Applied Statistics Abstract

article, summarize the evidence, and evaluate the article for the strength of its argument. It really should be no more than 1 page. In the grading, length, accuracy and clarity of presentation, grammar and spelling will all be considered.

Epigraphs: 1. There are three kinds of lies:

Lies, damned lies, and statistics. Benjamin Disraeli, 19th century prime minister of England

2. Round numbers are always false.

Samuel Johnson, English author

3. Get your facts first and then you can distort ‘em as much as you please. Mark Twain, American humorist and author.

4. He uses statistics as a drunken

man uses lampposts— for support rather than illumination. Andrew Lang, Scottish author

Article:

Lies, Damned Lies, and Statistics By Aaron Tenenbein, Stern School of Business, in Sternbusiness

Why are all of these people poking fun at statistics? On the surface two plus two is always equal to four.

The problem isn’t the numbers. The problem comes with interpreting those numbers. While there are hundreds of ways in which statistics can be interpreted, the mistakes come in two basic flavors. Either the study designed to collect the numbers was faulty or the numbers collected were just fine; but someone either accidentally or on purpose misinterpreted the numbers.

The results can be funny and embarrassing.

Faulty Survey Design: The Presidential Election of 1936

In 1936 the Republican candidate, Alfred Landon, ran for president against the incumbent, Franklin, Delano Roosevelt. The Literary Digest, a magazine which was published in the 1930s, had accurately predicted the previous four presidential elections. The same methodology was used and predicted that Landon would be the next President. The Literary Digest was terribly wrong. Landon only carried Maine and Vermont. Roosevelt won in a landslide.

What went wrong? The problem was the way in

which The Literary Digest drew its sample, which included Literary Digest subscribers, telephone owners and people who owned cars. This produced a bias towards higher income groups which, in 1936, voted Republican in higher percentages than lower income groups. In the midst of the Depression, there were not a lot of people with money, as Landon learned the hard way.

There is an interesting postscript to this election. Before the 1936 elections, there had been a saying, “As Maine goes, so goes the nation.” After all, in all previous elections, the candidate who carried Maine won the Presidential election. This trend stopped in the 1936 election with Landon only carrying Maine and Vermont. As a result, the saying became: “As Maine goes, so goes Vermont.”

Errors in Interpreting Correct Data: The Ad for PLAX

An ad for the mouthwash PLAX, claimed that PLAX reduces plaque by 300% over brushing alone. The data upon which this claim was based were probably accurate. However, the

interpretation was faulty. The implication of this ad campaign was that brushing alone meant brushing using toothpaste but without rinsing with PLAX. However, in the data upon which this study was based, brushing alone meant brushing for only 15 seconds without the use of toothpaste. Much different results were obtained in another study in which people in the control group were allowed to brush unhurriedly using toothpaste. In that well-controlled study there was no significant statistical difference between the control group and the group using PLAX. In the words of Consumer Reports, the PLAX claim was “one claim you can brush off.”

Errors in Interpreting Correct Data, Part II: Advertising of Volvo Automobiles

A while back, Volvo undertook an advertising campaign using the following statement: “Over 95% of all Volvos registered here (in the U.S.) in the last 11 years are still on the road.” The implication of this fact is that the Volvo is a very durable car. This may very well be true, but this statement does not imply either longevity or durability.

If the result were that 95% of the Volvos registered in 1957 were still on the road in 1968, there would be stronger support. However, since all cars registered in the last 11 years were included, automobiles whose age varied from 11 years to 1 day were included.

As an extreme example, suppose 100,000 Volvos were sold in the last 11 years and the distribution of sales and of cars still on the road as of January 1, 1968, was as it is displayed in the table at right. Notice that of all 100,000 cars sold in the last 11 years, 95,000 (or 95%) are still on the road. However, 99,000 (or 99%) of the cars sold in the last 11

years were actually sold in the last 4 years. In point of fact, it turned out that the figure was closer to 50%.

The Volvo may in fact be a very durable car (I drive one that is now 10 years old). However, the fact stated in the advertising campaign does not support the assertion of durability.

Faulty Survey Design: New York State Thruway Poll

The New York State Thruway Authority undertook a survey to help determine the route of the proposed superhighway between New York City and Buffalo about 45 years ago. The study was conducted by the State Police on a Sunday. They stopped every fourth automobile on Route 17, which is one of the main arteries to upstate areas. The drivers were asked where their trip originated, their final destination and how frequently they made the trip. The survey caused a massive traffic jam on Route 17 (not a surprise).

Surprisingly the results of the survey were useless. First of all, the traffic jam created by the survey may have altered the very thing it was intended to measure. Motorists may have taken alternate routes, or changed plans,

Table 1 Hypothetical Sales of Volvos in the United States

Year of Sales

Number of cars sold

Number of cars still on the

road as of January 1,

1968 1957- 1963

1,000 100

1964 10,000 9,000 1965 19,500 18,000 1966 29,500 28,000 1967 40,000 39,900 Total 100,000 95,000

when they heard about the back-ups. Furthermore, the survey was conducted on a single Sunday in May during which traffic patterns would probably be appreciably different from weekdays or other times of the year.

Errors in Interpreting Correct Data, Part III: Baseball Salaries in 1994

The baseball strike of 1994 produced many conflicts between the owners and players association, but the major squabble was about money. The owners association used an average salary of $1.2 million to show how well off the players. The players association said that many players only earned the minimum of $109,000 and more than half of the 746 baseball players (385 out of 746) earned $500,000 or less.

Who is right? The owners or the players? The answer is, both. This issue illustrates the difference between two statistical summary measures, the man which is the average, and the median salary which divides the players into two equal groups: 50% of the players earn more than the median and 50% earn less than the median. In this situation the median salary was $500,000.

The owners’ position is that the measure which is more appropriate is the mean. If a baseball team owner wished to look at this total payroll, the mean is the more logical number. The total payroll would be the mean salary multiplied by the number of players on the roster. The median salary would not be as informative.

The players association, on the other hand, is more concerned about how many players are at given salary levels. A more realistic measure from the players point of view is the median.

In this situation 237 out of the 746 (32%) players earned more than the average or mean salary of $1.2 million. If these 237 players all were given a salary increase of $1 million with the remaining 509 players maintaining the same salary below $1.2 million, the average salary would go up to $1.52 million. But the median salary would remain at $500,000.

Of course, in any salary negotiation management will always use the higher number whereas the union will always use the lower number to describe current salaries. And there is always a statistic to bolster anyone’s claim!

The correct interpretation of statistical results is very important. The problem of misinterpretation occurs very frequently and some of these instances of misinterpretation are unfortunately intentional.

AARON TENENBEIN is a professor of statistics and actuarial science at Stern.

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