Writing, logic and numbers (4)

Part of clear writing is the clear use of logic and numbers. Whenever we include numbers in our copy, we should clearly and logically define the context of the numbers. If we don’t provide enough context, our readers won’t understand what the numbers mean.

Example

For example, the author of an August 13 article about a revamp of an employee intranet provides insufficient context.

The first mention of numbers is in Paragraph 2:

“Within the first week of its launch in April last year, more than half of all public service employees in British Columbia flocked to their new, souped-up social intranet, @Work, logging 16,000 unique visits.”

We readers silently ask, “More than half of how many employees?”

To answer this question, we have to look ahead three paragraphs, to Paragraph 5, in which the author tells us that “[t]he intranet @Work serves 30,000 public service employees…”

With this information, we return to Paragraph 2, notice that 16,000 is indeed “more than half” of 30,000, and guess that, by “more than half,” the author means 16,000 of 30,000. If that guess is correct, then the author should have written something like this:

“Within the first week of its launch in April last year, 16,000 employees, more than half of the Province’s 30,000 employees, flocked…”

We readers wonder: Did the author assume that 16,000 unique visits represent 16,000 unique visitors? This assumption may be incorrect.

Later in Paragraph 2, the author writes:

“By month’s end, double the number of staff had entered the online fray…”

This is an implied comparison; during one period, the number of staff who “had entered the online fray” was double the number who had entered during an earlier period. But the author has not clearly defined either period.

She defines the more-recent period ambiguously: “by month’s end.” Does she mean the period from the day the new intranet was launched through the end of that calendar month (this period would equal one full month in duration only if the launch was on April 1)? Or does she mean one month’s duration, starting on the day of the launch (for example, starting on April 19 and ending on May 19)?

She does not define the earlier of the two periods. Does she mean the first week of the new intranet, as mentioned earlier in the paragraph? Or does she mean the last month of the old intranet? Or the entire life of the old intranet? Or something else?

Then we receive a clue:

“…leaving twice as many comments than [sic] they had [left] on the previous site.”

This implies that the earlier period was the entire life of the old intranet. But we readers cannot know that for sure without clearer language from the author.

The Takeaway: When your copy includes numbers, make sure you clearly and logically define the context of the numbers. For example, when comparing performance results, make sure you carefully define the periods you are comparing. If you don’t provide enough context, your readers won’t understand what the numbers mean. Your argument may seem sloppy or specious – undermining your credibility.

See disclaimer.

Writing, logic and numbers (3)

If we wish to keep our writing clear, we have to be careful when writing about numbers. To do that, we don’t need to acquire a deeper knowledge of mathematics; all we need to do is take a few moments to pay close attention to the numbers we are discussing.

This post is specifically about numbers in the form of ratios. A dictionary definition of ratio is:

“A relationship between two quantities, normally expressed as the quotient of one divided by the other: The ratio of 7 to 4 is written 7:4 or 7/4.”

When writing about ratios, the most important thing is to get the logic right; that is, correctly match the numbers to the words. Unfortunately, we sometimes fail to do this.

Example

For example, here is an excerpt from an article published this morning:

“Economics is well known as the Dismal Science. In my opinion it is more dismal than ever as the world economy is being looted, pillaged, and run into the ground by a group of frauds and hucksters. The intellectual cover for this heist is being provided by people who call themselves economists but are really propagandists. Perhaps in these times the best quantitative measure of health for a society is the ration of true economists to propagandists. I would estimate that it is more than 1 to a 1000 today reflecting the current dire circumstances.”

The word ration is probably a typographical error; the writer likely means ratio. Also, he does not need the word a before 1000. And, in formal writing such as this, he should use the form 1:1000 or 1/1000.

But, setting all those details aside, let’s take a look at his logic: He wishes to say that for every true economist there are one thousand propagandists. So, when he states the ratio as 1 to 1000, he has the right numbers in the right places. That is, his numbers match his words. Good.

However, he goes astray when he uses the comparative phrase more than. From the context of his remarks (he is complaining that there are too few true economists and too many propagandists), we can safely assume that he means to say that he would estimate that the ratio of true economists to propagandists is less than 1:1000.

To be clearer, he could have inverted the ratio, changing it

FROM

1 true economist to 1000 propagandists

TO

1000 propagandists to 1 true economist

Then he could have said

I would estimate that it is more than 1000:1 today, reflecting the current dire circumstances.

This form is easier for the reader to grasp.

