Danger! Numbers in the Newsroom!

Compiled by Sarah Cohen, IRE and NICAR training director

This set of handouts has been used in various forms for IRE conferences and in-house training at Newsday, the St. Petersburg Times and The Tampa Tribune.

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Quotes about reporters and numbers

"We do not expect reporters to be mathematical geniuses. But we do expect them to sidestep their mind-numbing fear of mathematics long enough to ask, 'Does this make sense?' 'What would I conclude from these numbers?"

- A. K. Dewdney in 200% of Nothing, From "Percentage Pumping" to "Irrational Ratios," an Eye-Opening Tour through the Twists and Turns of Math Abuse and Innumeracy.

"Try to prove something to a reader by throwing three sets of figures at him, and he drops you and turns on the tube. Give him three quotes in a row by Authoritative and Informed Sources, and the same thing happens. He may even grow restive if you give him a long string of examples drawn from the direct experiences of primary actors in the story. ... But give him one of each of these elements mixed together and you've got him. He's convinced...."

and

"We need numbers in almost all our stories, and in some a number may be so important or startling that omitting or generalizing it would weaken the whole piece. I only argue that we be choosy in selecting figures and careful in their treatment.

"In placing numbers in a story, the good writer tries not to stack too many in one paragraph; this builds a wall of abstraction difficult to breach. It becomes impossible to breach when two or more such paragraphs are butted together, a construction that may lead to more unread prose than any other writing fault. Don't do this. Don't ever do this."

- William E. Blundell, in The Art and Craft of Feature Writing (The Wall Street Journal Guide).

"In popular writing on scientific matters the abused statistic is almost crowding out the picture of the white-jacketed hero laboring overtime without time-and-a-half in an ill-lit laboratory. Like the 'little dash of powder, little pot of paint,' statistics are making many an important fact 'look like what she ain't.' A well-wrapped statistic is better than Hitler's 'big lie'; it misleads, yet it cannot be pinned on you."

-- Darrell Huff, in How To Lie With Statistics , 1954.


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cheat sheet for computing percentages, percent differences and averages.

Figuring a Rate, a Ratio or a Percent

Rates and ratios are obvious ways to make numbers more meaningful for your readers. The most common kind of rate is a percent. Rates, ratios and percents are all ways of expressing fractions.. A percent is a decimal representation of a fraction, with the decimal point moved two places to the right.

Figuring a percent or rate

     
  1. Know your base. Think of the words "out of." It's the total of all groups you know.
  2. Divide the category you care about by the base. Remember that a fraction sign (/) means "divided by".
  3. For percents

  4.         * Multiply by 100, or move the decimal point two places to the right to get the rate per hundred, or percent.
    For per capita:
             * Multiply by some other number, such as 1,000 or 100,000 to get that kind of a rate
  5. Round the answer to one decimal place, or better yet look for an easier fraction your readers will understand.
Formula:

(Category / Base or Total) = Decimal , then Decimal x 100 = Percent.

Example:

If 58 people say they will vote in an upcoming election and 92 say they won't, here's how to figure the percent of people who will vote:

  1. Base = number of people asked = 92 + 58 = 150
  2. Rate = 58 / 150 = .386666...
  3. Percent = .38666... x 100 = 38.666666....
  4. Round = 38.7 percent, or more than a third (which would be 33.3 percent).
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Figuring a percent difference

A percent difference is the same thing as a percent, but it uses an earlier period as a base.

Figuring a percent difference or percent change:

     
  1. Subtract the old value from the new one. The answer might be negative. It might be bigger than the old value.
  2. Divide that by the old value.
  3. Move the decimal point to the right, round and simplify.
Formula :

(New - Old) / Old = Decimal.
Decimal x 100 = Percent.

Example:

If the agriculture budget for 1994 is $2,224,000 and the agriculture budget for 1992 was $2,100,000, then here's how to figure out the percent change:

Step 1: 2,224 - 2,100 = 124
Step 2. 124 / 2100 = .05857...
Step 4. .05857 x 100 = 5.857, or 6 percent.
 

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Finding Averages

The three common kinds of averages are means, medians and modes. Most news stories use the "mean" as the "average." A median is often called a "typical" value. You'll generally use medians for dollar values and means for most other values. Save modes for responses to a limited number of survey responses or a tally of votes.

