The Art of Deceptive Statistics Using statistics as a dishonest tool to achieve desired results, and how to determine the validity of statistical results

Ways to use statistics for your own good Some ways that people use statistics for their own purposes are: Using a nonrandom sample that supports their conclusion Using different measures of center to describe similar data sets Reporting only some findings instead of all findings. Changing definitions to include more or less people

Not using a random sample Suppose a city council wanted to request federal assistance for their city. They would then want to show that their community is poor. One measure of which would be the value of their houses. If they decided to only take the price of houses from a very poor community, the average price of a home of the sample would be much lower than the true average price of a home. It’s not that they didn’t calculate the sample mean correctly, but they took a sample that wasn’t representative of the entire city. This is a prime example of purposely using misleading statistics.

What should have been done Houses from all over the city should have been taken, to get an accurate representation of the city’s true economic housing climate. The city could get in trouble if someone found out they deliberately used a nonrandom sample to report their findings.

Using different measures of center Another situation that statistics could be used to deceive people is when using measures of center. Remember that the three measures of center are mean(or average), median, and mode. Depending on which one you use, the center of a data set could look drastically different.

ExampleExample We have two datasets, A and B A is the set { 2,3,4,4,5,6,90 } B is the set { 1,2,2,4,6,8,11 } B is the set { 1,2,2,4,6,8,11 } What does it look like if we use the mean, median, or mode to describe these sets?

Example continued Mean of A: ( )/7 = 114/7 = Mean of B: ( )/7 = 34/7 = 4.86 The means paint the picture that these two data sets are drastically different, even though the large observation in A is the biggest difference Median of A: 4 Median of B: 4 If we use the median, then the two data sets look like they have the same center.

Example continued again... Mode for A: 4 occurs twice, so our mode is 4 Mode for B: 2 occurs twice, so our mode is 2 Using mode, A seems to be bigger than B. All three of these measures of centers paint different pictures of the data sets. None of them are wrong, but if you want it to look a certain way, you could purposely choose one that would back up your conclusion.

Underreporting your findings If you fail to report all of your statistical results from a study, this is also a form of deceptive statistics. One result could make your company or yourself look good, whereas the other would make you look bad. Obviously, you would only want to choose the report the results that help you out.

Underreporting Example A company that makes helmets releases a report that their new helmets are making the army safer, citing that deaths from head wounds are down 50%. What they don’t report is that people are still getting injured in the head, but since the helmets are better, they do not die. There are still plenty of people getting hurt, but its just in the form of injury, not death.

Changing Definitions Companies may also choose to include or remove certain demographics in a study that contradicts the conclusions they wish to make. Once again, this is not incorrect, but the purposeful removal of these groups make the act deceptive.

Changed Definitions Example How do you define a car accident as caused by alcohol? You could say if there was any alcohol consumed by anyone involved in the crash, it is alcohol related. Or, you could say that if the driver was legally intoxicated, then it is caused by alcohol.

Alcohol Example Continued Using these two definitions, we will get very different results if we want to determine the proportion of car accidents that are alcohol related. If an alcohol producer was making this report, they would clearly choose the definition that led to the lowest proportion of alcohol related accidents.

Ways to identify misleading stats You always want to look at the sample. How large is it? Who was in it? Is it representative? Investigate the methods used. Did they use the same measure of center for all datasets? Are all assumptions met for whatever method they used? Be aware of any excluded results that should be there.