame':    532 obs. of  10 variables:
##  $ Species.Name  : chr  "Australian Blacktip" "Blacktip Reef Whaler" "Blacktip Reef Whaler" "Blacktip Reef Whaler" ...
##  $ Date          : Date, format: NA NA ...
##  $ Area          : chr  "Cairns" "Cairns" "Cairns" "Mackay" ...
##  $ Location      : chr  "Holloways Beach" "Buchans Point Beach" "Ellis Beach" "Harbour Beach" ...
##  $ Latitude      : chr  "-16°49.82" "-16°43.56" "-16°43.3" "-21°7.08" ...
##  $ Longitude     : chr  "145°44.85" "145°39.78" "145°39.01" "149°13.62" ...
##  $ Length..m.    : num  1 0.7 1.5 2.2 1.7 1.2 0.75 1.2 0.8 1.3 ...
##  $ Water.Temp..C.: num  27 27 27 26 26 29 30 31 29 29 ...
##  $ Month         : chr  "November" "January" "January" "January" ...
##  $ Day.of.Week   : chr  "Wednesday" "Saturday" "Saturday" "Tuesday" ...

2.2 Research Question 1: Are there patterns in species population and distribution in regards to location?

Figure 1. Map of locations in Queensland that have nets and drums, in 2016, as part of the QLD Shark Control Program

#Bar graph showing the number of sharks caught at each location in 2016
library(ggplot2)
library(RColorBrewer)
library(forcats)
library(plyr)
library(ggthemes)
library(viridis)
rq1a<-data.frame(Location=c("Townsville","Sunshine Coast Sth & Bribie Is.","Sunshine Coast Nth","Rainbow Beach","Nth Stradbroke Is.","Mackay","Gold Coast","Gladstone","Capricorn Coast","Cairns","Bundaberg"),Catches=c(112,12,39,36,10,66,47,52,55,51,52))
ggplot(rq1a,aes(x=Location,y=Catches,fill=Location)) +
  geom_bar(stat = "identity") +
  scale_x_discrete(limits = c("Gold Coast","Nth Stradbroke Is.","Sunshine Coast Sth & Bribie Is.","Sunshine Coast Nth","Rainbow Beach","Bundaberg","Gladstone","Capricorn Coast","Mackay","Townsville","Cairns")) +
  scale_fill_viridis(discrete = TRUE, option = "H") +
  coord_flip() +
  theme(legend.position = "None",plot.title = element_text(face="bold", hjust = 0.5)) +
  xlab("") +
  ylab("Catches") +
  ggtitle("Number of Sharks Caught at Each Location")

Figure 2. Number of sharks caught at each designated location apart of the QLD Shark Control Program in 2016. The locations are in geographic order from north to south of the QLD coast.

#Staked bar graph showing location distribution of each species
Location=(rep(c("Bundaberg", "Cairns", "Capricorn Coast", "Gladstone", "Gold Coast", "Mackay", "Nth Stradbroke Is.", "Rainbow Beach", "Sunshine Coast Nth", "Sunshine Coast Sth & Bribie Is.", "Townsville"),each=24))
Species=(rep(c("Australian Blacktip","Blacktip Reef Whaler", "Bull Whaler", "Common Blacktip Whaler", "Creek Whaler", "Dusky Whaler", "Graceful Whaler", "Great Hammerhead", "Grey Nurse Shark", "Hardnose Whaler", "Long Nose Whaler", "Mako", "Milk Shark", "Pigeye Whaler", "Sandbar Whaler", "Scalloped Hammerhead", "Sharptooth Shark", "Slit Eye Shark", "Spot-Tail Whaler", "Tawny Shark", "Tiger Shark", "Unknown", "White Shark", "Zebra Shark"), 11))
Number=c(0,0,5,0,0,0,0,0,0,0,0,0,0,7,2,0,2,0,1,1,32,2,0,0,1,10,1,2,1,0,0,0,0,2,2,0,1,3,0,1,0,1,1,3,22,0,0,0,0,1,36,0,0,0,0,0,0,3,1,0,0,0,0,1,0,0,4,1,8,0,0,0,0,1,11,32,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,6,0,0,0,0,0,8,0,0,0,0,5,0,0,10,2,0,0,1,8,0,0,0,0,8,0,4,1,0,3,3,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,7,51,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,6,0,1,0,0,0,3,1,0,4,0,2,0,0,4,1,0,0,0,2,1,0,0,0,17,0,1,0,0,0,8,0,0,0,0,6,1,0,12,1,0,0,1,0,0,0,0,0,10,0,0,0,0,0,3,0,0,0,0,2,0,0,5,0,0,0,0,0,1,0,0,0,1,0,0,0,0,5,12,4,0,0,1,7,0,0,2,0,2,4,0,1,1,0,16,11,46,0,0,0)
rq1b<-data.frame(Species,Location,Number)
ggplot(rq1b, aes(fill=Location, y=Number, x=Species),width = 2) + 
  geom_bar(position="fill", stat="identity") +
  coord_flip() +
  scale_fill_viridis(discrete = TRUE, option = "H") +
  xlab("") +
  ylab("") +
  ggtitle("Location Distribution for Each Identified Species") +
  theme(legend.position = "none", axis.text.x = element_text(vjust = 1, hjust = 0, size=7), axis.text.y = element_text(size=7), plot.title = element_text(face="bold", hjust = 0.5))

