MATH1324 Applied Analytics Assignment 2
Hate crime in England and Wales from 2020 to 2021
Using Two-Sample T-Test
Siddharth Vangari s3894864
Last updated: 27 May, 2023
Data Cont.
Using the read.csv() function, the data set was imported into R.
Using the head() function, the data set was organized.
Hatecrime <- read.csv("C:/Users/vanga/OneDrive/Desktop/rmit/Sem 3/Applied Analytics/Final Assignment/hate_crime_data.csv")
knitr::kable(head(Hatecrime, 10))
| 2011/12 |
Avon and Somerset |
Disability |
113 |
| 2011/12 |
Bedfordshire |
Disability |
6 |
| 2011/12 |
British Transport Police |
Disability |
25 |
| 2011/12 |
Cambridgeshire |
Disability |
6 |
| 2011/12 |
Cheshire |
Disability |
7 |
| 2011/12 |
Cleveland |
Disability |
15 |
| 2011/12 |
Cumbria |
Disability |
17 |
| 2011/12 |
Derbyshire |
Disability |
12 |
| 2011/12 |
Devon and Cornwall |
Disability |
7 |
| 2011/12 |
Dorset |
Disability |
9 |
Preprocessing
colnames(Hatecrime) <- gsub("\\.", "_", colnames(Hatecrime))
head(Hatecrime, 5)
- Data Type Conversion of Number_of_offences variable to a numeric
data type by removing commas:
Hatecrime$Number_of_offences <- as.numeric(gsub(",", "", Hatecrime$Number_of_offences))
- Motivating_factor variable is filtered to exclude disability, sexual
orientation, and transgender
Hatecrimefiltered <- Hatecrime[Hatecrime$Motivating_factor %in% c("Race", "Religion"), ]
- Data type conversion from character to factor
Hatecrimefiltered[] <- lapply(Hatecrimefiltered, as.factor)
- Convert Number_of_offences column to numeric
Hatecrimefiltered$Number_of_offences <- as.numeric(as.character(Hatecrimefiltered$Number_of_offences))
Hatecrimefiltered <- Hatecrimefiltered[complete.cases(Hatecrimefiltered$Number_of_offences), ]
Descriptive Statistics and Visualisation
Compared to the average number of crimes motivated by religion,
the average number of crimes motivated by race is higher.
In this case, the data is positively skewed, because both means
exceed the medians.
Hatecrimefiltered %>% group_by(Motivating_factor) %>% summarise(Min = min(Number_of_offences,na.rm = TRUE),
Q1 = quantile(Number_of_offences,probs = .25,na.rm = TRUE),
Median = median(Number_of_offences, na.rm = TRUE),
Q3 = round(quantile(Number_of_offences,probs = .75,na.rm = TRUE),1),
Max = max(Number_of_offences,na.rm = TRUE),
Mean = round(mean(Number_of_offences, na.rm = TRUE),1),
SD = round(sd(Number_of_offences, na.rm = TRUE),1),
n = n(),
Missing = sum(is.na(Number_of_offences))) -> crime_by_Motivating_Factor
knitr::kable(crime_by_Motivating_Factor)
| Race |
51 |
418.5 |
744 |
1437.0 |
21938 |
1433.9 |
2435.3 |
483 |
0 |
| Religion |
0 |
19.0 |
43 |
105.5 |
2506 |
120.0 |
290.4 |
483 |
0 |
Decsriptive Statistics Cont.
# Create histogram plots
plot_Race <- ggplot(Hatecrimefiltered[Hatecrimefiltered$Motivating_factor == "Race", ], aes(x = Number_of_offences)) +
geom_histogram(fill = "blue", color = "white", bins = 10) +
labs(x = "Number of Offences", y = "Frequency") +
ggtitle("Histogram of Crimes Due to Race")
plot_Religion <- ggplot(Hatecrimefiltered[Hatecrimefiltered$Motivating_factor == "Religion", ], aes(x = Number_of_offences)) +
geom_histogram(fill = "red", color = "white", bins = 10) +
labs(x = "Number of Offences", y = "Frequency") +
ggtitle("Histogram of Crimes Due to Religion")
# Arrange the histograms side by side
grid.arrange(plot_Race, plot_Religion, nrow = 1)
Visual Representation of Outliers
# Calculate the quartiles and IQR
Q1 <- quantile(Hatecrimefiltered$Number_of_offences, 0.25)
Q3 <- quantile(Hatecrimefiltered$Number_of_offences, 0.75)
IQR <- Q3 - Q1
# Define the lower and upper bounds for outliers
lower_bound <- Q1 - 1.5 * IQR
upper_bound <- Q3 + 1.5 * IQR
# Remove outliers from the data
HatecrimeCleaned <- Hatecrimefiltered[Hatecrimefiltered$Number_of_offences >= lower_bound & Hatecrimefiltered$Number_of_offences <= upper_bound, ]
# Print the filtered data
head(HatecrimeCleaned)
- Using Tukey’s method of outlier detection, 45 outliers were found in
this data set.
is.outlier = function(x){(x < summary(x)[2] - 1.5*IQR(x))|(x > summary(x)[5] + 1.5*IQR(x))}
sum(is.outlier(HatecrimeCleaned$Number_of_offences))
## [1] 45
boxplot(Number_of_offences~Motivating_factor, data = HatecrimeCleaned, xlab = "Motivating Factor",
ylab = "Number of Offences", main = "Number Of Offences Motivated By Race To Religion", col=c("blue", "pink"))
Hypothesis Testing
H0: There is no statistically significant difference between the
average number of offences motivated by Race and Religion.
\[H_0: \mu_1 = \mu_2 \] HA: There
is a statistically significant difference between the average number of
offences motivated by Race and religion.
\[H_A: \mu_1 \ne \mu_2\]
Hypthesis Testing - QQ Plot
# Filter the data for offences motivated by race
raceData <- HatecrimeCleaned$Number_of_offences[HatecrimeCleaned$Motivating_factor == "Race"]
qqnorm(raceData)
qqline(raceData)
#title(main = "QQ Plot for Number of Offences Motivated by Race")
# Filter the data for offences motivated by race
religionData <- HatecrimeCleaned$Number_of_offences[HatecrimeCleaned$Motivating_factor == "Religion"]
qqnorm(religionData)
qqline(religionData)
#title(main = "QQ Plot for Number of Offences Motivated by Race")
Hypthesis Testing - Two-sample t-test
- We can now perform a t-test using two samples
t.test(
Number_of_offences~Motivating_factor,
data = HatecrimeCleaned,
var.equal = FALSE,
alternative = "two.sided"
)
##
## Welch Two Sample t-test
##
## data: Number_of_offences by Motivating_factor
## t = 25.194, df = 512.64, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group Race and group Religion is not equal to 0
## 95 percent confidence interval:
## 574.9778 672.2357
## sample estimates:
## mean in group Race mean in group Religion
## 721.18204 97.57531
# Difference between the two means
721.18204 - 97.57531
## [1] 623.6067