Shake that booty

Saw this study in the news:

"They found those with alluring walks were the furthest away from ovulation. A British expert said the research, featured by New Scientist magazine, supported the idea women disguise their fertility to deter unsuitable partners...The women who were most fertile at the time of the experiment walked with fewer hip movements and with their knees closer together. She now thinks the findings tally with other research suggesting that women want to conceal their ovulation from males other than their chosen partner."

And all the stories seem to be derived from New Scientist:

"This showed a correlation between the way the women walked and their time of the month. The women who were fertile walked with smaller hip movements and with their knees closer together."

Is this the media misrepresenting scientific research? Nope, this is evolutionary psychology! The study is an online pre-publication of Provost et al in Archives of Sexual Behavior (there are some great looking articles in there, like a book review of 'God hates fags'):

"In this study, we found that men responded to the changes in gait women demonstrate across the menstrual cycle. Without knowing the differences between the women they were rating, men were significantly more likely to rate women walkers in their luteal phase as more attractive. This finding contradicts research in face research, where men judge women to be more attractive at times of peak fertility (Roberts et al., 2004).

It is possible that faces and gait present different information because of the intimacy with which the stimulus is viewed. For example, faces can only be seen in a fairly close encounter, whereas gait patterns can be seen from a large distance. If women are trying to protect themselves from sexual assault at times of peak fertility, it would make sense for them to advertise attractiveness on a broad scale when they are not fertile, yet still being attractive to people they choose to be with (i.e., during face-to-face interactions). Thus, it is necessary to investigate how men prone to using sexual violence view the walking stimuli, as well as to test the use of sexual coercion both in and outside of couples across the menstrual cycle, to investigate if unadvertised ovulation is adequately protecting a woman’s reproductive fitness interests."

Yep, women protect themselves against sexual assault at times of peak fertility by getting themselves raped when they aren't fertile - clever girls. Not so clever men, clearly their 'sexy hips' detection module is dysfunctional.

So let's see what the study actually shows.

[Summary to avoid reading this overlong post: despite what the paper itself and the news articles say, although men did rate some gaits as more attractive than others, they actually find that they didn't differ in the attractiveness they assigned to women in their 'more' or 'less fertile' phases, and although there were some poorly characterised differences in gait between the 'more' and 'less fertile' phases, they didn't differ in their hip movements or knee distance].

They looked at first year undergraduates and "women from the community" with 36 off, and 23 on "hormonal birth control":

"A female researcher met the participants, informed them that the study was investigating motion across the menstrual cycle, and obtained their informed consent."

Blinding doesn't appear to be big in evolutionary psychology research, I like to think the students knew exactly what they were trying to show and deliberately fucked up the results.

So they then estimated the phase of these subjects in their menstrual cycle (from date of last period and cycle length):

"NHBC[non-hormonal birth control] women participated during the late follicular phase (high fertility phase; 14–16 days before their next period) or the luteal phase (low fertility phase; 5–7 days before their next period, to limit the influence of pre-menstrual symptoms[***]). Cycle stage was confirmed using salivary ferning"

If you don't know about female menstrual cycles have a look here, basically peak fertility is around five days before ovulation and two days after, the follicular phase is after menstruation and before ovulation so the late phase here is around about ovulation (i.e. peak fertility). The luteal phase follows ovulation and the point here is around a week after ovulation (the luteal phase is normally 14 days long, and the follicular phase is also around 14 days long but varies with cycle length). Salivary ferning is a rather old-fashioned and unreliable technique similar to looking at cervical mucus and is popular in 'natural' family planning. Personally I'd have at least used tests of urinary luteinising hormone (LH) to detect ovulation*. Still, they are likely to have at least vaguely segregated on ovulatory phase.

