noldo: Mai from A:tLA. (electrons!)
[personal profile] noldo
Like almost everyone else, I've been watching That One Show over the last few weeks. I recently had an argument with an obsessive-minded scientist type regarding whether or not the non-whites on the show died in disproportionate droves. I therefore decided, being an obsessive-minded scientist type, to write everything down. (Obligatory note: this isn't terribly grammatical, or well-written. It's also poorly-formatted. Other obligatory note: I make the simplifying assumption that anyone who looks to be PoC can be identified as such for the purposes of analysis, similarly presented gender, et cetera.)



Notes: I disregard the Doctor, Amy, and Rory throughout. I disregard a few of the names listed on the credits, mostly for being voice actors -- whenever I think the discard needs extra rationalisation, I do mention it. Aliens disguised as human beings count as human beings for this purpose.


The Eleventh Hour --

13 people listed on the credits. I disregard four: younger Amy (since one character counts once), Atraxi Voice, Prisoner Zero Voice, and Patrick Moore. Of the remaining 9:

4 are white and male (Barney Collins (presumably Man With Dog), Ice Cream Man, Jeff, Mr. Henderson (from whom Amy commandeered car keys))
4 are white and female (Mrs. Angelo (Amy's next-door neighbour), and the mother + two children that Prisoner Zero impersonates.)
1 is a woman of presumably Indian origin (Dr. Ramsden).

Of these people, anyone impersonated by Prisoner Zero presumably survives the episode. We have no reason to believe that Jeff, Mr. Henderson, the ice-cream man, or Mrs. Angelo don't. It is strongly implied that Dr. Ramsden doesn't. Dead: 1, presumed not dead: 8


The Beast Below --

10 people listed in the credits. I disregard Winston Churchill (since his appearance is essentially a token to set up the next episode), and the voice actor for the Smilers; I also disregard 'the Winder' (presumed male). Of the remainder (7),

1 is a non-white woman (Liz Ten)
1 is a non-white man ('Peter', I assume That One Winder.)
2 are white and female (Mandy and the poetry-reciting Test Card Girl -- the inclusion of the latter is somewhat dubious, I admit.)
3 are white and male (Hawthorne, Morgan, Timmy.)

No deaths in this episode.


Victory of the Daleks --

Ten people listed in the credits. I disregard three of them for, well, being Daleks. Of the remainder,

2 are white women (Blanche, Lilian)
5 are white men (Winston Churchill -- well, to be fair, I think that's standard -- , Bracewell, Childers, Todd, the Air Raid Warden)

I believe two Spitfire pilots die, both white males. Not dead: 5


Time of the Angels/Flesh and Stone --

In total, 10 people listed in the credits. Of these,

1 is a white woman (River)
3 are non-white men (three of the clerics: I believe they were Angelo, Christian, and Pedro)
6 are white men (Octavian, Bob, Marco, Phillip, Alistair, and the hapless security guard).

River survives this two-parter. Nobody else does. Dead: 9


Vampires of Venice --

There are 11 people listed in the credits. Of these,

6 are white women (Rosanna, and five vampire girls).
1 is a non-white woman (Isabella).
1 is a non-white man (Guido).
3 are white men (Francesco, the Inspector, the Steward).

Dead: 9 -- Rosanna, the vampire girls, Isabella, Guido, Francesco. Not dead: 2 -- the Inspector, the Steward.



Amy's Choice --

There are 4 people listed in the credits. Of these,

2 are white women (Mrs. Poggit, Mrs. Hamill).
2 are white men (the Dream Lord, Mr. Nainby).

They are all fictional. I have decided not to count them at all in character totals.


The Hungry Earth/Cold Blood --

9 characters in total are listed in the credits. I disregard 4 for being green (breakdown: two female, two male, one male survives). Of the remainder,

1 is a non-white woman (Nasreen)
3 are white and male (Mo, Tony Mack, Elliot)
1 is a white woman (Ambrose)

All of these characters presumably survive. 3 Silurians dead.


