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# Reasoning Skills and Statistics Help (page 3)

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## Comparing Apples and Oranges

In 1972, a Hershey's chocolate bar cost only 5 cents. Today, the same bar costs at least 50 cents. That's an increase of over 1,000 percent!

This increase sounds extreme, doesn't it? But is it really as severe as the math makes it seem? Not quite.

The problem with this claim is that while the actual price of a Hershey's bar may have increased 1,000 percent, it's not a fair comparison. That's because 5 cents in 1972 had more market value than 5 cents today. In this situation, the actual costs can't legitimately be compared. Instead, the costs have to be compared after they've been adjusted for inflation. Because there has been such a long time span and the value of the dollar has declined in the last 30 years, maybe 50 cents today is actually cheaper than 5 cents was in 1972.

It's important, therefore, to analyze comparisons like this to be sure the statistics are indeed comparable. Any monetary comparison needs to take into consideration market value and inflation. When dealing with figures other than money, however, there are other important concerns. For example, read the following argument:

In 1990, there were 100 unemployed people in Boone County. In 2000, there were 250. That's an increase of 150 percent in just ten years. Unemployment in this country is becoming an epidemic!

What's wrong with this argument? Clearly, there has been a sharp rise in unemployment in the last decade. But what the claim doesn't tell you is that during that same time period, the population of Boone County increased by 250 percent. Now how does that affect the argument?

If the population increased from 100,000 to 350,000, is the rise in unemployment still evidence that can be used to support the claim "Unemployment in this country is becoming an epidemic"? No. In fact, this means that that the number of unemployed per capita (that is, per person) has actually decreased. This is a case of comparing apples to oranges because the population in 1990 was so different than the population in 2000.

You should beware of any comparison across time, but the same problems can arise in contemporary comparisons. Take the following statistic, for example:

Charleston Medical Center physicians perform more arthroscopic knee operations than St. Francis physicians, who use a technique that requires a large incision.

If you need to have knee surgery, should you go to Charleston Medical Center? Not necessarily. Consider this fact, first: St. Francis physicians specialize in complicated knee surgeries that cannot be performed arthroscopically. Because their pool of patients is different from those of Charleston Medical Center, so will the number of nonarthroscopic knee operations.

#### Tip

Numbers don't lie … but resources can. When putting together statistics to use in your argument or to analyze in someone else's, make sure that they come from sources that you can trust. Your mother's guess on the current unemployment rate or your younger brother's estimate on how many days it has rained this year may be convenient to obtain but not likely very accurate. Take the time to get numbers from reliable sources.

## Reasoning Skills and Statistics In Short

The truth about statistics is that they can be very misleading. When you come across statistics, check the source to see whether or not it's credible. Then find out the sample size and decide whether it's substantial enough. Look for evidence that the sample is representative of the population whose opinion you wish to reflect, or randomly selected and not biased. Finally, beware of statistics that compare apples to oranges by putting two unequal items side by side.

#### Skill Building until Next Time

• Look for survey results in a reputable newspaper with a national circulation, like The New York Times, Washington Post, or San Francisco Chronicle. Notice how much information they provide about how the survey was conducted. Then, look for survey results in a tabloid or a less credible source. Notice how little information is provided and check for the possibility of bias.
• Think about a survey that you would like to conduct. Who is your target population? How would you ensure a representative sample? How large should your sample be?

Exercises for this concept can be found at Reasoning Skills and Statistics Practice.

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