Thanks to my brother I became aware of this article about bat cunnilingus today. My brother, knowing how entertained I
had been by a bat felating itself at
Disney on my honeymoon, decided that this would be just the sort of article
that I’d like. Knowing the kind of examples I put in my textbooks I suspect his
email is the first of many. Anyway, this article suggests that male bats engage
in cunnilingus with females. Female bats, that is. They have videos to prove
it. Male bats like cunnilingus so much that they don’t just use it as foreplay, but
they get stuck in afterwards as well. The article has two main findings:

- The more that males (bats) engage in
cunnilingus, the longer the duration of intercourse,
*r*= .91 (see their Figure1). They tested this with a Pearson*r*, based on 8 observations (although each observation was the average of several data points I think – it’s not entirely clear how the authors came about these averages). They conclude that this behaviour may be due to sperm competition in that males sort of ‘clean out’ the area before they procreate. They argue that the longer intercourse duration supports this argument because longer duration = greater chance of paternity. - The more that males engage in pre-intercourse
cunnilingus, the less they engage in post-intercourse cunnilingus,
*r*= -.79 (see their Figure2). They again tested this with a Pearson*r*, based on 8 observations. They conclude “… the negative relationship between the duration of pre- and post-copulatory cunnilingus suggests the possibility of sperm competition. Thus, the male removes the sperm of competitors but apparently not its own – lick for longer before but less after copulation, if paternity uncertainty is high.”

There are several leaps of faith in their conclusions. Does
longer duration necessarily imply greater chance of paternity? Also, if sperm
competition is at the root of all of this then I’m not sure post coital cunilingus
is really ever an adaptive strategy: consuming your own sperm hardly seems like the best method of impregnating your mate. Yes, I’m still talking about bats here,
what you choose to do in your own free time is none of my business.

### Enough about Cunnilingus, what about Statistics?

Anyway, I want to make a statistical point, not an
evolutionary one. It struck me when looking at this article that finding 2 is
probably spurious. Figure 2 looks very much like two outliers are making a
relationship out of nothing. With only 8 observations they are likely to have a
large impact. With 8 observations it is, of course, hard to say what’s an outlier
and what isn’t; however, the figure was like a bat tongue to my brain: my
juices were flowing. Fortunately, with so few observations we can approximate
the data from the two figures.

*I emphasises that these are quick estimates of values based on the graphs and a ruler*. We have three variables estimated from the paper:**pre**(pre-intercourse cunnilingus),**post**(post-intercourse cunnilingus),**duration**(duration of intercourse).
We’re going to use R, if you don’t know how to use it then
some imbecile called AndyField has written a book on it that you could look at. We can input these
approximate scores as:

pre<-c(46, 50, 51, 52, 53, 53.5, 55, 59)

post<-c(162, 140, 150, 140, 142, 138, 152, 122)

duration<-c(14.4, 14.4, 14.9, 15.5, 15.4, 15.2, 15.3, 16.4)

bat<-data.frame(pre, post, duration)

Ok, so that’s the three variables entered, and I’ve made a
data frame from them called

**bat**.
Let’s load some packages that will be useful (if you don’t
have them installed then install them) and source Rand Wilcox’s very helpful
robust functions:

library(ggplot2)

library(Hmisc)

library(boot)

source("http://dornsife.usc.edu/assets/sites/239/docs/Rallfun-v20")

Let’s draw
some rough replicas of Figures 1 and 2 from the paper:

qplot(pre, post, date = bat, ylim = c(85, 200), xlim = c(44, 60)) + stat_smooth(method = "lm")

qplot(pre, duration, date = bat, ylim = c(13, 18), xlim = c(44, 60))+ stat_smooth(method = "lm")

As you can see the figures - more or less - replicate their
data. OK, let’s replicate their correlation coefficient estimates by executing:

rcorr(as.matrix(bat), type = "pearson")

gives us

pre
post duration

pre 1.00
-0.78 0.91

post
-0.78 1.00 -0.75

duration 0.91
-0.75 1.00

n= 8

P

pre post duration

pre
0.0225 0.0018

post 0.0225 0.0308

duration 0.0018 0.0308

So, we replicate the pre-intercourse cunnilingus (Pre) –
duration correlation of .91 exactly (

