Exploratory Data Analysis: The First (and Sometimes Last) Step

by Matthew Barsalou, guest blogger

A good way to begin researching a topic is with exploratory data analysis (EDA). In his 1977 book Exploratory Data Analysis, John Tukey suggested using EDA to collect and analyze data—not to confirm a hypothesis, but to form a hypothesis that could later be confirmed through other methods.

In some cases, EDA can even eliminate the need for a more in-depth hypothesis test. Here's a case in point.

When I heard about the new Star Trek movie, I had started to complain to anybody who would listen (which was not many people) that director J. J. Abrams had used such a young cast in the 2009 Star Trek film.

With a tentative hypothesis of “the new Star Trek films use very young actors and actresses compared to the older Star Trek series,” I decided to look into this further. The first thing I did was collect data to use later in boxplots, which are a part of Tukey’s EDA.

Collecting Data for the Exploratory Analysis

I needed to determine the ages at which each main Star Trek actor first appeared; however, before I started looking for ages, I needed a method to determine whom I should consider as a main character in each series. To select the actors to consider I went to www.StarTrek.com and observed which characters were listed for each Star Trek series. This way I avoided biasing my results by selecting older or younger crewmembers who may not have had as much relevance as others.

The tables below list the characters and the episode or movie in which they first appeared. The name of the actor playing each character is then listed, and their year of birth as determined by viewing their entry at the Internet Movie Database. To determine the person’s age, the date of birth was subtracted from the year of first appearance. This resulted in rough calculations which could be wrong by a year, because month of birth and month of first appearance were not considered.

Table 1: Star Trek: The Original Series

Name	Character	First appeared in	Year of birth	Year of first appearance	Age +/- 1 year
William Shatner	James T. Kirk	The Man Trap	1931	1966	35
Leonard Nimoy	Spock	The Man Trap	1931	1966	35
DeForest Kelley	Leonard “Bones” McCoy	The Man Trap	1920	1966	46
James Doohan	Montgomery “Scotty” Scott	The Man Trap	1920	1966	46
George Takei	Sulu	The Man Trap	1937	1966	29
Nichelle Nichols	Uhura	The Man Trap	1932	1966	34
Walter Koenig	Pavel Andreievich Checkov	Amok Time	1936	1967	31

Table 2: Star Trek: The Next Generation

Name	Character	First appeared in	Year of birth	Year of first appearance	Age
Patrick Stewart	Jean-Luc Picard	Encounter at Farpoint	1940	1987	47
Jonathan Frakes	Will Riker	Encounter at Farpoint	1952	1987	35
Brent Spiner	Data	Encounter at Farpoint	1949	1987	38
Levar Burton	Geordi La Forge	Encounter at Farpoint	1957	1987	30
Michael Dorn	Worf	Encounter at Farpoint	1952	1987	35
Marina Sirtits	Deana Troi	Encounter at Farpoint	1955	1987	32
Gates McFadden	Beverly Crusher	Encounter at Farpoint	1949	1987	38
Wil Wheaton	Wesley Crusher	Encounter at Farpoint	1972	1987	15

Table 3: Star Trek: Deep Space Nine

Name	Character	First appeared in	Year of birth	Year of first appearance	Age
Avery Brooks	Benjamin Sisko	Emissary	1948	1993	45
Nan Visitor	Kira Nerys	Emissary	1957	1993	36
Rene Auberjonois	Odo	Emissary	1940	1993	53
Alexander Siddig	Julian Bashir	Emissary	1965	1993	28
Colm Meany	Miles O’Brien	Emissary	1953	1993	40
Terry Farrell	Jadzia Dax	Emissary	1963	1993	30
Armin Shimerman	Quark	Emissary	1949	1993	44
Cirroc Lofton	Jake Sisko	Emissary	1978	1993	15
Michael Dorn	Worf	The Way of the Warrior	1952	1995	46
Nicole de Boer	Ezri Dax	Image in the Sand	1970	1998	28

Table 4: Star Trek: Voyager

Name	Character	First appeared in	Year of birth	Year of first appearance	Age
Kate Mulgrew	Kathryn Janeway	Caretaker	1955	1995	40
Robert Beltran	Chakotay	Caretaker	1953	1995	42
Tim Russ	Tuvok	Caretaker	1956	1995	39
Robert Duncan McNeill	Tom Paris	Caretaker	1964	1995	31
Roxann Dawson	B’Elanna Torres	Caretaker	1958	1995	37
Garrett Wang	Harry Kim	Caretaker	1968	1995	27
Robert Picardo	The Doctor	Caretaker	1953	1995	42
Ethan Phillips	Neelix	Caretaker	1955	1995	40
Jennifer Lien	Kes	Caretaker	1974	1995	21
Jerry Ryan	Seven of Nine	Scorpion: Part 2	1968	1997	29