Vincent and the Doctor --

There are 7 people listed in the credits.

5 are white males (Vincent van Gogh, Maurice, Bill Nighy, two schoolchildren).
2 are white females (the mother, the waitress).

None of these characters are killed.


Now here are some quick numbers:

Of the 56 characters in total, 21 are women (38%).
Of the 56 characters in total, 9 are PoC (16%).

There are 29 white men. There are 17 white women. There are 5 non-white men. There are 4 non-white women.

Disregarding Silurians and imaginary people, 21 characters are killed in total. Of these,

3 are non-white women. This is 75% of non-white women and 14% of all deaths.
4 are non-white men. This is 80% of non-white men and 19% of all deaths.

In total non-whites make up 33% of all deaths. Women make up 38% of all deaths.

The percentage of non-white characters that die is 78%. The percentage of white characters that die is 26%.




Here is some interpretation: non-white characters die twice as often as they would if the number of deaths were exactly proportional to population representation. White characters die about a third as often as demographics say they ought to. Only about a fifth of all non-white characters survived their episodes. Three-quarters of white characters did. While women make up a smaller percentage of the cast than the overall population of the world would seem to suggest, they die exactly proportionally to their representation.


How statistically significant is this? I offer without comment that in 21 deaths, we expect 3.375 PoC deaths. To test the hypothesis that non-white characters and white characters would in the long term have an identical probability, given existence, of dying (i. e. if non-whites made up 50 percent of the population, we would expect in the long term half of the deaths to be of non-white people), we can use the chi-squared statistic: using my observed and expected values for PoC and white deaths -- assuming that the total number of dead is 21, which gives me a) numbers and b) requires a chi-squared distribution with one degree of freedom, since the count for whites completely determines the count for non-whites, etc. -- I arrive at a χ² value of 4.64. Using Mathematica to look up the chi-squared distribution (with "CDF[ChiSquareDistribution[1.], 4.64]", but I think tables of this distribution are widely available), I get the number 0.97. Or, to helpfully interpret, the probability that non-white characters and white characters are not equal in their chance of dying is 0.97 (if this doesn't quite make sense: the chance that non-white characters and white characters will continue to die at unequal rates, given past trends, is 97%).

Edit, 11 June: Redoing this while less sleep-deprived, & additionally noting some rather helpful commenters below, I have the following points to add:

1. My chi-squared analysis in fact missed some of the information, i. e. didn't take into account that we were drawing 21 deaths from a pool of 56 people. Including this and redoing the test, the probability above is rather closer to 0.997 than 0.97 (oh dear, it's worse!).

2. [livejournal.com profile] danalwyn has some further discussion in this comment, using Python.

3. [livejournal.com profile] eve11 has both some redone chi-squared and an analysis of the problem using the binomial distribution instead (since chi-squared is better for larger sample sizes): here, using R.

I leave it to the reader to decide whether this meets their criteria for statistically significant racism.

Date: 10 Jun 2010 02:18 am (UTC)
adalger: Earthrise as seen from the moon, captured on camera by the crew of Apollo 16 (Default)
From: [personal profile] adalger
I'm ... enough of a math geek to almost understand this. To make it clearer for the less mathematically inclined though, you might want to express that as "97%", because there are those who would automatically add the % after 0.97 where it doesn't belong.

Date: 10 Jun 2010 03:27 am (UTC)
avendya: cover art for Jo Graham's Black Ships (Default)
From: [personal profile] avendya
Isaac again, or someone else?

Date: 10 Jun 2010 08:21 am (UTC)
such_heights: martha looking serious, her face shadowed (who: martha looking fierce)
From: [personal profile] such_heights
*sigh* Stop it, show! But thanks a lot for putting this together.

Date: 10 Jun 2010 09:09 am (UTC)
such_heights: mickey looking badass (who: mickey [big damn hero | brontide])
From: [personal profile] such_heights
*nod nod* Well, I'm going to link to this next time I do linkspam, if that's all right with you? I promise my flist will not come and yell at you (or if they do, they know I'll yell at them right back). But posting to comms at large - I don't know, I don't know how receptive Who fandom is to this stuff right now. :/

Date: 10 Jun 2010 02:15 pm (UTC)
From: [identity profile] danalwyn.livejournal.com
Testing OpenID login...also deleted and reposted because I can't count.

