Statistical Analysis or Half-Truth?

If you are like most people, you believe that numbers tell the truth. A news story has a bigger impact and seems more believable when it tells you how many people attended a political rally, what percent of the population voted for each candidate, and what the average increase in the price of a gallon of gasoline was over the past year. Backing up a story with numerical facts intuitively seems like a fail-proof way to prove its credibility.Unfortunately, numbers are not intuitive to the human brain. You cannot always instantly interpret the numbers and understand them, and that is why media coverage, government reports, and summaries of scientific research can be misleading. Sometimes the misconceptions are intentional and sometimes they are not, but you can become better informed by learning about these basic facts on statistics and how they are commonly used.“Average” Has a Statistical and an Everyday Meaning – And They Are Different!In everyday English, you casually use “average” to describe the majority. For example, you might observe that the average college student likes to eat ice cream and pizza, or that the average driver waits until the gas gauge is showing empty before filling up the gas tank. But these have nothing to do with math, and the use of the mathematical average can seem counter to these statements. For example, the average American family may include 3.14 people, but that hardly describes the majority. In fact, you do not know a single family that has 3.14 people. The life expectancy of American men is 76 years; how many men do you know who died on their 76th birthdays?A statistic that is more telling in many ways is the median, or the value right in the middle. Half are above, and half are below. So, if the median salary in the U.S. in 2013 was $34,750, half of American workers earned less than $34,750, and half earned more. The median is also used for home sale prices and levels of education.How Fast Does It Need to Grow Before It Becomes Important?Being the “fastest-growing” sounds impressive, whether it is the fastest-growing company, neighborhood, or religion, but you need to look at a few other factors to make sense of this. A company that has a net profit of $1,000 per year and grows to $2,000 per year is growing much faster than a company that grows from $1 billion to $1.1 billion, but which company is more likely to affect you? Just because a company is growing fast does not mean that it is big enough to be of significance.Cause and Effect or Correlation?You hear all the time about new discoveries of relationships between things like cancer and respiratory illnesses and living near factories or freeways. While the factories and freeways may play a role in disease development, the epidemic may not actually be related to the factories and freeways. Imagine that you drew a map of your neighborhood and the flower gardens in your neighborhood and wrote the names of all of the residents in the neighborhood. You notice that 14 percent of the individuals who maintain a flower garden have a first name starting with the letter “K,” while none of the individuals without a flower garden do. Does that mean that having a flower garden causes people to have names starting with “K?” Of course not. The same is true for other relationships – it is important to distinguish cause and effect from relationships.Sharpshooter or Texas Sharpshooter Fallacy?The Texas sharpshooter fallacy is named after a Texas sharpshooter who shoots several times, then draws a target around where most of the shots fell, claiming that was his original goal. This is an example of seeing patterns where there is really only randomness. A politician may claim that the increase in crimes in one neighborhood is due to an increase in allocations for food stamps, while ignoring the fact that crime rates decreased in other neighborhoods where food stamps increased.Medical Diagnostic Tests: Check Your Calculations Before You PanicIf your doctor is a little shaky on her math, she can scare you needlessly. Take, for example, a positive result on a diagnostic test for an infection. Your doctor tells you that she needs to retest you because of your positive result. The test that she used, she says, gives a false positive only 1 percent of the time; that is, out of every 100 healthy individuals who take the test, 1 will receive a false positive. Therefore, your positive result is likely the result of being sick…or is it?Not necessarily. The doctor tests so many patients that some of them are inevitably going to receive a false positive, and that could be you. What you also need to know when analyzing your risk of being sick is what percent of the population gets the disease in the first place. This concept is also applicable when discussing screening tests at the airport – how likely is it for a bearer of arms to slip through security, and how likely is it for an innocent person to get stopped at a checkpoint?Statistics can paint a very useful picture and help guide you to critical decisions. Just make sure you are truly aware of the big picture your statistical analysis is painting before you act on that decision.