Quantity Street, or why there aren’t any Green Triangles left
This statistic measures how different the actual tin of sweets was from the expected one, with a bigger statistic meaning more differences. If we took a random number from the appropriate chi-squared distribution, it would be this big or bigger about 60% of the time. In other words, assuming that each type of sweet is as common as the next, this distribution for a particular tin isn’t too unusual.
Now, as I mentioned, journalists have started to take an interest in this question, and naturally they’ve asked Nestle how the makeup of each tin is determined. A Nestle spokesperson told the i newspaper in 2018 that each tub is split roughly into thirds according to three categories of sweet, with five different types of chocolates, four different toffees and fudges, and only two types of fruit creme. This gives us an alternative hypothesis to test: that there really are more Strawberry Delights and Orange Cremes than the others, since they are the only ones in their category.
We can re-run the same test as before, but calculating our expected numbers of sweets based on this new theory:
Here, we’ve calculated the expected number of each sweet by allocating 91 / 3 = 30.33 sweets to each of the three categories, and then dividing these equally among the types in that category. The test statistic this time is even lower, at 6.15, suggesting this hypothesis could be a better fit. A random tin would have a test statistic as big as this about 80% of the time, assuming the hypothesis about equal numbers of each category is correct.
Purely in the interests of scholarly research, I popped round to the local supermarket to pick up a tub of Quality Street for myself. My slightly smaller tub had a total of 66 sweets, and I re-ran the previous tests using a combined sample from Stephen Hull’s tin and my tub.
If the sweets were equally distributed, we would get a test statistic of 9.54 or bigger about half of the time, and if they were distributed by category we would get a statistic of 12.55 or bigger about one time in four. These are both definitely plausible.
So, based on this sample size, we can’t conclude much: the distribution might be biased to include equal numbers of each category, or it might not be biased at all. This analysis could be taken further by considering factors like cost, weight or nutritional information of each sweet, which Nestle have also suggested are taken into account in their plans. Alternatively, the same chi-squared tests could tell us more if we bought more tins of sweets to give us a bigger sample size, but since I’ve got a dentist’s appointment in a few weeks, I think I’d better leave it there. I hope you have a happy and peaceful holiday period, and find all your favourite sweets in the tin.
Michael Scanlon
December 2021
Carbon Permits and Offsets
How can governments use the free market to take action on climate change? Cristian tells all about carbon permits and offsets.
Actuarial Mentoring Programme
This interview-style article provides an insightful overview of the Actuarial Mentoring Programme (AMP), its objectives, and the invaluable benefits it offers to both mentors and mentees. Their experiences shed light on the AMP’s effectiveness and highlights the opportunities it provides for professional growth and development.
April 2023 Exam Results
The April 2023 exam results have been published and APR student staff achieved an impressive 83% pass rate across all IFoA exams and 100% in all CAA exams taken. In this article, Moses Vaughan highlights our success this sitting.
Office vs home – what is the ideal working environment?
What is your ideal working environment? Cristian and Hannah discuss how and why their ways of working benefits them the most.
The Last Remaining Defined Benefit Schemes: A Deeper Look
In this article Asees explores the rise and decline of DB Pension Schemes, and considers the impact of this on secure retirement for future generations.
APR’s Favourite Excel Shortcuts
Love it or hate it, Microsoft Excel has been a central part of an actuary’s work for decades. However, its a tool that often isn’t used to its full potential; Heather Wallace’s list of our favourite Excel shortcuts should help rectify that!
Impacts of the new Personal Injury Guidelines in Ireland
In this article David O’Mahony examines how the new personal injury guidelines have been affecting the Irish General Insurance market and considers the likely future impacts of the changes.
Which soft skills are most valuable in actuarial work?
How important really are ‘Soft Skills’ in business? Gary Heslop takes a deep dive into how strong skills in areas such as Communication, Judgement and Management can make all the difference for high-performing Actuaries.
Basics of Property Direct and Facultative Insurance
The UK Commercial Property Insurance market is worth close to £7 billion and has been the subject of considerable disruption in the last few years. But how has this shaped the market? Jack Foley and Thomas Pycroft explain.
JFAR Risk Perspective 2022
In this article, a handful of APR’s newest recruits summarise the 2022 JFAR Risk Perspective and give an insight to the current risks high-quality actuarial work is facing, including topics such as sustainability and technology.