I have long wanted to give vent to the thoughts in this talk and therefore I should start by saying ‘Thank you’ for providing me with an audience. Although the broad ideas have been in my mind for a long time, when it came to the point I had considerable difficulty in deciding just what to say and particularly in choosing a suitable title. I am far from satisfied with the somewhat pretentious name with which I have christened the infant, but it does I hope convey the thought that although I shall be talking about statistics—a fact which may or may not be an attraction and was therefore better not concealed—it will not be in a detailed technical sense. Indeed one of my first duties must be to disavow, not only any desire but any considerable ability to expound on statistics in detail.

I have reached the age in life when I begin to gain much comfort from the thought that what matters is not the facts you know but the way you think. It is a comforting thought when you have forgotten most of the facts.

In the following remarks I have attempted to approach my subject (necessarily in a somewhat random fashion) from a slightly different angle from that of Clarke's text-book. It must be understood that any opinions expressed are personal ones, and have no official authority.

All insurance has as its basic conception the pooling of risks, but whereas ordinary insurance is an individual contract, and steps are taken to ensure that the insured person is a reasonably healthy life when the policy is effected, social insurance brings under its cover the whole population of a country, or at any rate some more or less well-defined section of the population, and its concern is that the bad lives or heavy risks should gain protection equally with the healthy lives and lighter risks.

These notes are an attempt to answer a question which is often asked and might at first sight appear to be a simple one, viz. ‘What is the tax and estate duty position where a company effects an assurance on the life of an employee (or director) and what would be the position were the man to take out the policy himself, the company providing the premiums?’ The first point to settle is— ‘What is the purpose of the policy?’—and then, related to that, ‘What class of assurance is intended?’ Besides the tax and estate duty aspects there is the question of the respective rights in the disposal of the policy proceeds which may in some cases over-ride the financial considerations.

Where alternative procedures are available the relative financial effect can, in some instances, only be assessed by someone with an intimate knowledge of the accounts of the company and the affairs of the life to be assured. It is desirable in any case that the inquiries should be dealt with through the company's accountant. It might well be asked whether such matters are not entirely the province of the professional accountant. Whatever opinion may be held about this, the fact remains that life offices are to an increasing extent consulted on technical matters involving taxation and estate duty even by members of the legal and accountancy professions.

The concept of a power function in statistics often proves rather difficult to absorb. Johnson & Tetley (1950) develop the theory at some length, and Forster (1947) in an admirable article in this Journal provides some extra reading which is of necessity in rather general terms. It is hoped that the problem discussed in this article may prove a useful example of the application of the power concept to a particular problem and clarify the underlying theoretical ideas.

In any statistical test two kinds of error may arise. The first kind of error occurs when the hypothesis tested, usually called the null hypothesis, is rejected when it is in fact true. The second kind of error occurs when the null hypothesis is accepted when it is in fact false. The hypothesis with which the test is concerned will in general be denoted by Hi. In our case simple hypotheses will be considered which are concerned with the value of some parameter defining the probability law of the individuals.