Red(shirt) Alert: Stats of expendable crewmen

Statistics-first research planning is a relatively new concept to me, though one that I’m increasingly seeing as important. Over the past few weeks, Dr. Murphy has mentioned several times that a researcher should know exactly which tests they want and use them to guide their experimental design. Scientists are often trained, however, in an experiment first, analysis later manner. Rarely have I seen a lab class include the use of a statistical test to examine data besides linear regression. Instead, statistical testing is often taught in standalone classes where data is contrived. Even working in a non-academic laboratory, the mentality was data now and we’ll ask the staff statistician what to do with it later.

Though, through several stats courses, I’m familiar with most of the standard statistical tests used often in lab work, they are still an afterthought. Combatting years of procedural habits is difficult, but there’s time to get into the habit of statistics-first planning before I really begin in my thesis work. The first step to that is to integrate the use of statistical tests into my daily thoughts and, since many of my musings revolve around one topic in particular, I thought it best to begin there. Ahead, full impulse, Mr. Sulu!

One well-known joke arising from Star Trek: The Original Series is that of the ominous red shirt. (But only TOS red shirts, not any subsequent series) Kirk, Spock, and Bones beam to a planet with a small force of red-shirted security and within a few minutes those escorts are victims of the latest alien/ plant/ disease/ energy/ weather mishap. Just observationally, it seems that wearing a red uniform increases chances of death. But how does that stand up to the rigors of statistics?

In 2013, Matt Barsalou wrote a post for Significance Magazine exploring that idea and several people used his ideas as a springboard for further analysis. Of the 40 on-screen crew deaths (of people wearing uniforms), 24 of them wore red shirts. But Barsalou pointed out that viewing those numbers on their own isn’t necessarily fair considering that there are varied numbers of crewmen of each of the three uniform colors and that multiple departments wear the same colors. One of those departments using red is the security team, which is often included in more dangerous work than, say, the similarly red-shirted engineers. Using Bayes Theorem, he showed that there’s a 64.5% chance that any given red-shirt casualty is on the security team despite security making up a minority of red shirts. Of the remaining non-security red shirts, he calculated that they have an 8.6% chance of being that casualty. Rather than the color of the uniform being the issue, Barsalou concluded, it’s actually the occupation. This makes more sense than a universe-wide aversion to a uniform color.

Jim Frost, an author on the Minitab blog, also confirmed Barsalou in another post where he examined the same data with different tests. When looking at whether red-shirt deaths exceed the overall average of deaths, he found with the chi-square test that red shirts actually have a rate of death that is about average of the three groups, as they die more often but derive from a larger pool of crewmen, whereas gold uniforms die with a higher rate than average due to being such a minority overall. Noting, as Barsalou did, that shirt color isn’t the correct variable to examine, Frost used the two proportions test to look at occupation. With a very low p-value, he found that the rate deaths of red shirts in the security department far exceeded those of other red shirts. Thus, being in security is dangerous, not your shirt color.

Other people on the internet have looked into other Trek-related topics using statistics, including one post using the Mann-Whitney test on Trek film ratings to see if the odd- or even-numbered films are better. Realizing how applicable these statistical tests actually are brought statistics out of the realm of rat stressors and confusion and into the streamlined Federation star ships that I know and love. Spock might agree that statistics-first organization is the logical choice to make, if not the natural choice, and better-designed experiments and better-informed test choices will be the result.

//The video is a song about red shirts performed by the Enterprise Blues Band, a group made of actors from Trek that I saw in person last month. Unless they're all security team, stats says they don't have much to worry about.