Quantitative Analysis of Car Park Usage at Heathrow Airport: A Report

This report presents a quantitative analysis of car park usage at Heathrow Airport, examining data collected by traffic counter devices at four terminals. The analysis investigates the relationship between car park usage and school holidays, non-school holidays, and different car park terminals. The methodology includes data formatting, descriptive statistics, and inferential statistics, such as t-tests and ANOVA, to identify statistically significant relationships. The report explores the use of boxplots, scatterplots, and correlation coefficients to visualize and interpret the data. The findings indicate a positive correlation between car park usage during school holidays and non-school holidays, as well as variations in car usage across different terminals. The report also discusses the appropriateness of t-tests and ANOVA for this dataset, highlighting the importance of meeting assumptions for statistical validity. The report concludes that t-tests and ANOVA confirm the findings that there is no any statistically significant difference observed from the two tests and that p-value is less than 0.05 in both cases.

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<University>
ICT Research methods
<Author>
31 August 2024
<Professor’s name>
<Program of Study>

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Introduction
Usually, it is expected that the use of carpark increases during school holidays than non-
school holidays, (Hensher, 2017). This is because, during school holidays, learners are
expected to be back home hence utilize carpark areas while socializing. On the same note, the
results indicated in the paper established whether there is a relationship between carpark
usage and school days. The selected dataset is quantitative in nature hence can be easily
prepared, explored, analyze, presented and validated based on the variables. In addition, this
type of dataset can be analyzed using both descriptive and inferential statistics. The
descriptive statistics are used to describe and summarize the data in the form of frequencies,
percentages, and means. The inferential statistics, on the other hand, are used to help make
inferences and draw conclusions. Statistical test including t-tests, variances, standard
deviations, and ANOVA is also used to test the hypothesized statements. All tests of
significance can be computed at α = 0.05. Given that this is a social science, setting alpha at
0.05 and a confidence level at 95% is ideal since it gives the best assumption should the
results be statistically significant.
Keywords: carparks, t-tests, ANOVA, car usage. school days and non-school days.
1. Describe and illustrate the relevant data selected from the full dataset.
Data was formatted and renamed by generating new codes to help in the analysis, (Jackson,
and Bazeley, 2019). Relevant data selected entailed data on date, carparks terminals and usage.
2. Are there differences between car park usage during school holidays and non-school
holidays?
o Select the appropriate data
The appropriate dataset for this question is the data on the date and car usage.
o Plot data using an appropriate chart

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Figure 1: Boxplot on the school and non-school days
In figure 1, the boxplot for the original dataset indicates that the weight data is not normally
distributed. However, the boxplot for the change dataset indicates that the weight data is
normally distributed. Hence, it is important to test if the change is statistically significant.
In addition, the results in figure 2 shows that the school days have the highest car usage; 55%
compared to non-school days; 45%. This implies that during school days, several terminals
are used, and this is probably be contributed to school busses ferrying students to school as
well.
Figure 2: Car usage vs school and non-school days

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Given that school days have the leading number of car usage, it is important to establish the
association between car usage and school and non-school days. According to the results of
the correlation coefficient of the scatterplot drawn, there is a positive correlation between car
park usage during school holidays and non-school holidays as indicated by positive slant on
the trendline, and the correlation coefficient is +0.141421, (Akoglu, 2018) meaning that the
car park usage during school holidays is higher than that of non-school holidays.
o Perform a t-test and discuss the results
Table 1: T-test results for the comparisons between car usage and school and non-school days
t-Test: Paired Two Sample for
Means
School_Holydays and
Non_Holidays Car Usage
Mean 3875.715068 1.753424658
Variance 5764262.615 0.185903274
Observations 1460 1460
Pearson Correlation -0.141519499
Hypothesized Mean Difference 0
Df 1459
t Stat 61.65223437
P(T<=t) one-tail 0.0005
t Critical one-tail 1.645898687
P(T<=t) two-tail 0.0005
t Critical two-tail 1.961591268
The results of the t-test above indicate that there is a positive statistically significant
relationship between the car park usage during school holidays and car park usage during
non-school holidays since the p-value is <0.05 with a mean difference of 3873.962.
o Discuss whether a t-test is appropriate for this data
Normally, a t-test is used while making comparisons of two proportions or means of a given
dataset, (Marshall, and Boggis, 2016). Therefore, this test is only considered useful when the
statically of interest is based on mean comparisons only after all the assumptions are met,
(Silberholz, Golden, Gupta, and Wang, 2019). Furthermore, t-tests are basically relevant in
situations where means and proportions are viewed to be the best measures to be considered.
Based on this, a t-test was not appropriate test for this dataset now that school and non-school
holidays may not have appropriate measure of means and proportions as compared to car
park usage. However, t-test was made possible by reformatting dataset, renaming, and coding
of new variable names to generate binary outcomes.