Anyway, experimental verification. What I was interested in is the probability that, given that your chance of dying is universal (x), seven people out of one pool of nine would die, and fourteen out of a second pool of forty-six would die (I think this is how your numbers work). Unfortunately, I got a different answer...

My calculation (indentations all screwed up):

#!/usr/bin/env python


import random


def probCalculator(nTimes = 1000):
"""
Silly calculator for running probabilities

"""
random.seed()

results = {}

for prob in [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]:
results[prob] = 0
for iteration in range(nTimes):
# Do this however many times you want
nPOC = 0
nWh = 0
for person in range(9):
# Do it over nine people
if random.uniform(0.0, 1.0) < prob:
nPOC += 1
for person in range(46):
# Do it 46 people
if random.uniform(0.0, 1.0) < prob:
nWh += 1

if nPOC >= 7 and nWh <= 14:
# If we meet the critera, record it
results[prob] += 1


for prob in results.keys():
print "The percentage chance of this happening for probability %f is %f" % (prob, float(results[prob])/nTimes)


Results from first iteration:
>>> probCalculator(nTimes = 500000)
The percentage chance of this happening for probability 0.500000 is 0.000510
The percentage chance of this happening for probability 0.200000 is 0.000334
The percentage chance of this happening for probability 0.400000 is 0.002974
The percentage chance of this happening for probability 0.800000 is 0.000000
The percentage chance of this happening for probability 0.300000 is 0.002680
The percentage chance of this happening for probability 0.600000 is 0.000008
The percentage chance of this happening for probability 0.100000 is 0.000004
The percentage chance of this happening for probability 0.900000 is 0.000000
The percentage chance of this happening for probability 0.700000 is 0.000000


For the second iteration, scan over probabilities from 0.30 to 0.45:
The percentage chance of this happening for probability 0.430000 is 0.002090
The percentage chance of this happening for probability 0.360000 is 0.003758
The percentage chance of this happening for probability 0.400000 is 0.002928
The percentage chance of this happening for probability 0.330000 is 0.003212
The percentage chance of this happening for probability 0.440000 is 0.001822
The percentage chance of this happening for probability 0.370000 is 0.003514
The percentage chance of this happening for probability 0.300000 is 0.002574
The percentage chance of this happening for probability 0.410000 is 0.002774
The percentage chance of this happening for probability 0.340000 is 0.003388
The percentage chance of this happening for probability 0.450000 is 0.001474
The percentage chance of this happening for probability 0.380000 is 0.003612
The percentage chance of this happening for probability 0.310000 is 0.002910
The percentage chance of this happening for probability 0.420000 is 0.002558
The percentage chance of this happening for probability 0.350000 is 0.003500
The percentage chance of this happening for probability 0.390000 is 0.003142
The percentage chance of this happening for probability 0.320000 is 0.003112


So I'm getting the chances being even lower, that is for a maximal chance of about 36% that a given character dies, the chance of 7 or more characters out of nine dying while fourteen or less out of forty-six die is 0.376%, or 99.7%, much less then you calculated. Since this is a deterministic problem and the Chi squared method should be absolute, I've obviously screwed up a number somewhere, or there's a very narrow peak...

Date: 10 Jun 2010 07:03 pm (UTC)
glass_icarus: (bey telephone still)
From: [personal profile] glass_icarus
..........

All right, signal-boosting this shortly. (If people want numbers, they can have numbers, dammit.)

Date: 10 Jun 2010 09:30 pm (UTC)
legionseagle: (Default)
From: [personal profile] legionseagle
Not challenging the general hypothesis, but isn't Angelo white?

