Articles in Teaching Statistics have approached the subject mainly as the mathematics of probability, or occasionally as a practical way of collecting information, such as questioning people in the rain! However, many years of teaching elementary statistics to social science students at university have convinced me that an essential early need is an understanding of statistical tables.

Many people meet these in their every-day work, yet only four out of forty in this year’s group admitted having met them at school. Statistical tables are a clear, concise way of presenting numerical information, but their use needs thought and practice. Most people need advice, but I have never seen any given in text-books.

For example, take the following table from Social Trends, 1976

Deaths from Accidents Occurring in the Home or Residential Accommodation
 

	1969			1974
Cause	Males	Females		Males		Females
Poisoning:by solid/liquid substance	178	266	231		296
by gases or vapours	167	215	88		47
Falls	1072	2820	1016		2502
Fires and flames	269	432	289		412
Other	602	486	462		404
Total	2288	4219	2086		3661

Source: Social Trends 1976

Most students when asked to write a summary of what is in such a table start pecking away at odd figures as they catch the eye. While it is impossible to give rules which will cover all tables, a few guidelines will make the process more methodical.

a. Before looking at the numbers, decide what the table is about and what sort of information we are likely to derive from it. Here, for example, are numbers of accidental deaths, but they exclude those at work or road casualties. They are given for men and women separately and for two years and are divided according to their cause. We should therefore be looking at differences between the two sexes, changes over time and variations in cause. This gives a framework within which to work.

b. It is usually best to look at the totals first. The main findings in this case are that more women die than men and that in each case deaths had decreased between the two years. The cause of death figures show the components of these differences.

c. Consider whether any figures which could be derived from the ones in the table would throw further light on the picture. For example, should we calculate totals for each cause for the two sexes combined, or some percentages. Notice that percentage change from year to year may be useful as may the percentage of total deaths attributable to each sex. Choosing meaningful ratios is important. However, avoid using percentages automatically. The actual fall in the number of poisonings by ‘gases and vapours’ is revealing. My experience is that students do not try to derive new figures unless instructed to do so.

After having examined the table in this way—not while still examining it—write down what you have discovered. Here a few dos and don’ts seem appropriate:

Do start by writing down what you are talking about. A useful introduction here might be "Figures for accidental deaths in the home given in Social Trends reveal that...

Do make your points methodically, stressing the important and omitting the trivial. For example, follow the order in (b) above.

Do pay attention to definitions, units and soon. The figures here are actual numbers, but often tables give thousands or millions. State these correctly.

Don’t guess reasons. Many students will write "This"—often without saying what ‘this’ is—"is because women spend more time in the home than men do". In fact, a high proportion of these deaths were of the elderly and the fact that women live longer than men on average is an important contributory cause, but there is nothing in the present figures which tells us this. If you want to explain or hypothesize, start "Possibly this is because".

These are, of course, guidelines, not rules. Each table presents different problems and the ability to extract and explain the information contained can only come with practice. Reading examples of good comment on tables is a help. The publications of the Office of Population Censuses and Surveys maintain a high standard in this respect.

A particular problem arises when figures are given in the form of percentages. In the General Household Survey, for example, most tables are given with either the rows or columns totalling 100%, the direction in which the percentages run being shown by the position of the percent sign. For example, the General Household Survey, 1977, slightly abridged, offers:

Occupation of Head of Household by Type of Accommodation

From such figures, we can discover such things as "the proportion of non-manual workers who live in detached or semi-detached houses is higher than that of other workers". That is, we can say what sort of accommodation each type of worker lives in, but we cannot say what type of worker lives in each sort of accommodation. However, as the bases from which the percentages were obtained are given, we can, roughly, invert the table as follows:

Type of Accommodation According to Occupation of Head of Household
 

	Detached or semi-detached (%)	Terrace (%)	Flat or other (%)
Non-manual	48	28	38
Skilled or semi-skilled manual	8	63	52
Unskilled manual	4	9	10
Base (=100%)	5508	3186	2631

(Note: You may get slightly different results according to the degree of accuracy used at each stage).

We can now see that almost two-thirds of terrace houses are lived in by skilled or semi-skilled manual workers and that only a small proportion of any type of accommodation is occupied by households whose heads are unskilled manual workers.

The General Household Survey, in common with most surveys, only gives such tables in one form. The other can be derived from it easily enough, but few people will do this unless it is suggested to them and I have not seen it done in a text-book. Nevertheless, the ability to make such a conversion is important, as is that of realising that percentages in one direction mean something different from those in the other. Furthermore, it is important that students can write down clearly which meaning they have in mind. If someone writes "Few skilled or semi-skilled workers live in flats", they may mean a small percentage of them. On the other hand, more skilled or semi-skilled workers live in flats than do other types of worker. The statement can be read as implying the reverse of this.

Statistical tables abound. They are convenient ways of presenting large quantities of numerical information and the amount that can be extracted from them with care, thought and experience is often surprisingly large. Surely anyone with some statistical training should be able to handle figures in this form and to write down their meaning clearly. If we start with analyses like those above, we shall not only be equipping our students to use fully the facts available to them. We shall be striking a, blow for the clear and precise use of language and we shall be making them think in one of those not uncommon situations where we can offer guidance but not firm rules in the handling of numbers.

University of Exeter

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