Table 5: Star Trek: Enterprise

Name	Character	First appeared in	Year of birth	Year of first appearance	Age
Scott Bakula	Jonathan Archer	Broken Bow: Part 1	1954	2001	47
Jolene Blalock	T’pol	Broken Bow: Part 1	1975	2001	26
Connor Trinneer	Charles “Trip” Tucker III	Broken Bow: Part 1	1969	2001	32
Dominic Keating	Malcom Reed	Broken Bow: Part 1	1962	2001	39
John Billingsley	Phlox	Broken Bow: Part 1	1960	2001	41
Linda Park	Hoshi Sato	Broken Bow: Part 1	1978	2001	23
Anthony Montgomery	Travis Mayweather	Broken Bow: Part 1	1971	2001	30

Table 6: Star Trek (2009)

Name	Character	First appeared in	Year of birth	Year of first appearance	Age
Chris Pine	James T. kirk	Star Trek (2009)	1980	2009	29
Zachary Quinto	Spock	Star Trek (2009)	1977	2009	32
Karl Urban	Leonard “Bones” McCoy	Star Trek (2009)	1972	2009	37
Zoe Saldana	Nyota Uhura	Star Trek (2009)	1978	2009	31
Simon Pegg	Montgomery “Scotty” Scott	Star Trek (2009)	1970	2009	39
John Cho	Hukaru Sulu	Star Trek (2009)	1972	2009	37
Anton Yelchin	Pavel Andreievich Checkov	Star Trek (2009)	1989	2009	30

EDA: Interpreting the Data with a Boxplot

Simply looking at the results in tables 1 through 6 led to me suspect my hypothesis may have been incorrect, but I still proceeded to create a Minitab boxplot with the data.

boxplot of star trek ages

The boxplot depicts the ages of the actors and actresses in each Star Trek series as well as in the 2009 reboot. The rectangular boxes represent the middle 50% of each data set and the vertical lines on top of the rectangular boxes represent the upper 25% of the data. The vertical lines on the bottom of the rectangular boxes represent the lower 25% of the data—except in the case of outliers. Outliers are unusually large or small observations and are represented by an asterisk. There is only one outlier in this boxplot, and that is Will Wheaton as Wesley Crusher in Star Trek: TNG.

The symbol that looks like a plus sign inside of a small circle is used to represent the average of the data set. The average age of actors and actresses in the 2009 reboot is 33.57 years, and this is just slightly lower than Star Trek: TNG, which had an average of 33.75 years of age. The highest average age was for Star Trek: TOS with an average of 36.57.

What truly stands out in the boxplot is the spread of the data. The distribution of actors' ages in the reboot was less than that of all of the other series. This would make sense as it would not be plausible to use actors or actresses in their 50s or 60s to portray people who are still attending Star Fleet Academy.

The hypothesis that originally started this was “the new Star Trek films use very young actors and actresses compared to the older Star Trek series,” but a look at the boxplots in figure one show that this may not be the case. In fact, there is no reason to proceed on to confirmation testing because my hypothesis can be discarded at this point.

It looks like I owe director J. J. Abrams an apology.

Exploratory Data Analysis Raises New Questions

Even a hypothesis that was discarded after performing EDA can lead to the...um...next generation of hypotheses, and new insights. In this case, my new hypothesis could be, “The actors and actresses in Star Trek are not getting younger; I am getting older.” The new hypothesis could also be explored with EDA prior to moving on to more robust methods.

However, in this case, I will not investigate my new hypothesis. I would rather just change the subject.

About the Guest Blogger:

Matthew Barsalou is an engineering quality expert in BorgWarner Turbo Systems Engineering GmbH’s Global Engineering Excellence department. He has previously worked as a quality manager at an automotive component supplier and as a contract quality engineer at Ford in Germany and Belgium. He possesses a bachelor of science in industrial sciences, a master of liberal studies and a master of science in business administration and engineering from the Wilhelm Büchner Hochschule in Darmstadt, Germany.

Photo of Star Trek figures by Miguel Bernas, used under creative commons 2.0 license.