To figure averages:

A simple average or mean is the sum of the values divided by the number of values you've summed.
To figure a median, list the values in ascending or descending order. Count how many there are, then pick the value that lies in the middle. (If you have an even number of items, compute the average of the two middle values). Choose a mode by counting the number at each value and choose the largest.

Formulas:

Average: (Sum of values) / (No. of values)
There's really no easy formula for medians or modes. You'll have to get your sources to give them to you or use a spreadsheet if they're not obvious.

Examples:

Here's a list of home values:

             $60,000            $85,000         Average =  $1,000,000 / 8 = $125,000
             $65,000            $140,000        Median = $82,250 (halfway between the 2 middle values)
             $70,000            $250,000        Mode = $250,000
             $80,000            $250,000


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NEWSROOM NUMBERS TIPS

Rates and percents

  • Remember to take away two decimal places (or multiply by 100) when figuring percents.
  • Wrong:  + = 0.5 percent                 Right:  + = 0.5 = 50 percent
  • Try to find an easy way for your readers to picture a rate. Simple fractions give the image of a pie and are easy to digest.

  • Correct: Agriculture consumed 35 percent of the budget
    Better: About a third of the budget went to agriculture
    or One of three tax dollars in the state went to agriculture
     

  • For very small rates, use a larger base than 100 or percent. This is most common in medical stories, like the number of infant deaths per 100,000 instead of per 100.

  •  
  • Keep your bases similar; compare similar numbers.

  • Correct but meaningless: "Eleven percent of blacks voted for Bush, but 10 percent of Clinton's vote came from blacks." This mixes bases: the number of black voters then the number of Clinton voters.

    Better: "Eleven percent of blacks voted for Bush and 60 percent voted for Clinton." The sentence keeps the base as the number of black voters.
    Or: "Two percent of Bush's votes and 10 percent of Clinton's votes came from blacks." It has two bases (the number of votes for each candidate) but keeps the comparison similar.

    (with apologies to Phil Meyer's Precision Journalism)
     

  • With percent changes greater than 100, revert to ratios, not percent changes. This is expressed as "times as many" or "times as much," not "times more". (Hint: It's impossible to get a 100 percent decline or more unless the new value is negative, like losses on a financial statement. You've done something wrong.)

  • Here are three ways to compare 400 arrests for drunken driving this year compared with 100 last year:

    Wrong: "Four times more" is not only confusing but wrong. Three times more or four times as many. (Compute it as a percent change: (400-100) / 100 = 300/100 = 3.00 or a 300 percent increase.)

    Correct: "Three times more people...." This is correct but confusing for many people who share your confusion.

    Better: "Four times as many people..."
     

  • When you subtract numbers expressed as percentages, the result is a percentage point difference not a percent change. It's easy for you (or your sources) to make changing rates seem huge or insignificant, depending on how they're expressed.

  • Wrong: Joblessness has grown by 1 percent since the 1960s, from about 4 percent to a little over 5 percent.

    Both of these are right; choose your weapon carefully:

    "Joblessness grown by one-quarter since the heyday of the 1960s, when unemployment stood at just 4 percent."
    or
    "Joblessness has grown by only 1 percentage point since the 1960s."
     

  • Compound, don't multiply, when you have to project changes. Remember to compound, not divide, when you have to figure an annual rate.

  • Wrong: If a budget grows 4 percent a year, it will grow 40 percent in 10 years (4 x 10)

    Right: The budget will grow about 48 percent.
    The formula is confusing: 1.04, or 104 percent of each year's value, to the 10th power minus 1 times 100. Or ((1.04^10) - 1) x 100
    (^ stands for "to the power of", and is what you'd use in a spreadsheet)


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Rounding

  • Round by adding 1 when the next digit is 5 or higher.

  • Wrong: $2,578,904 = $2.5 million
    Right: $2,578,904 = $2.6 million
     

  • When deciding how much to round, consider your point. Can you get away with "about," "nearly," or "more than" instead of having to put more numerals in your story? They scare readers.

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  • Decimal points are for meaning, not emphasis. Use only the level of precision you need to make your point.