So then they either recorded the women then and there (if they were in one of the correct menstrual phases, or if they were on 'hormanal birth control'). They got other NHBC women back to take measurements in both menstrual phases. So they recorded 41 body markers and used these to calculate "15 virtual markers corresponding to the major joints in the body". Then they did some complicated maths:

"To reduce the dimensionality of the data, the time series of the virtual markers were decomposed into a Fourier series, and then a principal components analysis was applied to the resulting Fourier representation"

This essentially tried to summarise the data in terms of simple mathematical functions (Fourier analysis) and then to come up with a smaller number of factors that best summarises the larger data set (principal component analysis) potentially discovering hidden structure. They then took this 12 principal component model and used the 12 factors to try and construct an equation that could categorise the women as being in the follicular or luteal phase based on them (discriminant function analysis) (they also compared follicular phase women to women on birth control).

Obviously there is a big risk here of overfitting the data - you've got 12 different factors that can be combined together in any way you want to try and distinguish the two groups - and only data from 19 women to compare the follicular and luteal phases (20 women available to compare follicular and birth control). Ideally you'd go and get another sample of women to test your discriminant function on to see if it can accurately classify them. In this paper they attempt the somewhat less ideal approach of removing one woman from the analysis and fitting an equation to the remaining women, and seeing if the removed woman is then correctly classified. Then they use a Z-test to compare the results of removing each woman in turn to what would be expected by chance (50% misclassified).**:

"The linear discriminant function for NHBC women significantly discriminated women at peak fertility from women in the luteal phase (z = 2.59, p < .01, n = 38). A total of 71% of the walkers were classified correctly.2 79% of the ovulation phase walks were classified correctly (four women were misclassified), and 63% of the luteal phase walks were classified correctly (seven women were misclassified). Only one woman was misclassified in both stages. The linear discriminant function for HBC women and NHBC women in the late follicular phase did not significantly discriminate women of peak fertility from women using hormonal birth control (z = 1.26, p > .05, n = 40), with 40% of women classified correctly with this linear discriminant function."

That is the data from the other women lead to equations that could predict the correct menstrual phase by some combination of the 12 gait-derived factors in 9/19 women (3 misclassified on the follicular phase, 6 on the luteal phase, 1 on both phases). Women on hormonal birth control could not be discriminated from women in the follicular phase by using these 12 factors.

So there is some limited evidence that there might be some differences in the gait between women in the follicular phase of their cycle and women in the luteal phase. But they didn't stop here. They then went on the generate hypothetical extreme women using their disciminant function (see here for an animation):

"Upon visually observing these two walkers, the lateral distance between the knee and ankle joints and the hip movement appeared to be the major differences between fertile and non-fertile women"****

But, when they actually looked at the real (as opposed to hypothetical) data they found no statistically significant difference in these measurements between the follicular and luteal stage women. Now you or I might conclude that the findings of a difference using discriminant functions was a rather slim and unreliable one, but not our intrepid researchers, the real evolutionary psychology is yet to come. But we do have one problem, women using hormonal contraceptives have hormone levels that mimic the luteal phase (remember that diagram?), therefore they ought to differ from follicular phase women if these differences are hormonally driven:

"It is possible that this result was due to fluctuations in personality dimensions of women not using hormonal birth control. For example...perhaps HBC in comparison to NHBC women are more extroverted or agreeable in general, so their gait reflects such traits at all times, but such extroversion or agreeableness is pronounced in NHBC women only during times of peak fertility...It is reasonable to assume that HBC women, in contrast to NHBC women in general, are more open to engaging in sexual relations...NHBC women at peak fertility are more interested in sexual activity, especially with extra-pair partners...Thus, walking patterns may be similar because of the interest in sexual activity of NHBC women at peak fertility and HBC women...However, it may simply be that hormonal levels in HBC women may affect their walk so that they are indistinguishable from NHBC women at peak fertility. Women using hormonal birth control have more circulating sex hormones than NHBC women in their luteal phase, when estrogen begins to drop. These extra-elevated levels of estrogen may affect the muscles and ligaments of the body, and thus women’s gaits "

Hmm, yeah, maybe women on the pill walk like dirty slags, I'm not sure I'd like to speculate. If only we had some way to know if higher levels of oestrogen in women on hormonal contraceptive compared to women in the luteal phase means that women on contraception don't differ from follicular stage women. Maybe, and this is just a hunch, we could compare the women on contraceptives to the luteal phase women, or did that not occur to them?

