If anyone's interested, I decided to take on board the suggestion of
@GooseOnTheLoose and try to answer some of the questions raised in this thread empirically. Buckle up, folks, because it's about to get statistical in here! (Don't say I didn't warn you...)
In terms of the method I decided to use; I decided to go with a methodology something along the lines of the following:
- I decided to look at the parks index on queue-times.com as my source for queue time data: https://queue-times.com/parks
- From there, I decided to scan every listed park from every European country on the site and take its top 10 queue times for both "average queue time" and "average maximum queue time". Where the park did not have 10 queue times, I just took all of them.
- To reflect the current permanent offering, I tried to exclude things that are "Archived" on the site or that I know to not currently be permanently extant at the park in some capacity. This includes seasonal Halloween/Christmas attractions and past attractions. The one exception to this is where everything in the park was archived and/or some things that I know to be operating were considered "Archived" and there was no obvious non-archived alternative average (for example, Helix was strangely "Archived" at Liseberg even though I know very well that it's still operating).
This methodology brought out the following numbers of parks and attractions for the following European countries:
- Austria (1 park/10 queue times)
- Belgium (4 parks/40 queue times)
- Denmark (3 parks/30 queue times)
- France (9 parks/80 queue times)
- Germany (7 parks/70 queue times)
- Italy (1 park/10 queue times)
- Netherlands (4 parks/36 queue times)
- Poland (1 park/10 queue times)
- Spain (4 parks/40 queue times)
- Sweden (2 parks/20 queue times)
- United Kingdom (6 parks/60 queue times)
And in terms of operators, the numbers were as follows:
- Compagnie des Alpes (7 parks/70 queue times)
- Disney (3 parks/21 queue times)
- Looping Group (1 park/6 queue times)
- Mack Rides (2 parks/20 queue times)
- Merlin (8 parks/80 queue times)
- Other (13 parks/129 queue times)
- Parques Reunidos (4 parks/40 queue times)
- Plopsa (2 parks/20 queue times)
- PortAventura World (2 parks/20 queue times)
I would also like to raise a few caveats about this method:
- Of course, these queue times are advertised, and derived from park apps and such. Whether actual queue times reflect these at all times is unknown (I'd say it's unlikely, in all honesty, and accuracy varies between parks/operators).
- This method also only encompasses the scope of parks covered by queue-times.com in a given country. This means that some countries will have a greater sample size than others.
- The average and maximum queue times are all time averages, as this is the only level of granularity at which queue-times.com shows queue time averages.
- Parks of course have different operating calendars, which may also affect the averages shown.
- As stated above, I was unsure about which "Archived" attractions to exclude and which to keep in some cases. I did a scan of the park website where I was unsure, and if I couldn't find it there, I excluded it. This is of course prone to human error, so do bear this in mind.
Now we've got the methodology and caveats out of the way, let's dive into some data!
So, the first question this thread initially posed is;
do UK parks have longer queue times than those of other European countries?
To answer this question at a basic level, we could do some boxplots and look at the means (calculated average) and medians (middle value) for each European country in terms of both average and maximum queue times. In terms of
average queue time, the boxplot and figures per country are as follows (for clarity, the boxplot shows the complete spread of queue times for a country, with the dots denoting outliers that fall outside of the "typical" range, the whiskers denoting the range of the non-anomalous data, the coloured box denoting the interquartile range between the 25th and 75th percentiles, and the line in the middle denoting the median/50th percentile/central value):
Country | Mean (1dp) | Median (1dp) |
Austria | 13.5 | 12.5 |
Belgium | 18.2 | 17.5 |
Denmark | 12.6 | 12.5 |
France | 24.9 | 23 |
Germany | 19.6 | 20 |
Italy | 22.1 | 19 |
Netherlands | 20.9 | 21 |
Poland | 22.7 | 16 |
Spain | 28.9 | 27.5 |
Sweden | 20.2 | 18 |
United Kingdom | 27.3 | 26 |
And in terms of
average maximum queue time, the boxplot and figures per country are as follows:
Country | Mean (1dp) | Median (1dp) |
Austria | 19.1 | 18.5 |
Belgium | 34.6 | 30.5 |
Denmark | 23.8 | 23 |
France | 41.5 | 40.5 |
Germany | 30.6 | 31 |
Italy | 37.2 | 33.5 |
Netherlands | 35 | 31.5 |
Poland | 30.4 | 26.5 |
Spain | 44.1 | 41.5 |
Sweden | 33.5 | 30 |
United Kingdom | 42.6 | 42 |
Based on this, I think it's probably fair to conclude that the United Kingdom is
one of the countries with the highest average queue times in Europe. Out of the 11 countries studied, the UK had the second highest mean and median average queue time behind only Spain, the second highest mean average maximum queue time behind only Spain, and the highest median average maximum queue time. If you look at the boxplots, we can see that the UK's upper quartile is not quite as high as France's or Spain's, and interestingly roughly level with or slightly lower than that of the Netherlands, but that lower quartile and minimum value is stubbornly higher than that of any of those countries, perhaps indicating generally longer queue times across the board.