The Takeaway: When setting up a ratio, be careful of three things: (1) Make sure that you are matching the right numbers with the right words. For example, if you say there are “two girls for every boy,” as in the 1963 hit song, “Surf City," performed by Jan and Dean (photo), the ratio of girls to boys is 2:1. (2) When you use comparative adjectives and phrases such as higher, more than, lower, and less than, remember that you are referring to the first number in the ratio. For example, if you say, “the ratio this summer is more than 2 to 1,” or “the ratio this summer is higher,” you are saying that there are now more than two girls for every boy. (3) If you decide to invert a ratio, make sure you invert both the numbers and the words. For example, if you want to state that the Surf City ratio is “one boy for every two girls,” the ratio of boys to girls is 1:2.

Writing, logic and numbers (2)

In a recent post, I discussed the need to pay close attention to logic when writing about numbers, especially when comparing numbers. In that post I explained, with examples, how to say that one number is larger than another.

Today’s post looks in the opposite direction: how to say that one number is smaller than another.

Example

An article about the 2008 presidential campaign carried the headline, “McCain’s Crowd Disturbingly Small, Ten Times Less Than Planned For.”

In the text of the story we learn that the crowd consisted of about 1,000 people and that campaign organizers had expected ten times that number of people. In other words, 10,000 were planned for and 1,000 showed up.

Therefore the headline, in effect, says that 1,000 is “Ten Times Less Than” 10,000. But this is illogical. Consider:

One times 10,000 = 10,000.
Ten times 10,000 = 100,000.
Therefore, ten times less than 10,000 = 10,000 minus 100,000 = negative 90,000.

The idea of negative people is absurd. It would be correct to say:

McCain’s Crowd Disturbingly Small, One-Tenth the Size Planned For.

It would also be correct to say:

McCain’s Crowd Disturbingly Small, 0.90 Times Less Than Planned For.

But for numbers less than 1, most people are more comfortable with percentages. So:

McCain’s Crowd Disturbingly Small, 90% Less Than Planned for.

The Takeaway: When writing, always use logic and numbers carefully. Remember that the phrase times less than and the phrase less than are not interchangeable.

Writing, logic and numbers (1)

Pay close attention to logic when writing about numbers, especially when comparing numbers. For example, keep in mind the difference between the phrase as much as and the phrase more than.

Example

Imagine two boxes (A and B), full of office supplies. Imagine that you and I know that A weighs 12 pounds. If I say to you, “B weighs as much as A,” or “B is as heavy as A,” I mean B weighs 12 pounds.

If I say, “B weighs four times as much as A,” or “B is four times as heavy as A,” I mean B weighs 48 pounds. That is, B is equivalent to four A’s. (4A = 4x12 pounds = 48 pounds)

But if I say “B weighs four times more than A,” or “B is four times heavier than A,” I mean B weighs not 48 pounds, but 60 pounds. In other words, I mean that B is equivalent to four A’s plus A. (4A + A = 4x12 pounds + 12 pounds = 60 pounds).

Most people learn as much as, more than and other basic concepts of arithmetic in elementary school or even before elementary school. One learning method involves the manipulation of Cuisenaire rods (shown in picture above).

For example, if a pupil lays down three white rods in a line, and then one white rod and one red rod in a line parallel to the first line, and then one light-green rod parallel to the other two lines, he can easily perceive that 3 is 3 times as much as 1, and 2 times more than 1.

Journalists and PR people

Unfortunately, most journalists and PR people did not learn these concepts (or have forgotten them). They confuse as much as and more than. For example, a press release issued last Thursday begins with this headline:

“MEPs cost taxpayers five times more than UK MPs”

The second paragraph of the text contains the numbers behind the headline:

“Open Europe’s comparison finds that the European Parliament costs taxpayers a staggering £1.8 million for each MEP per year. This is in contrast to the House of Commons, which costs taxpayers £364,000 for each member….”

Now, £1.8 million divided by £364,000 is approximately 5. But this means five times as much as, not “five times more than.”

An article in the Mail Online gets the concepts right:

“[A study concluded that] women talk almost three times as much as men, with the average woman chalking up 20,000 words in a day – 13,000 more than the average man.”

If you subtract 13,000 from 20,000, you get 7,000 (the men’s rate); 20,000 is almost three times 7,000.

The Takeaway: When writing about numbers, mind your logic. For example, remember that as much as and more than are not interchangeable. Look at the numbers you are comparing and then select the correct phrase to express the comparison.