RPubs link information

• Rpubs link : https://rpubs.com/AynG/YearlyPatronageMetroVIC

Introduction

• To begin with users can examine patronage patterns by mode by looking at the monthly total patronage for Victoria’s regional coach, urban and regional bus, and metropolitan and regional train services.
• Patronage is a count of customers boarding aboard services, omitting train transfers that do not include a direction change.
• All individuals 5 and older who are not station employees or drivers are considered patrons.

Introduction Cont.

• The Victorian Public Transport Patronage dataset provides detailed insights into public transportation usage in Victoria, including metro and regional trains, buses, trams, and regional coach services.
  • Myki Ticketing Data is the primary source for regional buses and metro patronage information, with adjustments made through a patronage survey to determine the transaction rate.
  • Metropolitan train patronage is calculated using barrier count data instead of surveys as of January 2021, which is essential to consider when analyzing trends.
• Although the data can be analyzed in various settings, our focus is on the patronage of metro train over the years and and what factors may have raised or lowered this figure.

Problem Statement

• In this report, we have tried to analyse Yearly Patronage Trends: Look into the patronage trends for metro trains over the past year (2018 - JUN 2023). Looking around if it there has been a change in the amount of customers over time and what elements could be causing these trends.
• Summary statistics will be performed on the Metropolitan_train variable, which will be grouped by the years.
• Outliers will be checked for using box plot visualisations and missing values will be checked for as well.
• Two sample hypothesis testing will be performed.

Data

• The dataset can be gathered in the Department of Transport section of the Victorian Government Open Data website, which makes data collected by organisations in the state’s public sector open. The link to the website is provided below.
• Dataset Link - https://discover.data.vic.gov.au/dataset/monthly-public-transport-patronage-by-mode
• Variables :
  • Year - The year for which the data is collected INTEGER
  • Month - Respective month of the calender INTEGER
  • Month.name - Particular month name with respect to month number CHAR
  • Metropolitan.train - Patronage count for metro rail CHAR
  • Metropolitan.tram - Patronage count for yarra tram CHAR
  • Metropolitan.bus - Patronage count for PTV Buses CHAR
  • Regional.train - Patronage count for VLine regional trains CHAR
  • Regional.coach - Patronage count for VLine regional coaches CHAR
  • Regional.bus - Patronage count for buses on VLine bus services CHAR

Viewing Data

MonthlyTransportMode <- read.csv("Monthly public transport patronage by mode.csv")

knitr::kable(head(MonthlyTransportMode,5))

Pre processing

• Replacing dot with spaces in columns name
• Dropping Metropolitan.tram, Metropolitan.bus, Regional.train, Regional.coach and Regional.bus column from the table.
• Converting variable Metropolitan_train to a numeric data type
• Converting Month_name to factor type

Filtered and Tidy Data

knitr::kable(head(MonthlyTransportMode,5))

Descriptive Statistics and Visualisation

• The number patronages is seen to be dropped by 65 percent in the year 2020
• The means and median are quite close to each other hence the data can be said it is in normal distribution.

MonthlyTransportMode %>% group_by(Year) %>% 
  summarise(Min = min(Metropolitan_train,na.rm = TRUE),
  Q1 = quantile(Metropolitan_train,probs = .25,na.rm = TRUE),
  Median = median(Metropolitan_train, na.rm = TRUE),
  Q3 = quantile(Metropolitan_train,probs = .75,na.rm = TRUE),
  Max = max(Metropolitan_train,na.rm = TRUE),
  Mean = mean(Metropolitan_train, na.rm = TRUE),
  SD = sd(Metropolitan_train, na.rm = TRUE),
  n = n(),
  Missing = sum(is.na(Metropolitan_train))) -> table1
knitr::kable(table1)

Data Visualisation - Histogram

plotNormalHistogram(MonthlyTransportMode$Metropolitan_train, col = '#7AC5CD', main = 'Patronage Distribution', length = 500)

ggplot(data = MonthlyTransportMode) + 
  stat_summary(
    mapping = aes(x = Year, y = Metropolitan_train),
    fun.min = min,
    fun.max = max,
    fun = median
  ) +
  labs(
    title = "Patronage by years in Metropolitan Trains",
    caption = "Data from discover.data.vic.gov.au",
    y = "Patronage Count (Million)"
  )

Outlier Visualisation

• We check for outliers using the Tukey’s method of outlier detection, no outliers were detected.

is.outlier = function(x){(x < summary(x)[2] - 1.5*IQR(x))|(x > summary(x)[5] + 1.5*IQR(x))}

sum(is.outlier(MonthlyTransportMode$Metropolitan_train))

## [1] 0

MonthlyTransportMode %>% boxplot(Metropolitan_train ~ Year, data = ., ylab = "Patronage(Million)")

Hypothesis Testing

• From the graphs and boxplot we can see that their is a significant drop in the metropolitan train patronage from the year 2019 to 2020 and we would like to further our analysis on these years by peforming hypthesis testing on these years
• Testing the Assumption of Normality using the Q-Q plotwill be performed on the year 2019 and 2020 to check for normality as the sample size n < 30 ( 2019 n = 12 , 2020 n =12 )
• Homogeneity of Variance using the Levene’s test to check for equal variance
• The type of Two sample t-test will be perofrmed based on the Levene’s test.