Figure 3. Location distribution of shark species caught as part of the QLD Shark Control Program in 2016.

#Line graph of location distribution of shark species caught as part of the QLD Shark Control Program in 2016
Loctemp=(rep(c("Bundaberg", "Cairns", "Capricorn Coast", "Gladstone", "Gold Coast", "Mackay", "Nth Stradbroke Is.", "Rainbow Beach", "Sunshine Coast Nth", "Sunshine Coast Sth & Bribie Is.", "Townsville"),12))
Month=(rep(c("January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"), each=11))
Avtemp=(rep(c(25, 28.625, 27.3, 26.3, 24.5, 26.125, 27, 25.4, 25, 24, 29.3, 26.5, NA, 26.9375, 27.875, 23.3, 27, NA, 25.1, 24, 24, 30.8, 25.2, 29, 26.2, 27, 27, 27, NA, 26.6, 24, NA, 29.3, 23.66, 27.625, 26, 26.3, 25, 26, 26, 25.5, 24, NA, 27.09, 23.125, 25.5, 25, 25, 23, 25, NA, 24, 23.25, 24, 25.7, 20.5, 25, 23.3, 21.75, 22, 25, NA, NA, 23, 22, 24.41, 17.3, 23, 21, 18.5, 19.75, 24, 20, 20.5, 21, NA, 22.75, 17, 22.6, NA, 19.6, 20.3, 24, 20.5, 20.5, 23, NA, 22.72, 20.3, 24.5, 23, 22, 19.83, 23.42, 21, 21, 22, NA, 25.25, 22.5, 26, 23.3, 23.8, 19.5, 24.6, 21, 22.3, 22.2, NA, 26.6, 24, 27.28, 25.66, 25.66, 23.8, 25, NA, 23.5, 23, 22, 28.18, 25, 28.3, 26, 27, 22, 27, NA, 25, 23.3, 24, 29.4)))
Yeartemp<-data.frame(Month,Avtemp,Loctemp)
ggplot(Yeartemp,aes(x= fct_inorder(Month), y=Avtemp, group=Loctemp, color=Loctemp)) +
  geom_line() +
  geom_point(size=2.5) +
 scale_color_viridis(discrete = TRUE, option = "H") +
  xlab("") +
  ylab("Temperature (°C)") +
  ggtitle("Comparison of Average Monthly Water Temperatures") +
  theme(legend.position = "none", axis.text.x = element_text(angle =-70, vjust = 1, hjust = 0, size=8), axis.text.y = element_text(size=8), plot.title = element_text(face="bold", hjust = 0.5)) +
  ylim(15,35)

Figure 4. Comparing the average monthly water temperatures in 2016.

#Scatter plot of water temperature for each species
p=sharks$Species.Name
q=sharks$Water.Temp..C.
pq<-data.frame(p,q)
ggplot(pq,aes(x= fct_inorder(p), y=q, color=q)) +
  geom_point(size=2.5) +
  scale_color_viridis(discrete = FALSE, option = "B") +
  xlab("") +
  ylab("Temperature (°C)") +
  ggtitle("Water Temperatures for Each Species Caught") +
  theme(legend.position = "none", axis.text.x = element_text(angle =-70, vjust = 1, hjust = 0, size=7), axis.text.y = element_text(size=7), plot.title = element_text(face="bold", hjust = 0.5)) +
  ylim(15,35)

Figure 5. Specific water temperature for every shark caught, divided into species.

