John Croucher

Macquarie University · Department of Actuarial Studies and Business Analytics

Jury trials have long been a cornerstone of common law and one of the essential liberties of a free country. There are times when the accused can elect for their case to be heard by a single judge or a jury and they will naturally make the decision that they feel will maximise their chance of an acquittal. In a non-jury trial, a judge has the respo...

The onset of COVID-19, along with its various mutations, has played havoc with many activities, not the least of which is education. For the majority of 2020 and 2021 in Australia, much of the teaching in both schools and universities was undertaken online, leading to a re-think of how learning and teaching might look in the future. This paper exam...

This is the standard textbook in PNG in their MBA program. It is written specifically for the students in PNG, using local currency, examples and exercises.

How statistics and quantitative methods can be used in medical research.

1. ABSTRACT The assertion that “We Are All Narcissists” explores the pervasive nature of narcissistic traits within contemporary society, examining their roots in psychological, cultural, and technological influences. Narcissism, characterised by grandiosity, a need for admiration, and a lack of empathy, is analysed through psychological constructs...

This paper identifies the ripple effects of house prices of China’s key three regions including first tier 5 cities (LOG(ALL5)), second tier top 8 cities (LOG(ALL8)) and second tier 16 cities (LOG(ALL16)) for 2010Q1 to 2019Q2 periods, together with the impulses from fixed assets investments toward China three key regions’ house prices covering peri...

We examine information and volatility linkages among NATIONAL, NSW, VIC and QLD housing markets in Australia using the novel rational expectations framework of financial contagion and a combination of robust econometric methods including the Generalised Method of Moments (GMM), correlations and Generalised Impulse Response Method, etc. We find info...

Objective: The purpose of this paper is to highlight the difficulties encountered by both the patient and doctor when interpreting the results of clinical tests. Design: It is well documented that patients who have been given the news of a diagnostic test that suggests a very poor or even terminal diagnosis become quite emotional. A common question...

This article identifies the main drivers and assesses housing bubbles in China’s first-tier and second-tier main 13 cities’ aggregated house prices for 2007Q2 through 2018Q4. The empirical analysis is conducted using robust econometric multiple frameworks, undertaken using the forms of OLS and VECM techniques. The outcomes suggest that house prices...

This article considers issues facing management and their decision processes to deal with them effectively. The first develops an optimal strategy for leasing equipment in which there are three available management options, the criterion being to minimize the total cost of use. The first option is to stay with the status quo, the second to lease fa...

The use of real contexts and history in the teaching of statistical principles holds much attraction in the classroom. This is especially so when the examples used are in situations that are quite out of the ordinary but can lead to further investigation by the students. Previous instances of these have been used with great effect with sporting dat...

The mid-nineteenth century was a highpoint of empire building, and reliable navigation across the oceans was crucial. While the effects of magnetic variation and deviation on compasses were well known by 1800, iron ships brought with them an even bigger challenge. The nautical world divided between ‘applied’ and ‘theoretical’ approaches to addressi...

Purpose This paper aims to explore principal drivers affecting prices in the Australian housing market, aiming to detect the presence of housing bubbles within it. The data set analyzed covers the past two decades, thereby including the period of the most recent housing boom between 2012 and 2015. Design/methodology/approach The paper describes...

Objective: The purpose of this paper is to highlight and solve an issue of importance that affects the well-being and confidence of cancer sufferers world-wide. Design: It is well documented that there may be a relatively high risk, once a patient achieves remission, of the cancer returning and this is a question in the forefront of every patient's...

Survival rates in cancer

Class examples for a standard introductory statistics course usually involve a variety of applications. In this paper, we consider the teaching of statistics using forensic science and the law, an area that holds some fascination with many audiences.

The probability of winning a game of tennis from scratch in terms of the probability of winning an individual point has been well documented. However, once the game is underway this probability rapidly changes. This paper presents formulas for the conditional probabilities of a player winning a game from any scoreline. Each point is ranked in order...

This paper is concerned with 'Olympic lifting', in which the two types of lift are: Snatch: The contestant picks up the weight in one continuous movement and lifts it as high as possible. Clean and Jerk: The weight is lifted from the floor, rested against the chest and then lifted as high as possible upon the call from the referee. In early weightl...

Mrs Janet Taylor, ‘authoress and instructress in navigation’, received a Civil List pension in 1860, a modest amount of just £50. This was in sharp contrast to that awarded to another scientific writer, Mrs Mary Somerville, who received a pension of £200 in 1835, increased to £300 two years later. This article considers the nature of the accomplish...

Vanished from history is the story of the ‘Mariner's Calculator’, invented and patented at the Great Seal Patent Office, London, by Mrs Janet Taylor, in 1834. Dismissed by the Admiralty, it had no commercial future and only one instrument is known to remain in existence. The article traces the invention from its inception and provides relevant biog...

