Find out how Hypothesis Testing Helped Indict a Nurse for Murder

Ever heard of a Criminal or Forensic analyst? Well, it’s one of those slightly off-the-beaten-track exciting and challenging data analyst careers and involves systematic analysis for identifying and analyzing patterns and trends in crime and disorder.

We have seen an increasing effort by law enforcement establishments to fight and control crime using data analytics in the last decade. Information on patterns can help law enforcement agencies deploy resources more effectively, and help in identifying and apprehending suspects, sometimes even before a crime is committed. Crime analysis can also help in devising solutions to crime problems in society.

Though very popular in the west, it is encouraging to see that in India too, police departments have begun to use data to fight and control crime. Organizations like the National Crime Records Bureau (NCRB), a Government of India organisation and firms like Delhi-based ForensicsGuru (whose clients include the governments of Delhi, Orissa and Uttarakhand, the NIA and CBI) actively engage in crime analysis solutions, together with most big consulting companies like KPMG, Ernst and Young and KPMG.

 So what skills does a crime analyst need?

Crime analysts must have strong communication and analytical skills, as well as great writing ability. They need to be able to locate and interpret data and must be able to repackage and present it in a way that can be easily understood by others. They should have a passion for research and a genuine desire to assist and support law enforcement in preventing and solving crime.

Sounds interesting? Well, let’s hear of an actual example that I discussed in a post originally published in the Silicon India Blogs, where I talk about how the technique of hypothesis testing was used in a courtroom trial as a key piece of evidence to secure an indictment in a murder case.

The Kirsten Gilbert Case

Kirsten Gilbert was a nurse at the Veterans Affairs medical centre in Northampton, Massachusetts. She had built up quite a reputation among her colleagues at the hospital. Usually, she was the first one to notice that a patient was going into cardiac arrest and her colleagues had observed that she would remain calm, injecting epinephrine in an effort to restart the heart before emergency teams arrived. Some of the patients would survive but a large number would perish. Her colleagues named her “Angel of Death”.

Some staff members at the hospital showed concern over the unusually high death rates during Kirsten’s shift. Hospital authorities launched an investigation but the investigation could not implicate Kirsten as authorities concluded that the death rates for cardiac arrests in Veterans Affair medical centre were comparable to similar establishments elsewhere. Some staff members were not convinced and demanded another probe.

The hospital administration then hired a University of Massachusetts Professor, Stephen Gehlbach. He looked into hospital records on cardiac arrests and subsequent deaths. He then looked at the data on an annual number of deaths at the hospital from 1988(the year Gilbert joined) to 1997, broken down by shifts.  He then correlated the instances of deaths with the shifts in which Gilbert was present. This is what he observed:

Gilbert present Death on shift
Yes No Total
Yes 40 217 257
No 34 1350 1384
Total 74 1567 1641

As can be seen from the data there were a total of 74 deaths out of 1641 cases of cardiac arrests but 40 of these deaths occurred when Gilbert was on shift. Clearly, the data seems to suggest that there is a relationship between Gilbert’s presence and death on a shift. But one can also argue that this observation can be due to coincidence or random chance only!!! The challenge before Stephen Gehlbach was to show that it was very unlikely to observe the numbers that were being observed if Gilbert’s presence in the shift and Deaths on the shift were independent. He then computed how the data should have looked like had there been no relationship between Gilbert’s presence and deaths on shift. These are the numbers he came up with:

Gilbert present Death on shift
Yes No Total
Yes 11.589 245.4107 257
No 62.410 1321.589 1384
Total 74 1567 1641

Now the next thing that Gehlbach had to do was to figure out what were the chances of observing 40 deaths when you expected to observe only 12 (11.589) deaths. This can be seen as a simple coin toss in which the number of deaths can be thought of as the number of heads. The probability of seeing death is 74/1641 = 0.045. If we treat the 257 instances in which Gilbert was present as 257 coin tosses, what are the chances of seeing 40 or more deaths? It turns out we can use the binomial distribution to approximate this, on computing, this probability is 1 in 100 million!!! In other words, it is impossible to get 40 shifts with deaths from an ordinary chance-like variation.

This crucial analysis by Dr Gehlbach became an important piece of evidence which prompted the hospital administration to initiate a formal criminal investigation and try her in a court of law. Eventually, she was found guilty of murder and sentenced to life imprisonment.

The long arms of data analytics are indeed reaching far and wide. So for all you Sherlock Homes fans, here is an exciting career to think about. Use your aptitude for numbers, combined with your naturally curious and intuitive mindset to go about solving mysteries using data. Invest in some data analytics skills. Take charge…

Interested in a career in Data Science?
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Ch-02, pp 13-20, The numbers behind NUM3RS (2007), Keith Devlin, Gary Lorden

Applying Statistics in the courtroom: A new approach for attorneys and expert witnesses (2001), Philip Good

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