From this data it can be seen that the majority of the sharks caught were north of Rainbow beach. From the data 388 out of 532, or 72.9% of the sharks caught were between Cairns and Bundaberg. This could be because of the warmer water temperatures. Most sharks found off of the coast of Queensland are reef sharks or whalers. These species prefer warmer temperatures, shown in figure 5. As seen in figure 4, the median temperature of all locations in 2016 was 25°C. From Cairns to Bundaberg, the average annual temperature is equal to, or above 25°C. While from Rainbow Beach to the Gold Coast, the average annual temperature was below 25°C. The highest yearly average temperature was Cairns at 27°C and the lowest was the Gold Coast at 21°C, clearly showing the geographical temperature scale and explains why more sharks were found in the northern locations as there is a warmer temperature throughout the year.

Most of the different sharks were found in multiple places and reflect the known migration patterns of their species which extends up and down the entire coastline. However, there were a few species that were only found within a certain area. The Australian blacktip, creek whaler, graceful whaler, milk shark, and the slit eye shark were only found in the northern most locations, Cairns and Townsville. The grey nurse shark and the dusky whaler were only found in the Sunshine Coast North and Rainbow Beach, respectively. While the zebra shark was only found off of the Gold Coast. This is consistent with literature and reflects the known movement of their species.

Table 6. The number of shark catches at each location.

#Frequency of rows for each area
count(sharks$Area)
##                                       x freq
## 1                             Bundaberg   52
## 2                                Cairns   51
## 3                       Capricorn Coast   55
## 4                             Gladstone   52
## 5                            Gold Coast   47
## 6                                Mackay   66
## 7                    Nth Stradbroke Is.   10
## 8                         Rainbow Beach   36
## 9                  Sunshine Coast North   39
## 10 Sunshine Coast South & Bribie Island   12
## 11                           Townsville  112

The total number of shark catches from Cairns to Bundaberg and its percentage of the total number of shark catches in 2016:

#Number of sharks Cairns to Bundaberg & percentage of total shark numbers
51+112+66+55+52+52
## [1] 388
(388/532)*100
## [1] 72.93233

2.3 Research Question 2: Have the demographics of Tiger Sharks changed from 2001 to 2016?

Studies have found that, in the last 50 years, there has been a decline in the number of sharks present in Queensland waters (Pushaw, 2015). Using data from 2001, I wanted to look at the demographics of tiger sharks and see if there are any changes.

#QLD Shark Control Program data (2001)
sharks2001<-read.csv("/Users/brynnarollins/Desktop/MATH 1005/Assessments/Project 2/sharks2001.csv", header=TRUE)
str(sharks2001)
## 'data.frame':    734 obs. of  6 variables:
##  $ Species.Name  : chr  "AUSTRALIAN BLACKTIP" "BIG NOSE WHALER" "BLACKTIP REEF WHALER" "BLACKTIP REEF WHALER" ...
##  $ Date          : chr  "16/10/2001" "23/4/2001" "6/1/2001" "20/1/2001" ...
##  $ Area          : chr  "Bundaberg" "Sunshine Coast" "Bundaberg" "Bundaberg" ...
##  $ Location      : chr  "Kelly's Beach" "Coolum Beach" "Kelly's Beach" "Nielson Park" ...
##  $ Length..m.    : num  0.92 2.1 0.91 0 0.8 0.8 0.7 0.6 1.5 0.7 ...
##  $ Water.Temp..C.: int  22 23 26 27 26 27 29 29 29 29 ...

Table 7. Frequency of each shark species in 2016:

#Frequency of shark species in 2016
count(sharks$Species.Name)
##                         x freq
## 1     Australian Blacktip    1
## 2    Blacktip Reef Whaler   20
## 3             Bull Whaler   91
## 4  Common Blacktip Whaler   39
## 5            Creek Whaler    1
## 6            Dusky Whaler    4
## 7         Graceful Whaler    1
## 8        Great Hammerhead   22
## 9        Grey Nurse Shark    1
## 10        Hardnose Whaler    6
## 11       Long Nose Whaler   36
## 12                   Mako    5
## 13             Milk Shark    3
## 14          Pigeye Whaler   14
## 15         Sandbar Whaler    5
## 16   Scalloped Hammerhead   16
## 17       Sharptooth Shark    5
## 18         Slit Eye Shark    1
## 19       Spot-Tail Whaler   22
## 20            Tawny Shark   23
## 21            Tiger Shark  207
## 22          Unknown Shark    2
## 23            White Shark    6
## 24            Zebra Shark    1

