I am in the process of writing an introductory statistics book for market researchers. This post and some of the following posts are taken from that book, in an attempt to field test the style, approach, and depth I am employing. All comments welcome.
My recommendation is that most numbers in presentations and reports should be presented as 2 or 3 significant digits. I feel that the issue of significant digits is more important than the more frequently discussed issue of decimal places.
In a number, the significant digits are those that carry the key details. If a bank robber steals $56 million, the 5 and the 6 are the significant digits – and the million gives the scale of the number. If we say that PI is 3.1416 then we are showing it to four decimal places and five significant digits.
Table 1 shows the number of internet users in five key, original, members of the EU; showing the raw numbers and the same numbers using two significant digits.
Column B shows the estimates in the format they were downloaded from the InternetWorldStats website. These raw numbers contain 7 or 8 digits, and commas are used to help make the numbers more readable. These values, presumably, represent the best estimates for each country, but they require an active act to read and interpret. By contrast, Column C shows the numbers using just two significant digits.
The use of two significant digits in Column C has two advantages, when compared with Column B.
- It is much easier see the relationships in Column C, compared with Column B. For example, in Column C, it is easy to see that Italy has just over twice as many internet users as the Netherlands, and about half as many as Germany. This information is harder to see at a glance in Column B.
- Almost all numbers have errors in them, and they tend to relate to a specific moment in time. Statisticians talk of spurious accuracy when too many digits are displayed, for example when saying 37.67% plus or minus 10%. If we use all of the digits, as in Column B, then we are implying (to most readers) that all the digits are equally accurate. By using just the two most significant digits, Column C gives a message to the reader that these are approximations.
Methods of utilising 2 or 3 significant digits
Here are some tips for different situations:
- Percentages. Only use round numbers, e.g. 36% rather than 35.67%.
- Salaries. Round them to the nearest thousands, for example $136K, rather than $135,670.
- 7-point rating scales. One decimal place, for example 4.6 rather than 4.634.
- Sales. Round the numbers to the nearest thousands, million, or billions. For example, numbers like 36,785 and 76,230 could be expressed as 37K and 76K (two significant digits). However, 36,785, 76,230 and 148, 102 would need to be shown as 37K, 76K, and 148K (three significant digits).
Ralph Waldo Emmerson said “A foolish consistency is the hobgoblin of small minds”, and it would be foolish to think that every set of numbers can be shown to two or three significant digits. Background documents, notes, and tables are often better with more digits.
However, in most cases, and in most presentations and reports, two or three significant digits are going to help the audience/reader understand the message better than showering them with digits.