Cargo Cult Statistics

Did first-class passengers on the Titanic get preferential treatment during the evacuation? James Cameron’s movie certainly seems to suggest so, but let’s look at the data.

 

Survived Died
First class 203 122
Third class 178 528

 

The data is compelling.  75% of the third-class passengers perished compared to only 38% for the first-class passengers.  The statistically inclined among you might run a Chi-squared test to confirm these observations, and not surprisingly the results will be statistically significant. The difference in the proportion of first-class passengers that perished versus the proportion of third-class passengers that perished is unlikely to have occurred by chance. Well, that must be the end of the story. An analyst might create some pie charts or some stacked bar charts to illustrate the results, but that is the end of the story…right???...not quite.

 

Consider a more detailed breakdown of the same data:

Survived Died
First class
Men 57 118
Women and children 146 4
Third class
Men 75 387
Women and children 103 141

Now the data suggests a possible different story. With this data, it is now evident that 79% of the men died, compared to 37% of the women and children. So which was it? Was it class privilege or chivalry? Or was it something else?

These are questions of history, and there are many lessons to be learned from history. And there is much to be learned from the over simplistic analysis that suggested the cause was class privilege:

  • Just because the numbers are overwhelming, it doesn’t mean your hypothesis is true.
  • When analyzing data, t is wise to remember the words of Sherlock Holmes; “when you have eliminated the impossible, whatever remains, however improbable, must be the truth”.

The failure in the initial analysis was not a failure of mathematics or statistics, but a failure of the analyst. They failed to consider other alternatives. Richard Feynman described this error in his essay: Cargo Cult Science, in which he recommends, among other things, that we should not fool ourselves and we should not fool others. We accomplish these goals with a profound honesty, by challenging ourselves to look for other explanations, and by carefully performing and re-performing experiments. And while the systems that we study may be more complex and more dynamic than the systems that a physicist studies, there is no excuse for cargo cult statistics.