Table 8. Frequency of each shark species in 2001:

#Frequency of shark species in 2001
count(sharks2001$Species.Name)
##                         x freq
## 1     AUSTRALIAN BLACKTIP    1
## 2         BIG NOSE WHALER    1
## 3    BLACKTIP REEF WHALER   53
## 4             BULL WHALER  112
## 5  COMMON BLACKTIP WHALER    5
## 6            DUSKY WHALER   22
## 7         GRACEFUL WHALER    1
## 8        GREAT HAMMERHEAD   13
## 9       GREY CARPET SHARK    2
## 10       GREY NURSE SHARK    1
## 11       GREY REEF WHALER    7
## 12      HAMMERHEAD SHARK    25
## 13        HARDNOSE WHALER    1
## 14       LONG NOSE WHALER   44
## 15                   MAKO    1
## 16             MILK SHARK    1
## 17          PIGEYE WHALER   18
## 18     PORT JACKSON SHARK    1
## 19         SANDBAR WHALER   10
## 20   SCALLOPED HAMMERHEAD   38
## 21       SHARPTOOTH SHARK    5
## 22           SILKY WHALER    7
## 23       SPOT-TAIL WHALER   19
## 24    TASSELLED WOBBEGONG    1
## 25            TAWNY SHARK   26
## 26            TIGER SHARK  287
## 27          UNKNOWN SHARK    3
## 28               WHALER *    5
## 29            WHITE SHARK    4
## 30      WHITE-CHEEK SHARK    7
## 31      WINGED HAMMERHEAD    1
## 32            ZEBRA SHARK   12

The total number of sharks caught in 2001 was 734, which decreased to 532 in 2016. The number of Tiger Sharks declined from 287 to 207 in the 15 years. These numbers could be used to support the statement that shark populations are declining, however there is not enough information to accurately draw these conclusions. I decided to look specifically at the size of tiger sharks caught in 2001 and 2016. While this does not directly relate to population numbers, it can investigate population demographics. For example, if the size of a specific shark species significantly changed over time, there may be issues with nutrition, change in habitat or change in the age demographics of the species.

Mean of Tiger Shark length in 2001:

#Mean of Tiger Shark length in 2001
mean(2.73,3.67,3.57,3.7,3.42,3.4,2.17,1.93,1.1,1.15,3.49,2.15,3.21,1.92,2.48,3.47,4.07,3.14,3.86,2.79,3.12,3.2,1.97,2.7,1.56,1.6,2.9,2.27,2.37,3.1,2.8,3.6,2.3,2.2,1.6,0.8,3.1,4.2,2.1,2.9,2.6,2.2,2.2,3.6,0.8,3.6,2.4,3.7,2.1,0.7,0.7,2.1,0.8,1.3,3.2,3.2,3.5,3.4,2.1,2.3,2.3,2.2,1.4,4,3.8,2.3,2.4,3.2,3.5,3.6,3.2,3,2.1,3.1,3.1,4.5,3.4,3.3,3.2,1.6,4,4.2,3.2,2.1,4.1,2.7,2.7,2.3,3.6,3.7,3.2,0.4,4.1,3.7,3.4,3,3,3.3,3.8,4,3.4,4,1.2,3.6,2.4,3.6,3,2.7,3.3,2.2,2.1,2,1.1,2.1,2.2,2,1.2,1.4,1.2,2.2,3.2,2.4,1.7,3.5,1.6,2.4,2.6,2.4,3,3.8,2.7,3.3,2.4,3.1,2.8,2.7,3,3.1,3.8,4.3,2.9,2.7,2.4,2.1,2.4,2.2,2.5,2.3,2.4,2.8,2.1,3,3,1.5,2.4,4.2,3.4,2.9,3,3.4,3.4,3.1,2.3,3,3.1,3.2,3.4,2.7,2.9,2.7,3,3.1,3.6,3.4,3,3.1,2.7,3.4,3.6,4,3.9,4.3,1.7,1.4,1.1,1.2,2.3,1.7,3,3.5,2.2,3.1,0,0,0,3.6,3.3,3.8,2.1,2,3.6,3.1,2.4,4.2,3.7,2.48,2.2,1.6,3.2,3.12,1.94,1.99,1.87,1.71,1.87,3.4,3.1,2.44,3,1,0.75,0.75,1,1.2,3.2,0.5,1.2,2.1,1.4,1,4.1,1.5,2.1,1,2.1,1.1,2.4,2.4,1,3.4,0.5,2.08,3.2,3.75,1.75,3.1,3.4,1.8,0.75,1.3,1.4,1.6,1,2.8,2.7,2.8,2.6,2.7,2.9,3.3,1.51,1.5,3.4,1.44,1.56,0.98,1.11,1.72,1.09,2.08,3.4,1.26,1.69,0.72,1.21,1.62,1.25,1.75,3.2,3,1.8,1.7,2.35,1.52,1.53,3.1)
## [1] 2.73