But we don't want to stop there, do we? To truly empirically conclude whether the UK has longer average queue times than the rest of Europe, we need to determine if the difference between the UK and the rest of Europe is
statistically significant. In order to do this, we can wheel out a good old tool from the statistical toolbox known as
hypothesis testing! In essence, what you do in hypothesis testing is declare a null hypothesis (a "status quo" that you're trying to disprove) and an alternative hypothesis (the thing you're trying to prove), and sort of prove your alternative hypothesis by trying to reject the null. It's kind of a "proof by contradiction" sort of affair. In terms of how we determine whether the outcome is statistically significant; statistical significance is a slightly hand-wavey concept, but we determine the degree of statistical significance by calculating the test statistic and p-value (the probability of attaining a test statistic at least as extreme as that attained if the null hypothesis is true). The general gold standard of statistical significance is a p-value of 0.05 or lower, but this can vary (some might go for, say, 0.01 or lower if you want strong confidence). I'll go with a critical p-value of 0.05 here, for ease.
So how am I going to work out if the UK has higher queue times than the rest of Europe to a statistically significant degree? Well, I'm going to carry out a
two-sample z-test, with the United Kingdom queue times put into one sample and those of the rest of Europe amalgamated in the other. My hypotheses are as follows:
- Null hypothesis (H0): Mean average queue time in the UK is less than or equal to average queue time in the rest of Europe
- Alternative hypothesis (H1): Mean average queue time in the UK is greater than average queue time in the rest of Europe (As we're only interested in seeing whether the UK is higher, we perform a right-tailed test here)
My critical p-value to reject the null hypothesis is
0.05 or lower, and according to statistical tables, the critical region for the test statistic is
1.64 or higher in order to attain that. The test statistic must fall within the critical region if I want to reject the null hypothesis and prove our hypothesis that UK queue times are longer than those of the rest of Europe.
When performing a two-sample z-test on the average queue time data we have, the outcome is as follows:
Metric | Value |
Test Statistic (Z-Score) | 3.75 (2dp) |
p-value | 0.000086 (2sf) |
Retain or Reject H0? | Reject |
And when replicating the same process upon the average maximum queue time data we have, the outcome is as follows:
Metric | Value |
Test Statistic (Z-Score) | 2.98 (2dp) |
p-value | 0.0014 (2sf) |
Retain or Reject H0? | Reject |
Based on the fact that the null hypothesis was rejected in both tests, we can safely conclude that UK queue times are higher than those in the rest of Europe to a statistically significant degree on average. The difference is more statistically significant for average queue time than for average maximum queue time, but nonetheless, both returned p-values of below 0.01, providing very strong evidence in favour of rejecting the null hypothesis in favour of the alternative.
So I think we can conclude that the UK does indeed have some of the longest queue times in Europe on average. With descriptive statistics and boxplots showing that its average and maximum queue times put it right up there as one of the longest queue time countries on average (only narrowly beaten by Spain in most metrics and even on top in terms of median average maximum queue time) and our hypothesis tests proving that queue times in the UK are longer than those of the rest of Europe on average to a statistically significant extent, it seems as though the initial hypothesis of
@Bowser when creating this thread was correct.
But that is not the only question I'm answering today. I noticed that conversation drifted to our good old friends Merlin as the thread progressed, so I'm also going to try and answer a different question;
do Merlin parks in Europe have longer queue times than those of other European operators?
Let's repeat a similar process to what we did above, but for operators rather than countries.
At a basic level, we can once again look at boxplots, means and medians. For average queue time, the boxplots and figures by operator are as follows:
Operator | Mean (1dp) | Median (1dp) |
Compagnie des Alpes | 22.5 | 21 |
Disney | 34.9 | 34 |
Looping Group | 11.7 | 10 |
Mack Rides | 18.3 | 20 |
Merlin | 26.3 | 25 |
Other | 18.1 | 17 |
Parques Reunidos | 20.9 | 19 |
Plopsa | 15.3 | 14.5 |
PortAventura World | 33.7 | 33.5 |
And for average maximum queue time, the boxplots and figures by operator are as follows:
Operator | Mean (1dp) | Median (1dp) |
Compagnie des Alpes | 41.7 | 42 |
Disney | 57.7 | 54 |
Looping Group | 19.2 | 17.5 |
Mack Rides | 28.6 | 31.5 |
Merlin | 42.3 | 41.5 |
Other | 28.2 | 27 |
Parques Reunidos | 35.8 | 34 |
Plopsa | 21.3 | 22 |
PortAventura World | 49.1 | 50.5 |
So based on this, I think we can conclude that Merlin is potentially
on the higher end of European operators in terms of average queue times, but definitely not the highest of the 9 operators tested, with Disney and PortAventura World both quite noticeably higher in terms of both average queue time and average maximum queue time than Merlin. In terms of average maximum queue time, Compagnie des Alpes also roughly matches Merlin, with Merlin's mean being fractionally higher than CdA's, but CdA's median being fractionally higher than Merlin's. If you look at the boxplots for maximum queue time, you can see that Disney is notably above Merlin, with Disney's lower quartile being on par with Merlin's upper quartile, and PortAventura World is also notably higher than Merlin, albeit much more variable with a slightly lower lower whisker. The interquartile ranges of CdA and Merlin are actually very similar, albeit CdA exhibits more variation beyond the interquartile range area, with a higher upper whisker and a lower lower whisker.
