Chi-square analysis compares the counts of two categorical variables to tell you if a relationship exists between the variables or not. It's a tool with many applications in the world of business and quality improvement. For example, let's say you manage three call centers and you want to know if solving a customer's problem depends on which center gets the call. To find out, you tally the successful and unsuccessful resolutions for each center in a table, and perform a chi-square test of independence on the data.
Practical applications like this are all well and good, but you can also apply chi-square analysis to answer important questions about factors in everyday life, and even about events like elections....or Halloween.
For example, there's been a lot of talk about gender gaps during this year's election, but I have yet to see anyone answer this Halloween-related question: If you're a character in a slasher film, is there a connection between your gender and your dying in some horrible manner?
Your gut reaction is probably, "Well, in every slasher movie, some crazed maniac chases a young woman around with a weapon. So there must be a connection." Anecdotally, that answer feels correct. But could you back up that assertion at a heated Halloween party? What do the data say? Chi-square analysis can help.
Categorizing Data about Deaths in Two Popular Horror Film Franchises
A quick web search revealed a site that helpfully offers (appallingly detailed) summaries of all of the deaths that have occurred in most major slasher and horror film franchises. I loaded the death data for the Halloween and Friday the 13th franchises into Minitab to see what I could learn. (You can download my datasheets here and here.)
First, I needed to categorize the deaths: while the downloaded table includes helpful details about, for example, the startling range of weapons used in stabbings, for this analysis there's no real difference between being stabbed with a knife and being stabbed with a pitchfork. I also removed a few deaths for which a clear cause couldn't be determined.
Here are the five categories I divided the deaths into:
- Stabbed (with anything)
- Blunt force trauma (including crushing and, in one case, a "bear hug")
- Vital parts removed (beheadings and such)
- Shot (by bullets, arrows, quills, and other projectiles)
- Exotic (like being cooked, frozen, or burned up in the atmosphere)
Tally and Cross Tabulation of Horror Movie Deaths
Next, I used Minitab Statistical Software to tally the victims' gender and type of death for each series by selecting Stat > Tables > Tally Individual Variables and selecting Counts and Percents.
Here are the results for the Friday the 13th series:
And the Halloween series:
We can see a couple of interesting things. First, the proportion of each category of death seems to be remarkably even between the two series; a few more characters die from being shot in the Halloween films, but otherwise the proportions are remarkably similar.
But more eye-opening is the evidence that, in both franchises, the idea that victims are predominantly women appears to be wrong. Just 30 percent of characters who die in the Halloween series are women, and only 34 percent are women in the F13 series.
That got me wondering whether the type of death inflicted on a character in these series was associated with the character's gender. Exactly the type of question a chi-square test was made to answer!
Chi-Square Test for Gender and Cause of Death in Slasher Film Series
I did the test on the Friday the 13th data first, selecting Stat > Tables > Cross Tabulation and Chi-Square in Minitab, and selecting "Gender" as the categorical variable for rows, and "Death Category" as the variable for columns.
The p-values for this test are high, at 0.158 and 0.144. For this series, then, we can't conclude that there's a connection between gender and cause of death, at least not at the .05 significance level. In addition, the fact that two of the cells in our chi-square table had counts below 5 makes the analysis suspect.
Let's take a look at the Halloween series:
The p-values for this test are low, at 0.043 and 0.031. However, even though the p-values support a connection between gender and cause of death in the Halloween series, the fact that two cells in this chi-square table also had counts below 5 makes this analysis suspect, too.
But since the relative percentages of death types for men and women were pretty comparable across both series, what if we combine the cause of death data? I did that in another data sheet, and ran the analysis again:
The p-values are very low at .004 and .003, so we can reject the null hypothesis and conclude that there is an association between gender and cause of death for all of the characters across both of these series. If we run a cross-tabulation on this data to see the proportion of each type of death accounted for by gender, we get a clearer sense of how this association plays out. The Assistant in Minitab 16 does a very nice job of reporting these results visually:
We also can learn something from the Assistant's graphical display of the percentage difference between the observed and expected counts of each death type by gender:
It appears that men account for more deaths that involve blunt force trauma and being shot (82% to 18% for both). In fact, more men than women are killed in each of these categories, although the proportion of deaths in the "exotic" category is not as extreme as the rest.
We can also look at this using Pareto charts of death category counts for each gender:
It's clear that stabbing is the leading cause of death for characters in these films, regardless of gender. After that, however, the order of categories changes. It appears that men in these films are more frequently dispatched by blunt force trauma and the removal of vital parts, with more exotic exits ranking fourth. In contrast, the exotic methods rank second for female characters, followed by blunt force trauma and the removal of vital parts, respectively.
Of course, this is really...erm...just splitting hairs, isn't it? The bottom line is that regardless of gender, if you're a character in one of these films, you can count on something horrible happening to you.
Thank heavens it's only a movie, and happy Halloween!