Hypothesis Testing - Assumpiton of Normality

• Since our sample size < 30 , normality should be checked for to prove the assumption of normality.
• Majority of the points appear to follow a normal distribution very closely.
• However, we can see two data points falling a little outside to the line in both the years 2019 and 2020, but we can still assume the data follows normal distribution as these are very little skewness, which is expected.

MonthlyTransportMode19$Metropolitan_train %>% qqPlot(dist = "norm", 
                                                     main = "Patronage in 2019") 

## [1] 1 5

MonthlyTransportMode20$Metropolitan_train %>% qqPlot(dist = "norm",
                                                     main = "Patronage in 2020")

## [1] 2 1

Hypothesis Testing - Levene’s Test

• Levene’s test has the following statistical hypotheses :

  \[H_0: \mu_1 = \mu_2 \] \[H_A: \mu_1 \ne \mu_2\]

leveneTest(Metropolitan_train ~ factor(Year), data = MonthlyTransportMode19_20) %>% as.data.frame() -> ltest
knitr::kable(ltest)

• The p value for Levene’s test of equal variance for the patronage in the year 2019 compared to year 2020 was p = 0.039.

• As the p value < .05 which is statistically significant, this would imply that we need to reject H₀ . In other words, it’s not safe to assume equal variance.

• Hence we need to proceed with Two-sample t-test Assuming Unequal Variance.

Hypothesis Testing - Two sample t-test

• The two sample t-test not assuming equal variance uses an adjusted test statistic t :

  \(t = \frac{\overline{x1} - \overline{x2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}\)

t.test(
  Metropolitan_train ~ factor(Year),
  data = MonthlyTransportMode19_20,
  var.equal = FALSE,
  alternative = "two.sided"
  )

## 
##  Welch Two Sample t-test
## 
## data:  Metropolitan_train by factor(Year)
## t = 6.9804, df = 13.194, p-value = 8.881e-06
## alternative hypothesis: true difference in means between group 2019 and group 2020 is not equal to 0
## 95 percent confidence interval:
##   9008871 17067077
## sample estimates:
## mean in group 2019 mean in group 2020 
##           20398136            7360162

#differene in mean 
20398136 - 7360162

## [1] 13037974

Hypothesis Testing - Two sample t-test

A two-sample t-test was used to test for a significant difference between the patronage in the year 2019 and 2020. Upon inspection of the normal Q-Q plot we saw two data points showed a little deviation from the line but it is safe to assume the patronage for the years 2019 and 2020 exhibited normal distribution as they do not exhibit a non linear trend, so we can proceed with the t-test. The Levene’s test of homogeneity of variance indicated that equal variance could not be assumed. The results of the two-sample t-test assuming unequal variance found a statistically significant difference between the mean patronage in the year 2019 and 2020, t(df=13.194)=6.98, p=8.881e-06, 95% CI for the difference in means [9008871 17067077]. The results of the investigation suggest that patronage in 2020 have significantly dropped compared to the patronage in 2019.

Discussion

• The metropolitan train patronage in the year 2019 has a mean of 20398136 (20 million) whereas the mean of patronage in the metropolitan in the year 2020 has a mean of 7360162 (7 million), we can see a patronage drop of 13037974(13 million) in the year 2020.
• This was proved by a two-sample t-test which produced a p value less than 0.05, thus allowing us to reject the null hypothesis that there is no difference between the mean number of patronages
• The strength - the dataset is that it covers a span of several years, which is useful for identifying long-term trends and seasonality.
• The limitation - the sample doesn’t provide information about the demographics of the riders, which can be essential for understanding the user base.
• Further Improvements - integrating external data sources, such as economic indicators, weather conditions, public events, or changes in public transport policy, can help provide context for the ridership trends.
• A further analysis in to the year 2019-20 we can find the cause of the drop in patronage was due to the COVID-19 pandemic which had lock-down restriction and less public transport usage.
• In conclusion, the patronage was severely affected due to COVID-19 and we can see a steady rise in the number of patronage for metro trains.

References

Victorian Government Aus (2023), Monthly public transport patronage by mode - Victorian Government Data Directory, viewed 13 October 2023, https://discover.data.vic.gov.au/dataset/monthly-public-transport-patronage-by-mode.

Applied Analytics, Module 7 Notes - viewed 14 October 2023, http://rare-phoenix-161610.appspot.com/secured/Module_07.html.

RPubs, MATH1324 Applied Analytics Assignment 2, rpubs.com, viewed 14 October 2023, https://rpubs.com/CaptainJackHarkness/906830