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Last week I was sent an e-mail by a headhunter alerting me to two pieces of research about women on boards. As there is surely nothing left to say on this most worn-out of subjects, I was about to press delete when I noticed the comic juxtaposition of the two studies.

The first reported that big companies with more than one woman on the board outperform by 26 per cent those run entirely by men. The second said that nearly 80 per cent of women's jokes in board meetings fall entirely flat.

Which of these two contrasting statistics do you think should be taken more seriously? The first comes from a big piece of "thought leadership" put together by "the world's foremost experts" at Credit Suisse. As well as its delightfully upbeat conclusion, the study contains pictures of pretty young women in an expensive suit wafting though glamorous offices.

The only problem with this uplifting study is that it tells us nothing at all. Anyone who has had even the tiniest experience of board meetings will confirm that such outperformance could never be explained by adding a single non-executive – irrespective of sex, colour, experience or personality. So there must be something else at play. And the only even slightly plausible explanation is that better companies have been quicker to appoint women non-execs – which is something we know already.

By contrast, the second piece of research, carried out by a lone woman from Aston University, tells us something true – and troubling. Judith Baxter, an academic in linguistics, gave herself the thankless task of sitting through interminable meetings at seven big companies listening for jokes.

She found that more than three-quarters of women's jokes tended to be met by stony silence, while men's were greeted with great hilarity. The men engaged in flippant quips and rough banter; the women went for jokes that were too self-deprecating, and often ended up sounding defensive or downright horrid.

This all rings a distant bell, but I fear there is something more sinister at work. If laughter varies with gender, it varies even more with power. The single fastest way of understanding the balance of power and alliances in any group is by looking at who is laughing – and not laughing – at whose jokes.

You only need to watch the Queen or Prince Charles meeting ordinary people to note that even the lamest pleasantry is greeted by gales of laughter. So, if other board members don't laugh when their women colleagues crack a joke, it may not be because the joke isn't funny but because boards can be hierarchical places and women are too low in the pecking order to command much in the way of fawning laughter.

Ms. Baxter suggests that rather than trying to copy male banter there is another, more traditional way women can flourish in these male surroundings. Her suggestion is counterintuitive and politically incorrect and I like it a great deal. It is to adopt the very roles that feminists have long deplored, and play the parts of "Mother, Seductress, Pet and Iron Maiden."

These are the four "role traps" identified by Rosabeth Moss Kanter in the dark age of the 1970s, when there were hardly any senior women around. Now that there are lots of them we all assume that there is no further need for such roles.

But Ms. Baxter noticed that all four roles are still in use in the boardroom. The most successful women use all to great effect, dipping in and out where needed.

If I think of the most powerful women I know, all of them can pull off an excellent Iron Maiden. They can all be scary and tough. Most dabble with Mother, too, occasionally coming over as all nurturing.

The role of Seductress, the most traditional way for a woman to get what she wants, has fallen rather out of fashion. But, even so, Ms. Baxter gives examples of women using their sexuality to great effect. And, now I think of it, I've also seen it used recently by a woman executive who swiftly dealt with an obstructive male colleague by looking at him coquettishly, touching him on the arm and giving a throaty laugh. Watching this left me annoyed and impressed in equal measure.

The final role – Pet – is the least used. This is a shame, as it's the only one that I play like a pro. Though in my case – as perhaps befits a woman who writes a newspaper column – I'm a particular sort of pet. One that wags its tail and appears benign, until it turns and gives you a nasty little bite on the ankle.