ETA: sorry, no, stupid comment - I'd completely misremembered that scene. Who's the first red cassock to die? Is that Angelo?
Edited Date: 10 Jun 2010 09:38 pm (UTC)

Date: 10 Jun 2010 09:44 pm (UTC)
legionseagle: (Default)
From: [personal profile] legionseagle
Yes, I Googled him after making my first comment. Now, am I right in thinking that the two who die first (before Bob) are Angelo and A.N. Other (who is white)? Who's A.N. Other?

Date: 11 Jun 2010 07:04 am (UTC)
legionseagle: (Default)
From: [personal profile] legionseagle
I need to re-watch; however, what this discussion is clarifying (which supports your hypothesis) is that interchangeable cannon-fodder parts (who exist simply to die and so prove the Monster of the Week means business) are more likely to be cast using POC, while cosmically meaningful/memorable deaths (eg Fr Octavian) are more likely to be cast with white actors (Vampires of Venice is a bit of an outlier here, but then I think the Guido storyline there was riffing of Othello and in any event it's trends you're looking at, not specifics).

Date: 10 Jun 2010 11:33 pm (UTC)
sqbr: (torchwood spoilers)
From: [personal profile] sqbr
I'm glad you did this, I had a gut feeling this was going on but it's good to have concrete numbers to point to.

Would you mind if I reposted this to [livejournal.com profile] whoisms?

Date: 12 Jun 2010 02:35 am (UTC)
sqbr: pretty purple pi (I like pi!)
From: [personal profile] sqbr
Oh yeah, I'm not on any of the other Dr Who comms myself partly due to hearing stories of failyness.

Anyway, 'tis posted! I'm really glad you did the stats analysis, it's a nice counterargument to have prepared for any "Oh but it's just a coincidence" crap.

Date: 11 Jun 2010 12:49 am (UTC)
surpassingly: (geeky: well at least not undefined)
From: [personal profile] surpassingly
This is a brilliant analysis, thank you!

Date: 11 Jun 2010 04:29 am (UTC)
From: [identity profile] eve11.livejournal.com
It's a good idea to run some stats but I think the chi-squared statistic is not what you want in this case. The probability statements that come from chi-squared tests are based on large sample theory, and at least your POC sample is pretty small. For example I ran the table in R (the stats programming package) and it gave me (a) a more extreme p-value than you state, but (b) a warning that the chi-squared test might not be very good in this case:
 xchars
           survival
race        Died Lived
  Non-White    7     2
  White       12    35
> summary(xchars)
Number of cases in table: 56 
Number of factors: 2 
Test for independence of all factors:
        Chisq = 9.198, df = 1, p-value = 0.002423
        Chi-squared approximation may be incorrect


I would suggest that the best way to test your hypothesis is to use the Binomial distribution, because that is the exact distribution you are working with in terms of survival probabilities in two different groups. For example I can construct 95% confidence intervals for prob(die|non-white) and prob(die|white), again using R, based on the Binomial:
#non-whites
> binom.test(xchars[1,], conf.level=0.95)$conf
[1] 0.3999064 0.9718550  
attr(,"conf.level")
[1] 0.95

#whites
> binom.test(xchars[2,], conf.level=0.95)$conf
[1] 0.1394491 0.4034952
attr(,"conf.level")
[1] 0.95


So a 95% CI for Pr(die|non-white) is (0.39, 0.97), and a 95% CI for Pr(die|white) is (0.14, 0.40). Still very telling, isn't it? Note that the CI for non-whites is much larger than that for whites; this is because the sample size is smaller.

Also note that these intervals overlap juuust a tiny bit so if I were testing a two-sided hypothesis (equal vs. not) at the alpha = 0.05 level, I would just barely fail to reject the Null. That makes me think your true p-value is just a tiny bit larger than 0.05, probably less than 0.1 (which would correspond to a CDF probability as you calculated above of 0.95 to 0.90).

So um, yeah, all that math to say, I agree with you.

