# Analyzing Data about Lost Baggage: It’s All Relative (Frequency)

Most Lean Six Sigma projects use data analysis to examine and reduce the prevalence of defects in a product or service. Experienced quality practitioners know that defects can sometimes feel abstract when you analyze them, until you’re the customer who experiences them firsthand.

On my first trip to Rome, my luggage never showed up in the terminal.

So instead of gazing in awe at the Sistine Chapel, or savoring tortellini ricotta and a glass of chianti, I spent my first day in the Eternal City trying to get sales clerks in cheap discount stores to understand my botched pronunciations of the Italian words for toothpaste (dentifricio), socks (calzini) and underwear (biancheria intima).

To help protect air travelers from having to speak broken Italian when they shop for undergarments, the U.S. Department of Transportation publishes a monthly report on flight delays, mishandled baggage, and other related air travel statistics.

Suppose you want to use statistical software to analyze  that data to compare mishandled baggage among U.S. airlines for a given month. Your first inclination might be to simply compare the number of mishandled bags per airline, such as the bar chart below.

What’s wrong with this picture? Why don’t counts tell the whole story?

If you raised an eyebrow and thought, “Hey, that’s not a fair comparison,” you’re absolutely right. After all, larger airlines that handle more passenger volume are more likely to have more mishandled bags simply because they handle more baggage. If you look at the chart, sure enough, most of the larger airlines are on the far right.

In fact, one major airline had about 24,000 reports of mishandled luggage in one month. That sounds astronomical. But in relation to number of passengers, its rate of mishandled luggage was only about 0.0028, less than 3 reports for every 1000 passengers. A much better performance.

Now look what happens when the mishandled baggage is represented as a rate of the number of mishandled bags per 1000 passengers.

Notice the larger airlines now fare much better. For example, US Airways was in the bottom 5 for mishandled baggage based solely on frequency counts (top chart). But taking into account passenger volume (bottom chart) it’s now in the top 5, with one of the lowest rates of mishandled baggage for the month.

You might think it’s an obvious point, yet misleading charts of frequency counts are very common in newspapers and magazines, especially in the ubiquitous “top 10” and “top 5” lists that appear in many blogs.

How might you adjust data in these sets of rankings to better compare job availability or the potential for financial gain in cities?

So whenever you have frequency data, think carefully about whether it’s more appropriate to display and compare the data as a relative frequency or as a rate. If it’s continuous data, a proportion or a percentage might make more sense.

Of course, if you’re the customer with lost luggage, like I was, whether your mishandled bag is represented as a count or a rate doesn’t matter much when you don’t have any fresh socks. (Uffa!)

Name: Omar Mora • Wednesday, August 31, 2011

Dear Patrick,
Interesting post.
Would you recommend to use Minitab 16´s Poisson-Rate tests for a more sophisticated comparison between two specific companies (rates)?
Omar from Blackberry&Cross

Name: Patrick Runkel • Wednesday, August 31, 2011

Nice point, Omar. You can use Minitab's 2-Sample Poisson rate test to statistically compare 2 rates, such as a defect rate before and after a process improvement. What's nice about doing that is, you don't have to spend a huge amount of time and money that would be required for you to count every single defect of your process every single second, every single day. Instead, you can just collect a smaller random, representative sample and then use the rate test to infer whether the change in rate is statistically signficant--that is, is the rate difference likely due to the process improvement or is it likely just a fluke occurrence?

For the mishandled baggage data in this blog, the US Department of Transportation is counting every single instance of mishandled luggage, rather than taking a smaller random sample to represent all the handled luggage. So in this case, we can directly compare the rates without using a hypothesis test. But let's say, just for the sake of example, that we could say that the rate of mishandled luggage in May 2011 is representative of the whole year of 2011 (although it probably isn't). If that were the case, we could use the 2-Sample Poisson rate test to compare the rate between two airlines, such as Delta and American, to see whether the difference in rates for the entire year is really statistically significant.

When you think about this this way, statistical hypothesis testing is really just a great way to save you money and time.

Thanks for your comment! Cheers, Patrick