*p*= .0018), and we more or less get the right value for the pre-post correlation: we get*r*= -.78 (*p*= .0225) instead of -.79, but we’re within rounding error. So, it looks like our estimates of the raw data from the Figures in the article aren't far off the real values at all. Just goes to show how useful graphs in papers can be for extracting the raw data.
If I’m right and the data in Figure 2 are affected by the
first and last case, we’d expect something different to happen if we calculate
the correlation based on ranked scores (i.e. Spearman’s rho). Let’s try it:

rcorr(as.matrix(bat), type = "spearman")

pre post duration

pre 1.00
-0.50 0.78

post
-0.50 1.00 -0.51

duration 0.78
-0.51 1.00

n= 8

P

pre post duration

pre
0.2039 0.0229

post
0.2039 0.1945

duration 0.0229
0.1945

The Pre-duration correlation has dropped from .91 to .78 (

*p*= .0229) but it’s still very strong. However, the pre-post correlation has changed fairly dramatically from -.79 to*r*= -.50 (*p*= .204) and is now not significant (although I wouldn’t want to read to much into that with an*n*= 8).
What about if we try a robust correlation such as the
percentile bend correlation described by Wilcox (2012)? Having sourced Wilcox’s
functions we can do this easily enough by executing:

pbcor(bat$pre, bat$post)

pbcor(bat$pre, bat$duration)

For the pre
post correlation we get:

$cor

[1] -0.3686576

$test

[1] -0.9714467

$siglevel

[1] 0.368843

$n

[1] 8

It has changed even more dramatically from -.79 to

*r*= -.37 (*p*= .369) and is now not significant (again I wouldn’t want to read to much into that with an*n*= 8, but it is now a much smaller effect than they’re reporting in the paper).
The pre-duration correlation fares much better:

$cor

[1] 0.852195

$test

[1] 3.989575

$siglevel

[1] 0.007204076

$n

[1] 8

This is
still very strong and significant,

*r*=*.85 (**p*= .007). We could also try to estimate the population value of these two relationships by computing a robust confidence interval using bootstrapping. We'll stick with Pearson*r*seeing as that's the estimate that they used in the paper but you could try this with the other measures if you like:
bootr<-function(data, i){

cor(data[i, 1],data[i, 2])

}

bootprepost<-boot(bat[1:2], bootr, 2000)

boot.ci(bootprepost)

bootpreduration<-boot(bat[c(1, 3)], bootr, 2000)

boot.ci(bootpreduration)

If we look at the BCa intervals, we get this for the
pre-post correlation:

Level
Percentile BCa

95% (-0.9903,
0.5832 ) (-0.9909, 0.5670 )

and this for the pre-duration correlation:

Level
Percentile BCa

95% ( 0.6042,
0.9843 ) ( 0.5022, 0.9773 )

In essence then, the true relationship between pre- and
post-intercourse cunnilingus duration lies somewhere between about –1 and 0.6.
In other words, it could be anything really, including zero. For the
relationship between pre-intercourse bat cunnilingus and intercourse duration
the true relationship is somewhere between

*r*= .5 and .98. In other words, it’s likely to be - at the very worst - a strong and positive association.### Conclusions

What does this tell us? Well, I’m primarily interested in
using this as a demonstration of why it’s important to look at your data and to
employ robust tests. I’m not trying to knock the research. Of course, in the
process I am, inevitably, sort of knocking it. So, I think there are three
messages here:

- Their first finding that the more that males (bats) engage in cunnilingus, the longer the duration of intercourse is very solid. The population value could be less than the estimate they report, but it could very well be that large too. At the very worst it is still a strong association.
- The less good news is that finding 2 (that the more that males engage in pre-intercourse cunnilingus, the less they engage in post-intercourse cunnilingus) is probably wrong. The best case scenario is that the finding is real but the authors have overestimated it. The worst case scenario is that the population effect is in the opposite direction to what the authors report, and there is, of course, a mid ground that there is simply no effect at all in the population (or one so small as to be not remotely important).
- It’s also worth pointing out that the two extreme cases that have created this spurious result may in themselves be highly interesting observations. There may be important reasons why individual bats engage in unusually long or short bouts of cunnilingus (either pre or post intercourse) and finding out what factors affect this will be an interesting thing that the authors should follow up.