After the main text of your article there is a section, usually headed References, containing bibliographic details of those publications that you have used for support in the main text. Each entry contains information about items such as author(s), date of publication, title, name of publication, and pages, given in at least sufficient detail to allow a reader to locate the work. In the main text you point to a particular reference with a cue or key. The cue+reference is a citation, but the cue or key is itself commonly called a citation, and I follow that custom here. There are many styles of citation(cue) and reference, and each journal makes its own choice. In many journals the ‘Instructions to Authors’ are vague about the citation and reference system to be used, and about formatting details for both, but you can infer these from examples in recent issues of the journal or get a reference program to use the journal format template if it offers one.

Author−date system

Here is an example of ‘author−date’ citations, sometimes called the Harvard system, in one style using space and ‘,’ as separators; ‘and’ to link two authors; ‘et al.’ for three or more authors; and multiple citations ordered by date:

Interpreting P values

Suppose you have just finished the measurements in a simple experiment to compare the abundance of weeds on 1-m2 plots sprayed either with a weedkiller in solution or with the same volume of water alone. You adopt the null hypothesis: that the weedkiller has no effect, and make a suitable test of this hypothesis (t-test or U-test, as appropriate) obtaining the result P = 0.04. That is to say that, if the hypothesis is true, then in a large number of similar trials one would expect to have got mean values at least as different as these were in about 4% of trials. The statistics stops at this point. So what next?

Anything further is a judgement by you and your readers. A convention has grown that for routine work of no special importance, if P ≤ 0.05 then, as practical people we think we will make fastest progress by concluding provisionally that the hypothesis is false while accepting that on average 1 in 20 of these provisional conclusions will be incorrect. But the value 0.05 is arbitrary.

• If we had only four digits on each hand it seems likely that the value would be 3 / 82 (= 0.047 in base 10) rather than 5 / 102 = 0.050.

• If the experiments are important and cannot be repeated for some reason (expense, no more material, unavailable equipment) then you may argue that you are going to reject the hypothesis provisionally with P as high as 0.1 (for example).

• If your life depends on avoiding wrongly rejecting the hypothesis then you might be inclined to require that P be ≪ 0.000 000 1.

• And if your life depends on avoiding wrongly rejecting the hypothesis yet there is a reward of 1 000 000 €/£/$ for correctly rejecting it, then you might be inclined to gamble at P < 0.000 1 or even P < 0.001. This is the sort of subconscious judgement you make every time you get into a car: the weighing of advantages and risks of an adverse outcome.

If you never quote a numerical value, never use units, never use graphs, and never write equations then you can safely skip this chapter.

Numerical values

The meaning and usage of ‘number’, ‘numeral’, ‘digit’, ‘value’, and ‘figure’ is not entirely clear.

• ‘Number’ has the broadest meaning. Illuminating accounts of the relationships between different sorts of number – integer, rational, irrational, imaginary, complex, transcendental – are given in Feynmann, Leighton, & Sands (1963) and in Sondheimer & Rogerson (1981). ‘Number’ is commonly used as well for counted items: ‘The number of sheep’, and in a general sense as in ‘the numbers show …’.

• ‘Value’ applies to variables, variates, parameters, and constants. (The proper expression of such a value is considered later in this chapter.) Each has a ‘value’ that comprises two components: a number and zero or more units, as in ‘24.6 mg’. In most places in this book I use ‘numerical value’ for the number part of the overall value to emphasise this point, but the simple ‘value’ is widely used for the numerical component alone.

• ‘Numeral’ is most often used for Roman quantities (as in dates such as MCCCCLVIII).

• ‘Digit’ is one of the single Arabic symbols ‘0’ … ‘9’ corresponding to human fingers or toes. Thus all real numbers can be expressed as a combination of Arabic digits with the symbols ‘+’, ‘–’, ‘.’ and perhaps ‘e’, or ‘E’, or ‘×’.

• ‘Figure’ is unclear, and has a different and specific use for illustrations, so is best kept for them alone.

Style books often contain lists of words that are commonly misspelled or misunderstood. Many of these words form pairs, some with opposite or similar-sounding partners, others with a similar (or identical: ‘rowing’ and ‘rowing’) spelling but different meanings. I will not repeat here, except for a few hardy perennials, what is amply and expertly explained in other works. Buy a dictionary of about 1000 A5 pages or so (and use it) and consult Gowers revised Greenbaum & Whitcut (1986) and Fowler revised Gowers (1968).

What follows is in two lists: misused common words, then often misunderstood more technical terms (usually with longer explanations). The technical terms are also listed without details in the first list.

Many well-educated people would consider a lot of the distinctions that follow in the first list to be mere pedant-fodder – they are – but some impede understanding, and these are certainly worth noting. Remember, too, that a characteristic of good scientific style is that it causes no distractions. Why annoy even a few of your readers when you could easily avoid doing so?

Most scientists work at the intersection of three processes (the hatched area in Figure 8.1): (1) specifying what question to ask of Nature; (2) expressing the question as a model (often mathematically even if vaguely as, for example, ‘Is there a relation between variables x and y?’); and (3) collecting and analysing data from a survey or experiment.

It is easy to ask the wrong question or to specify the wrong model. A plant physiologist observed that the kinetics of uptake of nitrate from solution by the roots of young barley plants resembled the kinetics of enzyme action and asked ‘What is the Michaelis constant of the enzyme?’ But this was a blind alley: the kinetics he observed were overwhelmingly the result of diffusion through the unstirred layer around the roots. Even when he had recognised this he specified an incorrect mathematical model, though he got close agreement to it with his data. Asking the right question and specifying it in the right form for testing are at the core of advance in understanding. They are specific to the particular problem though and are therefore outside the scope of this book. But the analysis of data (Figure 8.1), and the sorts of error we need to recognise, are within our scope.

As scientific meetings got bigger some attendees were not able to give a talk because there was not enough time. The scientific poster was invented to allow these disadvantaged persons to display their work.

Poster sessions have been common for only a few decades, so procedures and poster design techniques are still evolving. The poster is the least formal of the three main communication methods, and corralling viewers for it is competitive. It has the same relationship to the formal article as a painted miniature does to a Vermeer portrait. The advantage of presenting a poster (at anything other than a small meeting for specialists) is that you have an opportunity to interest people outside your special field. It will be clear then that visual presentation is the key to designing a poster that gets noticed. Of the three forms of presentation the poster, as the name implies, is the one that has the largest element of deliberate advertising in it. You need to attract attention. Of course the substance of what you present must be interesting too.

You will probably get an opportunity to talk about your work before you have to write about it. You use some of the same evidence in a talk as in an article, though prepared differently, mostly in visual form with tables and figures as ‘slides’. But speaking is a performance art in real time and needs different skills from writing. When writing you have time to reconsider and revise; when giving a talk you have only one chance to get it right. Detailed preparation and at least some practice are essential. Giving a successful talk that interests the audience can be a satisfying, if nerve jangling, experience. It is a rapid way to recognition amongst peers in your subject .

When writing or showing a poster you are competing for attention, but a talk is different. Your audience is captive. This advantage is also a responsibility: the members of your audience have come hoping to learn something and, perhaps, be entertained too. The stakes are high.