Mean of Tiger Shark length in 2016:

#Mean of Tiger Shark length in 2016
mean(1.95,1.48,1.41,2.32,1.95,1.28,2.37,1.82,1.97,3.12,3.5,3.28,2.73,1.56,2.26,1.42,2.76,2.1,3.2,3.57,2,3.16,3.37,2.03,2.15,4.09,2.5,3.08,1.6,2.7,2.7,1.13,4.1,2.7,1.4,1.24,2.6,2.4,1.2,0.88,3.4,2.3,1,3.9,3.1,1.4,2.1,1.8,2.2,2.9,2.1,3.1,0.7,1.7,2.08,2.1,3.8,1.51,3.65,3.65,3.46,3.12,1.6,2.75,3.85,3.35,2.6,3.7,1.78,2.31,2.5,3.15,3.04,3.04,3.5,3.65,2.2,2,2.3,2.4,2.01,3.6,2.4,3.2,1.9,1.4,1.9,1.6,3.2,2.4,2.5,2.1,2,2.4,3.4,2.8,2.8,3.2,2.7,2.2,2,2.2,2.1,2.2,2.3,1.6,2,2.3,1.8,3.8,2.2,3.4,2.8,2,2.6,3.4,2.4,3,2.4,2.3,2.1,2.1,1.7,2,2,2,2.5,1.1,3.5,2.8,3,3.9,3.1,2.9,2.35,2.6,3.85,2.6,2.35,1.85,3.3,2.47,3.65,2.75,3.15,1.4,1.4,3.95,2.3,1.7,3.76,2.85,3.21,2.54,3.34,2.45,2.51,2.01,0.9,1.02,1,1.05,3.8,2.35,0.89,1.13,2,2,1.95,3.1,4,3.2,2.5,1.7,3.5,3.8,3.7,1.7,1.85,1.8,3.1,1.95,3,2.25,3.5,1.4,1.4,3,2.3,3.55,2.55,3.5,1.4,2.15,1.3,2.1,1.4,1.85,1.5,3.5,1.3,3.7,2,1.35,3.6,3.65,2.45)
## [1] 1.95
#Box plot of Tiger Shark length variances in 2001 and 2016
sharkone<-c(2.73,3.67,3.57,3.7,3.42,3.4,2.17,1.93,1.1,1.15,3.49,2.15,3.21,1.92,2.48,3.47,4.07,3.14,3.86,2.79,3.12,3.2,1.97,2.7,1.56,1.6,2.9,2.27,2.37,3.1,2.8,3.6,2.3,2.2,1.6,0.8,3.1,4.2,2.1,2.9,2.6,2.2,2.2,3.6,0.8,3.6,2.4,3.7,2.1,0.7,0.7,2.1,0.8,1.3,3.2,3.2,3.5,3.4,2.1,2.3,2.3,2.2,1.4,4,3.8,2.3,2.4,3.2,3.5,3.6,3.2,3,2.1,3.1,3.1,4.5,3.4,3.3,3.2,1.6,4,4.2,3.2,2.1,4.1,2.7,2.7,2.3,3.6,3.7,3.2,0.4,4.1,3.7,3.4,3,3,3.3,3.8,4,3.4,4,1.2,3.6,2.4,3.6,3,2.7,3.3,2.2,2.1,2,1.1,2.1,2.2,2,1.2,1.4,1.2,2.2,3.2,2.4,1.7,3.5,1.6,2.4,2.6,2.4,3,3.8,2.7,3.3,2.4,3.1,2.8,2.7,3,3.1,3.8,4.3,2.9,2.7,2.4,2.1,2.4,2.2,2.5,2.3,2.4,2.8,2.1,3,3,1.5,2.4,4.2,3.4,2.9,3,3.4,3.4,3.1,2.3,3,3.1,3.2,3.4,2.7,2.9,2.7,3,3.1,3.6,3.4,3,3.1,2.7,3.4,3.6,4,3.9,4.3,1.7,1.4,1.1,1.2,2.3,1.7,3,3.5,2.2,3.1,0,0,0,3.6,3.3,3.8,2.1,2,3.6,3.1,2.4,4.2,3.7,2.48,2.2,1.6,3.2,3.12,1.94,1.99,1.87,1.71,1.87,3.4,3.1,2.44,3,1,0.75,0.75,1,1.2,3.2,0.5,1.2,2.1,1.4,1,4.1,1.5,2.1,1,2.1,1.1,2.4,2.4,1,3.4,0.5,2.08,3.2,3.75,1.75,3.1,3.4,1.8,0.75,1.3,1.4,1.6,1,2.8,2.7,2.8,2.6,2.7,2.9,3.3,1.51,1.5,3.4,1.44,1.56,0.98,1.11,1.72,1.09,2.08,3.4,1.26,1.69,0.72,1.21,1.62,1.25,1.75,3.2,3,1.8,1.7,2.35,1.52,1.53,3.1)
