In Chapter 9 we discussed point estimation for a parameter or a vector of parameters. In Chapters 10 and 11, on confidence intervals and hypothesis testing, we needed the idea of the standard error of an estimator.

A common problem in statistics is to compare groups. Does a new drug work better at reducing the time of hospitalization from COVID? Which pop-up ad generates a higher click-rate? Which type of metal – aluminum, brass, or stainless steel – will produce the most reliable product? Usually, the question involves either the mean response or the proportion of responses.

The problem of statistical inference can be described as follows. There is a population and we would like to know certain aspects of the units that make up the population. For example, we might want to know what proportion have a certain property, or what the mean value (of some measure) of all units in the population is. The population is too large to sample in its entirety, so we rely on information from a sample taken from the population.

The Roman conquests in the western Mediterranean saw the arrival of Roman coins, but in the east the local coinages at first remained and were manipulated.

In Chapter 14 we studied multiple regression and polynomial regression and how these techniques can be used to determine the relationship between an outcome $y$ and several predictor variables $x_1,x_2,,\dots ,x_p$.

In Chapter 3 we learned about the fundamental ideas of probability, and in Chapter 4 we generalized the notion of probability from working with sets to working with random variables and distributions. In many ways, random variables and their associated distributions can simplify probability calculations and, appropriately applied, are useful models for real-world phenomena.

In this chapter, we look at the analytic studies that are our main tools for identifying the causes of disease and evaluating health interventions. Unlike descriptive epidemiology, analytic studies involve planned comparisons between people with and without disease, or between people with and without exposures thought to cause (or prevent) disease. They try to answer the questions, ‘Why do some people develop disease?’ and ‘How strong is the association between exposure and outcome?’. This group of studies includes the intervention, cohort and case–control studies that you met briefly in Chapter 1. Together, descriptive and analytic epidemiology provide information for all stages of health planning, from the identification of problems and their causes to the design, funding and implementation of public health solutions and the evaluation of whether these solutions really work and are cost-effective in practice.

This chapter discusses the general principles relating to the assessment of compensation for loss resulting from a civil wrong. Since courts and legislatures often lay down legal rules for a particular area of law, the assessment of compensation differs between areas. This is why Part 2 contains separate chapters for contract, tort, the Australian Consumer Law and equity. However, there are several commonalities between the areas, in particular, contract and tort. This chapter discusses the rules that are common to at least contract and tort. Most of them also apply in equity and under the Australian Consumer Law. Deviations from those rules in equity or under the Australian Consumer Law are discussed in the relevant chapters. This chapter also provides a brief introduction to those matters that differ between contract and tort. Comprehensive treatment is given to the date of assessment; even though there are significant differences between the causes of actions, there has been considerable convergence.

The Australian Consumer Law (‘ACL’) is the national consumer law and applies across Australia. It came into force on 1 January 2011. At the same time, the Trade Practices Act 1974 (Cth) changed its name to the Competition and Consumer Act 2010 (Cth). Schedule 2 of that Act now contains the ACL. The ACL replaced a number of consumer protection provisions in federal, state and territory laws. It was enacted with the cooperation of the federal, state and territory governments. This cooperation was necessary since the Commonwealth lacks the power to comprehensively legislate on consumer law.

The ACL applies as a federal law, or as a law of the relevant state or territory, or both. It is not necessary here to go into all the details of the demarcation since the same body of law generally applies. Broadly, the ACL applies as a law of the Commonwealth to the conduct of corporations and certain natural persons, and applies as a law of a state or territory to the conduct of corporate and natural persons with a connection to the relevant jurisdiction. The application of the ACL as a federal law and the application of the ACL as a state or territory law are not mutually exclusive (where there is no conflict).

This chapter is concerned with court orders made prior to final judgment, and with enforcement of final judgments. These are matters of civil procedure. They do not deal with final determinations of rights and are not remedies in the technical sense. Rather, they protect the ability of the court to award remedies.

First, if there is a dispute over certain subject matter, it is important that the subject matter of the dispute be maintained until the court can adjudicate the dispute. This is where interlocutory remedies and pre-judgment remedies are relevant. These remedies are awarded before the court makes a final determination of the proceedings and are generally intended to maintain the status quo pending the decision. Such remedies include interlocutory injunctions, which restrain or compel a person to do a particular thing. There are other pre-judgment remedies, such as freezing orders and search orders, which prevent the defendant from removing property from the jurisdiction or from destroying evidence before proceedings can be brought. These ensure that proceedings are not nugatory.

Secondly, after final judgment has been handed down, there must be a means of ensuring that the judgment debtor does what the court has ordered; otherwise the judgment lacks ‘teeth’. Courts have coercive mechanisms which ensure that a defendant complies with an order to pay damages or an order of specific relief.