  •  
  • Watch for false precision, especially in surveys. This is called "significant digits." Interest groups like to survey 20 people and express the results in percent. That means every response accounts for five percentage points. So that's the level of precision you actually have. As a rule of thumb, use the actual number (say, one of 20) when the survey had fewer than 100 responses.
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Averages

  • When possible, use medians -- not simple averages (means) -- when dealing with dollar values like income, house values or salaries. That's because extremely high values of a few will pull up the simple average for all.

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  • Medians are often called "typical" values; means are often called "average" values.

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  • You usually need to explain what a median is if you use the word in your story. A median is middle value. Half the salaries, for example, are above it and half are below it.

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  • Don't confuse a mode with "most." It's the most frequent category (usually in a survey), not necessarily a majority. Think of it as a vote.

  • Wrong: Clinton got most of the votes in 1992.
    Right: Clinton got the most votes in 1992.
     

  • Averages are usually used for physical characteristics and other types of numbers that don't vary that much, like weight and grade point averages.
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Indexing, Deflating and Adjusting

  • Check with your editor about how to handle indexes, such as the Consumer Price Index, consumer confidence surveys, housing affordability or similar comparative statistics. Some want the index levels; others want just the percent changes.

  •  
  • When reporting on dollar values over a long time, correct them for inflation.

  • Right: "Teachers' salaries have more than doubled since the 1970s, when educators began complaining the best teachers were leaving the field."
    This may be true, but read on.

    Better: "After inflation, teachers' salaries have risen just 5 percent since the 1970s, when they began complaining they could no longer afford to stay in the profession."
     

  • Some numbers require other kinds of adjustments. Consider adjusting budget numbers by population, inflation, income or all three. (Feel free to e-mail me to get formulas and help doing this.)

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  • Weekly, monthly and quarterly figures may need seasonal adjustment to account for changes that occur every year, such as the surge of young people entering the job market after school lets out. You won't be able to do that. Ask for it or make your comparisons to the same period in previous years, or to projections.
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Surveys and Polls

  • Know your pollster. Some reputable companies include: Gallup, Roper, Black, Mason Dixon, most big media and university polls and surveys. Obviously, there are others.

  •  
  • Beware of polls sponsored or conducted by candidates, special interest groups and companies with an obvious interest in the outcome. Ask who sponsored or paid for the poll.

  •  
  • Ask for the exact question wording. Better yet, ask for the full list of questions (or at least the relevant section) to see where in the list it falls. Look for:

  • Clarity. If you stumble over the questions, so did the respondents.

    Double-barreled questions. Just like a reporter in an interview, a pollster sometimes asks two questions at once. But unlike reporters, pollsters only allow one answer: "Do you favor or oppose health care reform and strict price controls?"

    Loaded questions. Rarely found among reputable pollsters, but rampant in special interest groups. Some are obvious: "Do you favor or oppose the president's health care proposal, which will lead to lower costs?" Some are less obvious: "Did you vote in the last presidential election?" Ask how you would answer: would you lie or stretch the truth?

    Leading questions. While an individual question might not be loaded, the one it follows often suggests the its answer. "Do you believe murder is a sin," might evoke a different response to a question on abortion than this lead-in: "Do you believe the government should stay out of peoples' personal lives?"

    Can respondents possibly answer the question? Whenever there's a big news event, pollsters ask what the effect will be. Examples include, "Will health care reform cost jobs?" and "Will the U.S. attack Iraq?" Although these questions might help you figure out whether the public is aware of a policy issue, it tells you nothing else of meaning the vast majority couldn't possibly know.

    (See The Newsroom Guide to Polls and Surveys for more caveats)
     

  • Ask for the margin of error, or significance. Check the confidence interval of that error, which is usually + or - 5 percent. Virtually all reputable polls and some government economic surveys have them. Just knowing they're available helps you know the survey is legitimate.

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  • Consider a sidebar or chart with the exact question wording and the responses.

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  • Don't get frightened by seemingly small sample sizes. Instead, examine the margin of error and confidence intervals. A thousand responses is adequate for virtually any poll, so long as the answers aren't broken into small subgroups. A typical size is between 350 and 450 respondents for a local poll, and about 1,000 for a national poll.

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  • Consider skipping a story on a poll or survey in which the sponsor will not give you the sample size, sampling method, response rate, margin of error, confidence interval or exact question wording. Your ability to get at least some of those items tells you the pollster is serious.