sharktwo<-c(1.95,1.48,1.41,2.32,1.95,1.28,2.37,1.82,1.97,3.12,3.5,3.28,2.73,1.56,2.26,1.42,2.76,2.1,3.2,3.57,2,3.16,3.37,2.03,2.15,4.09,2.5,3.08,1.6,2.7,2.7,1.13,4.1,2.7,1.4,1.24,2.6,2.4,1.2,0.88,3.4,2.3,1,3.9,3.1,1.4,2.1,1.8,2.2,2.9,2.1,3.1,0.7,1.7,2.08,2.1,3.8,1.51,3.65,3.65,3.46,3.12,1.6,2.75,3.85,3.35,2.6,3.7,1.78,2.31,2.5,3.15,3.04,3.04,3.5,3.65,2.2,2,2.3,2.4,2.01,3.6,2.4,3.2,1.9,1.4,1.9,1.6,3.2,2.4,2.5,2.1,2,2.4,3.4,2.8,2.8,3.2,2.7,2.2,2,2.2,2.1,2.2,2.3,1.6,2,2.3,1.8,3.8,2.2,3.4,2.8,2,2.6,3.4,2.4,3,2.4,2.3,2.1,2.1,1.7,2,2,2,2.5,1.1,3.5,2.8,3,3.9,3.1,2.9,2.35,2.6,3.85,2.6,2.35,1.85,3.3,2.47,3.65,2.75,3.15,1.4,1.4,3.95,2.3,1.7,3.76,2.85,3.21,2.54,3.34,2.45,2.51,2.01,0.9,1.02,1,1.05,3.8,2.35,0.89,1.13,2,2,1.95,3.1,4,3.2,2.5,1.7,3.5,3.8,3.7,1.7,1.85,1.8,3.1,1.95,3,2.25,3.5,1.4,1.4,3,2.3,3.55,2.55,3.5,1.4,2.15,1.3,2.1,1.4,1.85,1.5,3.5,1.3,3.7,2,1.35,3.6,3.65,2.45)
boxplot(sharktwo,sharkone,names=c("2016", "2001"), horizontal=TRUE, col=c("darkseagreen","bisque3"),xlab="Size (m)", main="Comparison of Size of Tiger Sharks Caught in 2001 & 2016")

Figure 9. Box plot comparing the sizes of Tiger Sharks caught in 2001 and 2016 by the QLD Shark Control Program

The mean in tiger shark length in 2001 was 2.73 m and in 2016 it was 1.95 m. As seen in figure 9, the two data sets did not have an equal variance. Therefore I performed Welch’s t-Test.

  • H1: µ1 -µ2 ≠ 0

    • The means of the two populations are not equal to each other

  • H0: µ1 -µ2 = 0

    • The means of the two populations are equal to each other
#Welch's t-Test
t.test(sharkone,sharktwo,var.equal = FALSE)
## 
##  Welch Two Sample t-test
## 
## data:  sharkone and sharktwo
## t = 0.82211, df = 479.38, p-value = 0.4114
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.09158115  0.22334325
## sample estimates:
## mean of x mean of y 
##  2.525350  2.459469

As seen from above:

  • t: 0.82

  • df: 479.38

  • p-value: 0.41

  • 95% confidence interval: (-0.09, 0.22)

Therefore, the alternative hypothesis must be accepted as 0.41 is larger than 0.05, which shows the population means are not statistically different. In other words, the sizes of tiger sharks has not statistically changed between 2001 and 2016.

3 References