Statistically Speaking

Nineteenth-century British Prime Minister Benjamin Disraeli is often credited with the statement, “There are three kinds of lies: lies, damned lies, and statistics.” This column has discussed the lies and the damn lies. Statistics are the most treacherous because even the most skeptical electrical contractors (ECs) respond to the power of charts, graphs, dollar signs and percentages as if they contain universal truth.

The simplest way to misuse data is to cite meaningless numbers or simply fabricate them. Few people take the time to verify supporting data or consider differences in the baseline. For example, a chart may show that there are more electrical contractors operating in California than in Rhode Island. The substantial difference in the total is due to California’s larger population. A more meaningful comparison would be to calculate the number of electrical contractors as a percentage of total businesses operating in each state to adjust for this baseline difference.

Data dredging and manipulation

Data can be manipulated by dredging or digging for a pattern that supports a position and ignoring or discarding numbers that do not conform. Ideally, that pattern should be verifiable. Scientists, for example, publish results with the expectation that they can be verified by replicating the experiments using the same methods. Unethical practices include fudging results that do not conform to expectations or selectively reporting only positive results. Although this is problematic in financial reporting, this practice is acceptable when you provide client references, choosing only the most positive testimonials.

Causality and correlation

Statistics may show correlations that are not necessarily due to cause and effect. For example, profits may increase for five years in a row, while sales revenue declines. There are several possible reasons for this correlation:

1. Lower sales cause higher profits.

2. Higher profits cause lower revenues.

3. Each partly causes the other.

4. There is another factor causing both.

5. The pattern is the result of chance.

If you conclude that reducing sales revenue further will cause profits to rise even more, you will be sorely disappointed.

Loaded questions

Surveys are a potential source of misleading statistics because there is almost no way to obtain a truly random sample of any group of people. So, the opinions of a few are extrapolated to reflect the opinions of a much larger population. For example, consumers surveyed by a lighting manufacturer prefer a certain type of lighting. The number of people studied, their demographics (age, location, type of residence, income), and the questions’ wording have all affected the results. For example, questions that do not allow for answer clarification create forced choices, and the closest answers are not necessarily the most accurate measures of opinion. If you survey customers, word the questions carefully and include a place for comments to gather more accurate feedback.

Dollars and percentages

Failing to consider both dollar amounts and percentage relationships can result in poor financial decisions. Here is an example. An EC earns $100,000 profit on sales revenue of $1 million (10 percent). The next year, revenue grows to $1.5 million, with a profit of only 8 percent. The owner is disappointed, until he sees that the business actually earned more money in dollars ($120,000). As revenue grows, profit percentages may shrink, but the profit in dollars may still be satisfactory.

Even a simple calculation, such as average job size, can be misleading. The same $1 million in sales revenue would produce an average job size of $100,000 if the firm completed 10 jobs in that year. The actual list looks like this:

The average job size is $100,000, but the distribution is also important. Without the $400,000 job, total revenue would shrink by 40 percent, reducing the average job size by one-third, to $66,667. When you calculate the average, or mean, it is important to recognize the range of values as well. The $400,000 job is an outlier, and it skews the average upward.

If you calculate the median as well as the mean (average), the effect of outliers will be obvious. The median is the middle value of the dollar amounts of the jobs; in this example, the midpoint between jobs 5 and 6, or $55,000 ($40,000 + $70,000 ÷ 2). The farther this value is from the mean, or average, the larger the effect of any outliers on the pattern.

You don’t have to be a statistician to make good financial decisions. Know that numbers can create false confidence. Always ask for supporting data, clarification of survey methods, and additional research before accepting an otherwise weak argument. Numbers are only part of the equation, so trust your instincts and experience to fill in the rest.

NORBERG-JOHNSON is a former subcontractor and past president of two national construction associations. She may be reached at

About the Author

Denise Norberg-Johnson

Financial Columnist
Denise Norberg-Johnson is a former subcontractor and past president of two national construction associations. She may be reached at .

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