No abstract

When I started teaching real analysis to first-year college of education students, I thought that at least I ought to be consistent in what I said. When I told the students what a word meant, I thought they ought to hear the same story as they heard from my colleagues who were teaching other branches of mathematics. I even thought I ought to tell them something like what they would find in a consensus of the real analysis books they might look at. I knew that I ought not to use different meanings for the same word on different occasions. Alas . . .

It is a great pleasure to welcome the Mathematical Association to Cambridge, which since Newton has always been one of the most important homes of mathematics in this country. Cambridge is a traditional home of advanced and research mathematics, and it therefore gives me particular pleasure to have the honour of giving my Presidential Address to the Association in Cambridge on the topic of primary mathematics the foundation and growing point of the ‘mathematics for all’ on which our increasingly scientific and technological culture makes greater and greater demands.

No abstract

CorrespondenceWhen is a hypothesis null ? DEAR SIR, At a recent meeting of the Midland Branch, the topic of the null hypothesis arose in discussion. It was clear on that occasion that the concept causes trouble in teaching statistics in schools, and examiners' reports confirm this from time to time.Since the meeting I have looked at a number of books on statistics and it appears to me that one of the causes of confusion amongst teachers is the vagueness of textbooks (my own included) and, indeed, differences in the interpretation of the term. Has, I wonder, the usage of the phrase changed since its introduction by Fisher? For instance, Siegel writes in Nonparametric statistics: "The null hypothesis is a hypothesis of no differences. It is usually formulated for the express purpose of being rejected." This would appear to exclude, for instance, a hypothesis about the ratio of (i) two heads, (ii) a head and a tail, (iii) two tails, on spinning two coins a number of times.My own experience suggests that it is partly the unfamiliarity of the concept that causes trouble, but also the word null-which does not convey to the modern person the essence of what is meant. If I may suggest another word (for the classroom, rather than the examination question), it would be skittle: a skittle hypothesis is specially set up in order to be knocked down. But, seriously, would any statistician be prepared to say what is the modern interpretation of the phrase null hypothesis-in words, please, that the average sixth-former can understand?Yours faithfully,