Statistics for Communicators

By Dr. M. Mark Miller

Many of us chose a communications major in part as a way to avoid mathematics, and it's true that journalists, public relations professionals and broadcasters have little use for trigonometry and calculus. But numbers are unavoidable. In fact, knowledge of some basic mathematics (or perhaps just plain arithmetic) is essential to being a skilled communicator.

Many of the things that communicators need to know are so simple that they aren't even covered in introductory statistics books But often it's the simple things that lead to the worst and most embarrassing mistakes. So let's begin with a review of the stuff that you probably first learned in grade school, but may have forgotten because you didn't need to use it often.

Percentages

Simple percentages probably are the most common and most useful of the descriptive statistics. In many situations it's easier to understand things in terms of percentages rather than raw numbers, e.g. in describing election results in a mayoral race, we'd understand the situation better if we read, "The incumbent won the race with 51.2 percent of the vote compared to the challenger's 48.8 percent," rather than, "The incumbent won with 6,420 votes compared to the challenger's 6,122 votes."

Most of us also know how to calculate percentages but just in case, here's the way:

Divide the number of one category by the total number and multiply the result by 100. In our election example, the incumbent's percentage is:

6,420 divided by 12,542 multiplied by 100 which equals 51.2 percent

and the challenger's percentage is:

6,122 divided by 12,542, which equals 48.8 percent.

Percent Difference

While percentages are fairly simple and require only a little arithmetic, there are subtleties in interpreting them. In our election example it would be correct to say that the incumbent won by less than two and a half percentage points, but not that she won by a two and a half percent difference.

That's because percent difference is a comparison of the relative number of votes of one candidate to another, not the difference in percentages. To see the difference let's figure out the percent difference between the incumbent and the challenger.

The percent difference is the difference in the vote counts, divided by the candidate used for the base comparison. So we calculate the difference

6,420 minus 6,122 equals 298

and divide the difference by the number of votes for the incumbent

298 divided by 6,420 equals .046

which we need to multilply by 100 yielding 4.6 percent. So it would be technically correct to say that the incumbent won by 4.6 percent, not by 2.5 percent. Interestingly, it wouldn't be correct to say that the challenger lost by 4.6 percent. That's because the divisor shifts in the calculation which becomes:

298 divided by 6,122, multiplied by 100 equals 4.9 percent.

All that is probably confusing and a good communicator probably would never bother with calculating the percent differences or reporting them. The solution to clear and correct communication in this case is to report things in terms of percentage points, rather than percentage differences.

Of course, there are times when percent difference is exactly what we want to report. Consider the situations where the Mayor's budget this year is $20 million and last year it was $18 million. What's the percent difference (or increase)?

$20 million minus $18 million equals $2 million

Divided by the base year, $18 million, multiplied by 100, equals 11.1 percent.

How does that compare to the situation where this year's budget is $18 million and last year's was $20 million? In this case we divide the difference $2 million, by the base $20 million and get a 10 percent decrease. So taxes are likely to go up at a higher percentage than they go down, simply because of rules for calculating percentage difference.

Relative Percent Difference

Consider the situations where the mayor of a suburb proposes increasing her city budget from $1.8 million to $2.4 million, while the mayor in a large city proposes increasing his city budget from $22 million to $23 million. Which mayor is increasing taxes the most?

One answer is that the large city mayor is increasing by $1 million while the small city mayor is increasing by $0.6 million, but is that the clearest way to put things? Let's calculate the percent increase.

For the small city the percent increase is $.6 divided by $1.8 times 100 which equals a whooping 33.3 percent.

How does that compare to the big city? The percent increase is $1 million divided by $22 million multiplied by 100 or 4.5 percent, a more reasonable figure.

Or course, there's more to accurately describing the budget situation than calculating the percent increases and comparing them. Possibly the population of the suburb has doubled in the last year while the population of the city has declined. Such contextual matters would make a big difference in how we report the figures, but they're beyond the scope of discussion here.

Frequency Distributions

Frequency distributions are a common way of reporting numbers, particularly when things are divided into more than two groups. For example, you might report survey results like this:

"Of the 680 voters interviews, 35 percent said they planned to vote Republican, 38 percent said Democrat, 4 percent Green Party, and 23 percent were undecided."

It might be better to make a table:

In either case you're reporting a frequency distribution, which is a convenient and comprehensive way to report numbers in many cases. In survey research, we often ask questions that offer respondents multiple categories. For example, consider the survey item:

Please indicate your level of agreement with the following statement. Parking is a serious problem for students at the University of Tennessee. Would you say you: Strongly Agree, Agree, Are Neutral or Can't make up your mind, Disagree, or Strongly Disagree?

Reporting the frequency distribution would be an obvious way to report the results from such a survey item.

Another way to report the results (and probably a better one) would be to collapse the agree categories (add the percentages together) and say:

"Some 92 percent of the respondents said they either agreed or strongly agreed with the statement: 'Parking is a serious problem at the University of Tennessee."

Collapsing the agree categories loses some information, but it compactly and accurately conveys the sentiment of the respondents.

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