But it's also a very interesting thought to consider how much of a hole they've dug themselves. For example, to reverse the trend they'd not only have to make an ep where no non-white characters die, but they'd have to start killing off whites. And because they tend to present characters in chunks (episodes) with generally more white characters than non-whites, the sample size for the whites will keep getting disproportionately large relative to the non-whites. The power of the test depends on the smaller sample size, which I guess is the stats-y way of saying "hey, let's see more POC at least!" ;)

Date: 11 Jun 2010 02:27 pm (UTC)
From: [identity profile] eve11.livejournal.com
No problem. I should say also that I am here via cofax7; I didn't want you to think I was just some crazy stats person trolling blogs ;) I think that the binomial analysis is probably the way to go, and in that case the numbers are marginally better than the ones you stated with the chisquare, but they are still not very good.

The interpretation for the confidence intervals is (I think) also easier to get one's head around than an interpretation of a chi-squared test. I think the chisquare is more like: repeat this same experiment with 56 people over and over again: Draw out 21 deaths at random from your population of 56 people, where 9 are non-white and 47 are white, and examine the breakdown of white vs. non-white for that specific number (21) of deaths. Even then, with such a small sample, the chi-squared approximation (which is based on large samples getting relatively Normally distributed) is not what you want. You want the hypergeometric distribution (http://stat.ethz.ch/R-manual/R-patched/library/stats/html/Hypergeometric.html), the "balls and urns" distribution that so plagues us in undergrad probability classes.

Again using R, let's say the white balls as described in that link are the white characters, and the black balls are the non-white characters (convenient, yeah?). Then to get a p-value for that characterization, you want to say, "Given that I draw 21 'deaths' at random out of a pool of 9 non-white characters and 47 white characters, what are the chances that 14 or fewer are white?". Because there's only 9 non-whites, this means that you draw either 12, 13, or 14 whites. In R:
> sum( dhyper(c(12,13,14),47,9,21))
[1] 0.01011127


So the P-value from the exact calculation is 0.01. If you repeated that experiment 100 times, on average only once would you obtain a result as extreme or more than what was observed. Null hypothesis of random assignment of death vs. life by race (at alpha=0.05) rejected. This is still a small probability, but slightly larger than the chisquare approximation of 0.003 you cite.

This is also different than the binomial confidence intervals and the p-value of about 0.06 for the test of equality of survival rates. You can think of the binomial intervals as estimating the probability of survival for white vs. non-white if you were drawing persons from two infinite populations, and flipping a coin with probability p for each one to determine whether they lived or died. The p-value is larger in this case because it kind of averages over all the possible total numbers of deaths you would care to draw. I think this is the way to think about the problem because it estimates the survival rate directly and also provides a better interpretation for what would keep happening in the future, as we add more random draws of random characters who could be either white or non-white. We don't particularly care about 21 deaths out of 56 people; we are looking at estimating a probability of survive vs. die for any one random person chosen out of the white population vs. chosen out of the non-white population.

Of course this is also all based on the idea that you have independence, too. Which is most likely not the case in assigning race to characters. For example the script for Vampires of Venice calls for a father and a daughter. And as written, before thinking about casting at all, it is known that both the father and the daughter will die. But the problem is that there is a very very high likelihoood that they will be assigned the same race in casting, since they are father and daughter. Same deal with Rosanna and Francesco. For these types of calculations, that dependence essentially makes your sample size smaller, which will tend to widen your confidence intervals, increase your p-values, and decrease your power.

Date: 12 Jun 2010 02:34 pm (UTC)
From: [identity profile] eve11.livejournal.com
I wanted to say, the more I think about it, the more I wonder what the effects of both episodes and family structure have on the numbers. Both of those phenomena will tend to cause dependence in the way characters within families and to a smaller extent within episodes are assigned to race. For example, everyone except the main characters dies or is erased from time in Time of Angels/Flesh and Stone. So the only way to "get ahead" in this episode is to totally whitewash the cast. Or maybe (and by this time we are at the point where samples are too small to get good stats and it is an ethical/emotional argument) make the commander a PoC instead of white and not kill off the first two PoC like redshirts in the episode.