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3. Are there differences in the number of cars using different terminal carparks?
Table 2: Proportions of the Car Terminals
Carparks Freq %
NE 365 25%
SE 365 25%
SE 365 25%
SW 365 25%
Total 1460 100%
According to the selected datasets, the proportions of the number of cars using different
terminal carparks are the same; 25% each.
o Select the appropriate data
The appropriate dataset for this question is the data on terminals and car usage.
o Plot data using an appropriate chart
Figure 3: Average car usage by terminals
The findings in Figure 3 confirms that SW and NE terminals have the highest average when it
comes to car usage. In addition, SE and S have the lowest average on car usage by terminal.
As a result of the above findings, it is prudent to find out if there is association between car
usage and terminals. After drawing a scatterplot, the correlation coefficient show that there is
a positive correlation between car park usage and different terminal carparks as shown by the
positive slant on the trendline, and the correlation coefficient is +0.01 (Akoglu, 2018)
implying that the car park usage varies different terminal carparks.

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o Perform an ANOVA
Table 3: The comparison of mean differences for the car usage by terminals
Carparks Mean Std. Deviation
Northeast 5969.01 1332.049
Southeast 2066.21 459.244
South 1343.75 307.967
Southwest 6123.89 1360.359
Total 3875.72 2400.888
According to the Table 3 above, there is a mean difference in the number of cars using
different terminal carparks with the highest terminal being Southwest followed by Northeast
and the lowest terminal with car usage is South.
Table 4: ANOVA Table
Sum of
Squares
df Mean Square F Sig.
Total *
Carparks
Between Groups (Combined) 6979291527.2
60 3 2326430509.0
87 2367.458 .000
Within Groups 1430767628.2
08 1456 982670.074
Total 8410059155.4
68 1459
The ANOVA table indicates that there are statistically significant mean differences when it
comes to car usage by terminals since the p-value is <0.05, (Caban, et, al, 2019).
o Based on the ANOVA result, run t-tests to confirm differences
Table 5: T-tests for comparison with the ANOVA findings
t-Test: Paired Two Sample for Means
Carparks Usage
Mean 3875.715068 2.5
Variance 5764262.615 1.250857
Observations 1460 1460
Pearson Correlation -0.012010624
Hypothesized Mean Difference 0
df 1459
t Stat 61.64156897
P(T<=t) one-tail 0.0005
t Critical one-tail 1.645898687

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P(T<=t) two-tail 0.0005
t Critical two-tail 1.961591268
The results of the t-test confirm the findings in the ANOVA table since there is no any
statistical significant difference observed from the two tests and that p-value is less than 0.05
in both cases.
o Discuss whether ANOVA and t-tests are appropriate for this data
Basically, ANOVA tests compare mean differences within a given variable of interest and
this is the most appropriate test in this case. However, t-tests are basically relevant in
situations where means and proportions are viewed to be the best measures to be considered
hence a t-test was not appropriate test for this dataset now that car terminals may not have
appropriate measures of means and proportions as compared to the car park usage.

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References
Akoglu, H., 2018. User's guide to correlation coefficients. Turkish journal of emergency
medicine, 18(3), pp.91-93.
Caban, J., Droździel, P., Krzywonos, L., Rybicka, I., Šarkan, B. and Vrábel, J., 2019. Statistical
Analyses of Selected Maintenance Parameters of Vehicles of Road Transport Companies. Advances
in Science and Technology Research Journal, 13(1).
Hensher, D.A., 2017. Future bus transport contracts under a mobility as a service (MaaS) regime in
the digital age: Are they likely to change?. Transportation Research Part A: Policy and Practice, 98,
pp.86-96.
Jackson, K. and Bazeley, P., 2019. Qualitative data analysis with Nvivo. SAGE Publications Limited.
Marshall, E. and Boggis, E., 2016. The statistics tutor’s quick guide to commonly used
statistical tests. Statstutor Community Project.
Silberholz, J., Golden, B., Gupta, S. and Wang, X., 2019. Computational Comparison of
Metaheuristics. In Handbook of Metaheuristics (pp. 581-604). Springer, Cham.