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  • Make sure your story doesn't revolve around meaningless differences or changes. A difference isn't "significant" unless it's greater than twice the margin of error.

  • Example:

    In a poll, 45 percent of the respondents said they would vote for Mayor Jones. Commissioner Smith got 40 percent. Fifteen percent were undecided. The margin of error is plus or minus 3 percentage points. So it's reasonably likely that Smith is actually beating Jones, 43 percent (or 40 + 3) to 42 percent (or 45-3). There's a small chance (usually 5 percent) that the error's even bigger.
     

  • Check any charts against your story. Nothing's more embarrassing than having one right and the other wrong (except getting both wrong).

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  • If you've thought of doing a story on it, there's probably a poll about it somewhere. Check the Public Opinion On-Line (available from the Roper Center in Connecticut) for reputable national polls.

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  • "Don't know," or "No opinion," are answers. Especially in campaigns, the number of undecideds can be even more important than the number who have decided.

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  • Polls can be wrong. The margin of error, say plus or minus 3 percentage points, can tell you that there's a 90 percent chance the true answer is within 6 percentage points (or, say, 41 percent to 47 percent.) True, the probabilities go down as you move away from the middle. But it does mean that there's a 10 percent chance the true answer is even further from the 44 percent average. Then all bets are off. If a poll tells you something you can't believe, consider not believing it.


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Writing with Numbers

  • Readers want people, not numbers. When you can't report on people politicians, regular people, people in business or effects on people at least keep your story short.

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  • A well-selected number, or set of numbers, can add depth and breadth to many spot news stories. Look for opportunities to put an event in perspective by gathering statistics on the growth, decline or scope of a seemingly isolated event.

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  • The most effective writing comes from selection, not compression, of facts. It's also true with numbers. Choose only the numbers that have meaning to your readers.

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  • Consider charting numbers instead of writing them. Removing them from the text not only improves your story; it often makes a bigger impression on readers.

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  • Pepper your story with just the right number in just the right place rather than cramming them all together. Use an anecdote, quote or observation to separate paragraphs with lots of numbers.

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  • Recast as many numbers as possible in simple terms that remove their abstraction. Ratios, rates, pictorial images and rounding can help simplify numbers.

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  • In a set of related numbers, decide what you want to say and construct a passage to do it as simply as possible. Remember that numbers in dates are just as difficult for readers as other numbers:

  • Correct: "Spending on redundancy research by the Office of Unessential Affairs rose from $847 million in fiscal 1994 to $1.26 billion this year, a 49 percent increase." (Four numbers with 12 digits)

    Better: "Over the past fiscal year, the Office of Unessential Affairs increased spending on redundancy research by almost half, to $1.4 billion." (One number with two digits)

    (With apologies to The Art & Craft of Feature Writing)

  • Images of numbers can help if those numbers are huge and incomprehensible. But although the just-right comparison can work well, the less-then-perfect comparison often falls flat and adds yet more confusion to an already difficult story. If you choose to try it anyway:

  • Make sure the image fits the story.
    Make sure your readers can picture the references.
    Avoid cliche images, like dollar bills placed end to end.
    Don't insert even more numbers with the image.
    Don't ask readers to repeat an image.

    Foreign references repeated: "Enough water to submerge the Rich Stadium 1,000 times."
    Better. "Enough to submerge Los Angeles a foot deep."

  • The bigger the number, the more difficult it is to visualize. Who really knows the difference between $960 million and $1 billion? For big numbers, cut them down to size for your readers by expressing them as a ratio or rate, but choose your base carefully.

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  • For small numbers, put them in perspective for your readers by emphasizing change or the lack of it.

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  • Read the Wall Street Journal.
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Further Reading

William Blundell, The Art & Craft of Feature Writing, Based on The Wall Street Journal guide.

A. K. Dewdney, 200 Percent of Nothing: An Eye-Opening Tour Through the Twists & Turns of Math Abuse & Innumeracy. Wiley. 1994

Darryl Huff, How To Lie with Statistics.

Philip Meyer, The New Precision Journalism, Indiana University Press, 1991.

Wilhoit & Weaver, The Newsroom Guide to Polls & Surveys

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