I guess, like what I said before, the strength of evidence for this is driven by the size of the smaller population, which is at least an argument for having more PoC in the stories. But the sample size is small enough that conclusions could still swing pretty wildly based on what happens in the next three episodes. *sighs* I'm a statistician by trade so it's essentially my job to go "but wait!..." and harsh people's results. :(

Date: 11 Jun 2010 05:10 am (UTC)
liviapenn: a little red bowtie rotating in space (who: BOWTIES ARE COOL)
From: [personal profile] liviapenn
In "Victory of the Daleks" I think you missed some deaths-- two "redshirt" security guards (both white) are zapped by a Dalek and die, in addition to any Spitfire pilots who died in space.

ETA: Also I know you're only counting deaths of people who were in the credits, but I feel like it would be more accurate to the feel of "did anyone die in this episode" if you counted the white girl who is killed by the monster in "Vincent and the Doctor." Even if she didn't have any lines beforehand, her death feels, to me, like a major part of the episode. (Although, again, it took someone else's review to point out that it's so typical to have the young girl as the default victim-- why couldn't it have been a beloved son or husband?)

It actually took me a second to recall who the Inspector was in "Vampires of Venice" -- before I read this post, I actually didn't think that episode came off that badly in terms of killing PoC, since really, *all* the characters who had names and were important to the plot died (ie, Guido, Isabella, Rosanna and Francesca). And at least Guido and Isabella both got to affect the plot in major ways and then die heroically and defiantly, as opposed to an episode like "Eleventh Hour," where the only PoC has no sympathetic traits whatsoever, and even if she had been a cool person, she still dies in a totally pointless way, basically just because the monster has to kill *someone*... But what it really goes to show show how *easy* it would have been to make both episodes balance-- all it would take is *one* PoC in each episode who (1) talks and (2) doesn't die.
Edited Date: 11 Jun 2010 05:15 am (UTC)

Date: 11 Jun 2010 01:09 pm (UTC)
petra: Paul McGann as the Eighth Doctor, text: and eats you when you're sleeping (Dr. Who - Zagreus)
From: [personal profile] petra
Thank you for this. It is good to have statistics on something I knew in the back of my head.

Date: 12 Jun 2010 04:04 am (UTC)
rhivolution: Freema Agyeman is badass (save the time lord save the world: Marth)
From: [personal profile] rhivolution
Adding this to my memories to come back to at a later date, thank you for doing this processing.

If you get a chance, it might be interesting to work back a season or two and see how an RTD series compares to a Moff series. I'd do it myself but I've never had training in statistics.

Date: 12 Jun 2010 04:23 am (UTC)
jaydeyn: Gwen asking What is this Fuckery? (WTF?)
From: [personal profile] jaydeyn

This is an excellent post and I'll definitely be using your analyses (great comments too!) whenever this comes up and people are being dense.

:)
Jaydeyn

Date: 20 Jun 2010 04:28 am (UTC)
wanderlight: (Default)
From: [personal profile] wanderlight
You are very awesome for doing this. And also very awesome in general, naturally. ♥

Date: 1 Jul 2010 05:23 am (UTC)
From: [personal profile] alephnul
I ran across this post when you linked to it here.

While it doesn't change any of what you are saying, I think you have an error in this. You state that 3 out of 4 non-white women characters die, but it is actually 2 out of 4 (Nasreen and Liz X survive, while Dr. Ramsden and Isabella die). This makes it 6 out of 9 non-white characters killed instead of 7 out of 9.

Date: 11 Jul 2010 09:27 pm (UTC)
shinyopals: (Default)
From: [personal profile] shinyopals
Just been linked to this from a friend who read my s5 overview. Thanks for the number crunching! It's definitely something to think about.

Do you know if you or anyone else has done similar for s1-4.5? I am curious as to whether the show's got any better or worse or just stayed the same over time.

Hmm... also makes me wonder if an analysis of the numbers of "good" PoC vs "bad" PoC compared to white characters might prove interesting. (Heh, sorry, I see some maths I start to make plans!)
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