Anyway, onto the main event:

"A total of 43 men in an introductory psychology course participated in this study for course credit."

Ah, psychology students, where would we be without them? So they got them too look at point-light displays using the 15 virtual joint markers:

"We told the participants that they would see point-light walkers of women on the screen, and their task would be to rate the attractiveness of the walkers on a 6-point Likert-like scale"

So what did they find?

"Late follicular walks had a similar attractiveness level (M = 3.66, SD = .5) as walks recorded in the luteal phase of the menstrual cycle (M = 3.56, SD = .5) when compared with a paired t-test"

No?! I thought men preferred the less fertile women? Well what they do next is either clever, or stupid, depending on your point of view. So basically, they assign each woman a 'degree' of menstrual cycle based on walk. That is they used the discriminant function to transform menstrual phase into a continuous variable ("menstrual cycle stage z-score"). Then they fitted various models relating "menstrual cycle stage z-score" to the attractiveness rating z-score to try and squeeze out a result. All you need to know is that eventually they managed to fit a model** that suggested that the more luteal-like the walk, the higher the rated attractiveness - and we have to bear in mind that the relationship is between the discriminant function score and the attractiveness rating - there are no real life measures of ovulation being used here - and there is an obvious caveat that extreme data points could be skewing all the results (which are pretty tenuous here) such that one woman had a weird sexy walk in one menstrual phase that drove the discriminant function (it's not like these women were blinded as to which menstrual phase they were in or the aims of the study!):

"Each SD of menstrual cycle score increase resulted in a 0.08 increase in the z-score of attractiveness rating, meaning lower perceived attractiveness"

So, when you look at gait scores 3 standard deviations from the mean, values so extreme that only .13% of scores would be more extreme than this, then the difference in attractiveness score would be .24 (41% of scores would be more extreme than .24 of a standard deviation). That is, the relationship is rather a weak one.

So the conclusion is that this isn't a completetely stupid paper, the use of statistics is puzzling (but that isn't what I intended to go into here), but the findings are a lot less exciting that the press, and even the paper makes out. We've got some evidence that women's gaits may vary in some poorly characterised way with menstrual cycle. We have some further evidence that if you try and find a way to use gait to generate a mathematical function to discriminate between women in the follicular and luteal phases of the menstrual cycle then men rate those gaits that score very highly on this discriminant function as being more attractive than gaits that score very low. Anything is else is pretty much just evolutionary psychology just-so stories. Remember, if they had found that women had 'sexier' gaits when in the 'fertile' follicular phase they would have declared it further evidence for women unconsciously signalling they were ready to breed - but instead they found the opposite, and yet they've got a bizarre theory that women are trying to look sexy when not ovulating to conceal when they're fertile. It doesn't take the most insightful evolutionary biologist to notice the evolutionary problem here - once you're broadcasting to the men what stage in your menstrual cycle you're in, why would they continue to find the non-fertile gait attractive?

*Interestingly they cite Guida et al claiming that it shows 78% of women in their most fertile period have salivary ferning. The paper actually found that "Urinary LH...yielded a 100%...correlation...with the ultrasonographic diagnosis of ovulation" but that "The salivary ferning test had a 36.8% simultaneous correlation with ovulation but had a high percentage (58.7%) of uninterpretable pattern."

**Note that there are all kinds of assumptions that underlie the statistical approaches used in this paper, and the authors are not at all clear about whether they have tested to see if these assumptions are true.

***I haven't talked about premenstrual symptoms but it should be obvious that these are present in women 5-7 days before their period before I even make the point that the cyclical symptoms with menstruation do not necessarily follow the simple lay belief in 'PMT', occurring only in the days running up to the period, but can in fact present throughout the cycle.

****Note this line from the news article:

"The women who were most fertile at the time of the experiment walked with fewer hip movements and with their knees closer together."

LIAR LIAR PANTS ON FIRE! That's what your disciminant function predicted was the case for the most extreme hypothetical values of your discriminant function. You didn't actually find any difference between the 'fertile' (follicular phase) women and the other women on those measures. And you have absolutely no evidence whatsoever that those women with the most extreme score on the discriminant function were more fertile!