This paper looks at some of the techniques that have been used to make the lecture theatre and classroom more effective and provides details of an astonishing Australian success story. There have been questions raised among academics about the usefulness of the traditional lecture approach that has been used for many years at universities and other...

The Wimbledon tennis tournament began in 1977 when the first men's singles final was played. In 1879 men's doubles were introduced and 1884 saw the advent of women's singles. Using elementary probability theory we can compare that the players and expected number of sets each match lasted under the hypothesis that the players were of equal ability....

The study of statistics has a reputation among students for being difficult, irrelevant, boring and an unwanted compulsory intrusion into their studies—and that reputation is sometimes deserved. But it does not have to be that way. John Croucher used sport and gambling to transform his lecture theatre, and turned the teaching of statistics into an...

A special but common type of scenario is one in which a company has a promotion that is designed to make the customer purchase more of their product than they otherwise might. Although this can be aimed specifically at children, it really applies to all persons. The basic premise is that the company issues a "set" of different items or coupons and...

Basic statistical principles are often widely misunderstood (and often mistrusted) by many members of the public at large. It comes as no shock that this also applies to legal practitioners. If there is an ignorance of the intricacies of statistics by the judiciary and counsel, it is not surprising that erroneous conclusions based on the evidence h...

This article discusses some strategies for playing roulette, making use of the binomial distribution and Normal approximation.

This article derives a simple upper bound for the sample standard deviation that could be useful in guarding against gross errors of calculation.

One of the most popular and played sports worldwide is soccer, also known as ‘Association Football’, with intense interest every four years in the World Cup between the 32 qualifying teams. The game is played between two teams each of 11 players including a goalkeeper who is the only player allowed to handle the ball.

Simple probability calculations show some of thedangers of gambling.

One of the more interesting uses of mathematics and statistics is their application to everyday situations in assisting people to make informed choices about their courses of action. Nowhere is this more evident than in the application of basic mathematical principles to the range of gambling opportunities. Indeed, a new university statistics cours...

This paper analyses the results of a survey of 204 students taken at an Australian business college in which respondents were surveyed, confidentially, on their attitude toward various types of academic honesty. Variables included self-assessment of ability, justification of cheating, the temptation and peer pressure to cheat, being aware of and be...

This paper examines the performance of over 1000 students in the introductory statistics unit at Macquarie University in 1993. It was found that while the male students generally had a more advanced mathematics background than females, the females tended to have higher TER scores. Overall there was no difference between males and females in their f...

This paper examines the increasing problem of students who go to great lengths to avoid or delay taking an examination. There variety of techniques used such as feigning illness, but the modern student has a wider range of options available. The use of new technology has also made it easier for students to cheat in exams, although there is a seemin...

The distribution of the means of large samples drawn from populations is well known. Little, if any, mention is ever made of the distribution of the standard deviations of these samples. This paper examines this aspect and derives relevant formulae.

The well known recurrence formulae for means and standard deviations have been extended to encompass bivariate data. The effectiveness of this technique is enhanced with the aid of a microcomputer.

There is a growing trend to ask students to carry out their own project work in statistics. Often they choose examples from sport. This article shows the sort of analyses that might be done.

A problem of practical importance since it may be used to model a number of resource distribution problems is that of multi-item scheduling. In particular, the scenario here is one in which an institution must allocate its courses to various periods in a timetable so as to satisfy certain constraints. It is realized that it may not be possible to s...

In the 96 Anglo-Australian Test matches played from the end of world war II to the final test in the 1980 series there have been over 3000 dismissals of batsman for both countries. A breakdown reveals interesting difference between the type of dismissal and (a) quality of batsman, (b) location of match, (c) team which is batting. In particular, the...

Sub-optimal Branch & Bound algorithm developed (by Broadfoot) to solve a real world integer programming problem (posed by Croucher) that could not be solved in 9 hours of compute time on a dedicated VAX 11/780. A solution was obtained in 15 minutes compute time using this modified algorithm that stops within any desired margin from the optimum.

This paper develops an algorithm for a “shortest route” network problem in which it is desired to find the path which yields the shortest expected distance through the network. It is assumed that if a particular arc is chosen, then there is a finite probability that an adjacent arc will be traversed instead. Backward induction is used and appropria...

This paper considers a two sided resource allocation game in which both players initially have fixed resources which may be distributed over various targets. Their effectiveness depends on the manner of distribution and also on the strategy of the opponent, a natural payoff function for such a situation being used. The complete solution to the game...

Although there is a first year statistics unit at Macquarie having an annual enrolment of around 2500 students, it does not mean that statistics is a wildly popular subject. Indeed, the reality is that virtually every student enrolled only does so because it is compulsory for them to do it as a prerequisite for another subject. There has always bee...