Now let's try and prove if Merlin's queue times are higher than those of other European operators to a statistically significant degree. As I did before, I'm going to perform a
two-sample z-test to determine this, with Merlin parks being in one sample and the parks of all other European operators being amalgamated within the other. I declare my hypotheses as the following:
- Null hypothesis (H0): Mean average queue time in European Merlin parks is less than or equal to average queue time in the European parks of other operators
- Alternative hypothesis (H1): Mean average queue time in European Merlin parks is greater than average queue time in the European parks of other operators (As we're only interested in seeing whether Merlin is higher, we perform a right-tailed test here)
Similarly to above, I'm going to declare the critical p-value for rejection of the null hypothesis as
0.05 or lower, and the critical test statistic region for rejection of the null hypothesis as
1.64 or higher.
When performing a two-sample z-test on the average queue time data we have, the outcome is as follows:
Metric | Value |
Test Statistic (Z-Score) | 3.81 (2dp) |
p-value | 0.000068 (2sf) |
Retain or Reject H0? | Reject |
And when replicating the same process upon the average maximum queue time data we have, the outcome is as follows:
Metric | Value |
Test Statistic (Z-Score) | 3.84 (2dp) |
p-value | 0.000060 (2sf) |
Retain or Reject H0? | Reject |
Based on the rejection of the null hypothesis in both tests, we can conclude that average queue times in European Merlin parks are higher than those in the European parks of other operators to a statistically significant degree. With a p-value below 0.0001 in both cases, this suggests that there is extremely strong evidence in favour of rejecting the null hypothesis in favour of the alternative hypothesis.
So based on all of that, I think we can safely conclude that Merlin is on the higher end of European operators in terms of average queue time length. The boxplots and descriptive statistics showed that they were beaten only by Disney and PortAventura World in terms of both average and maximum queue time among the 9 operators, albeit Compagnie des Alpes did roughly match them in terms of average maximum queue time.
Let's now wrap up and summarise our findings...
So, in conclusion...
In conclusion, these experiments found that the hypotheses behind the creation of and discussion within this thread were true, for the most part.
When looking at whether the UK has higher average queue times than other European countries, boxplots and descriptive statistics showed that the UK is right up there for queue time length, only being narrowly beaten by Spain in most metrics. The hypothesis tests also provided statistically significant evidence to suggest that UK queue times are higher than those of parks in other European countries on average.
When looking at whether European Merlin parks have higher average queue times than those of European parks of other operators, boxplots and descriptive statistics showed that Merlin are on the higher end of European operators for queue time length, albeit not quite the very highest (Disney takes that particular crown). Hypothesis tests provided statistically significant evidence to suggest that Merlin queue times are higher than those of other European operators on average.
Thanks for reading; I hope you found my analysis interesting! Just for transparency, here is the spreadsheet with all of the queue times used in it (this includes queue times from other continents, for some more global queue time analysis I'm pondering doing):
From: https://docs.google.com/spreadsheets/d/1Bd9XJM_8LDhWSUePkIjbKMBtPtvoW8DLv80apQvsQtk/edit?usp=sharing
TL;DR: I decided to empirically test out some of the hypotheses declared in this thread. When I tested out whether UK parks have higher queue times than parks in other European countries, boxplots and descriptive analytics found that the UK was right up there for queue time length, being only narrowly beaten by Spain in most metrics and even topping the charts in terms of median average maximum queue time. Hypothesis testing unearthed statistically significant evidence to suggest that UK parks have longer queues than those of other European countries on average. When I tested out whether European Merlin parks have higher queue times than European parks operated by other operators, boxplots and descriptive statistics found that Merlin was on the higher end of European operators for queue length on average, albeit Disney and PortAventura World came out higher. Hypothesis testing unearthed statistically significant evidence to suggest that European Merlin parks have longer queues than those of other European operators on average.