In just the last week or so we’ve seen Iain Duncan Smith publicly rebuked by the UK Statistics Authority for making claims about the government’s policy of capping benefits that were “unsupported by the official statistics published by the department” and Michael Gove caught using unscientific polls commissioned by UKTV Gold and Premier Inn in an effort to dismiss serious criticism of his new National Curriculum by leading academics.

One should not, therefore, be surprised to discover that a poll conducted by Ipsos Mori on behalf of the Royal Statistics Society and Kings College London shows that just 9% of the general public believe that politicians use figures accurately when talking about their policies while just 7% place any kind of trust in their use of official statistics and nor, indeed, can one blame the public for taking such a jaundiced view of numerical honesty of the political classes.

The abuse of statistics for political and ideological ends is, of course, by no means confined to any one political party. Harriet Harman, for example, has previous form when it comes to the misleading use of statistics so when she pops up in the press with the claim that she has evidence to show that female TV presenters ‘disappear’ from our screen once they reach the age of 50 then it’s only natural that we should take a close look at the data to see if it supports that claim.

Okay, so this is how the New Statesman presented Harman’s figures:

Harman wrote to the BBC, ITV, ITN, Channel 4, Channel 5 and Sky News in February requesting figures on the number of women employed on and off-screen and the statistics have now been published for the first time. Here are some of the most striking:

– Women account for 48 per cent of TV presenters under 50 but just 18 per cent of TV presenters above that age (despite representing 53 per cent of all over-50s).

– While TV presenters are broadly reflective of age in the general population (30 per cent of TV presenters are over 50 compared with 34 per cent of the UK population) they are wholly unrepresentative in terms of gender.

– Only 5 per cent of all presenters and 7 per cent of the total TV workforce (on and off-screen) are women over the age of 50.

– Out of a total of 481 regular on-air presenters at the BBC, Sky, ITN and Channel 5, just 26 are women aged over 50.

Of the broadcasters, ITV performed the best, with 55 per cent of their presenters women aged over 50, followed by the BBC with 20 per cent and Sky News with 9 per cent. ITN and Channel 5 have no women presenters aged over 50.

However, the full dataset from which these figures were taken was supplied to the Guardian’s Datablog, and from that data they provide it’s immediately apparent that there are some quality issues with these figures.

For starters, the TV companies were left to define for themselves what they consider to be a ‘regular presenter’, so there no way of being sure that the definition used by, say, ITV is the same as that used by the BBC.

Then we have the fact that the figures supplied by the BBC include both TV and Radio presenters and so their data does not reflect what the public see ‘on screen’ because it includes radio broadcasters nor is it directly comparable to the figures supplied by the other TV companies.

Channel 4 supplied no data at all, because it doesn’t produce it’s own in-house programming, but that doesn’t mean that Channel 4 doesn’t have ‘regular presenters’ on screen – what about ‘Countdown’? – only that that those presenters are actually employed by outside production companies that supply Channel 4 with its programming.

Then there’s ITV, which ostensibly performed the best on their percentage of female presenters aged over 50, except that they did not provide any raw numbers, only percentage figures. This mean that not only can ITV’s figures not be included in the aggregated statistics but there is also no way at all of judging whether or not their figures might be heavily skewed by the presence on just one or two specific programmes on their network.

For the record, ITV reported that just 14% of their regular TV presenters – how they define that – are over the age of fifty-five (and not 50, as the question specified) before stating that 55% of those were women but without any raw numbers to work with at all we could be looking here at a situation where, if the total number of presenters is small, then ITV’s entire roster of older women could come from just one or two actual programmes.

Put it this way, the minimum number of older presenters necessary to give a 55-45 female/male split in just nine (five female and four male) and at least four of the regular presenters/panellist on ‘Loose Women’ are either definitely over the age of 55 or very close to it (two were born in 1958 and so turn 55 this year).

Ultimately, what we have here is nothing more than a crude headcount of the proportion of older women in a narrow but otherwise ill-defined range of media roles with absolutely no contextual information to work with.

There’s no data on the amount of screen time older women are afforded.

Nothing on the relative prominence of these on screen roles – there is, of course, a world of difference between being the lead presenter on a programme and being a secondary presenter who pops up every couple of weeks to present a 2-3 minute report/segment.

Nothing on which times of days older women do and don’t typically appear on screen – again, in terms of prominence, there is a world of difference between appearing on a prime time TV show compared to one that goes out in the middle of the afternoon.

Nothing on which areas or genres of programming do or don’t feature older women as presenters – or, indeed women generally. That matters because not all presenting roles offer the same degree of longevity to either men or women – careers in TV news journalism can and do span 30-40 years without the need for presenters to change direction and branch out into other fields, something which is certainly not the case for presenters working in children’s television or on programmes aimed at teenagers.

So, straight away, we can see that Harman’s figures for what amounts to nothing than ageing female bums on seats do not really tell us very much at all about the prominence or otherwise of older women on our TV screens.

What people actually see on screen could actually be better than her figures suggest, if it were found that despite being fewer in number, older women tended to have more prominent roles on TV than their similarly aged male counterparts, or it could easily be worse, if older women are not only fewer in number but also more likely to be used in smaller, secondary, presenting roles. We just don’t know on the back of these figures because they provide nothing more than a crude snapshot of the number of older women employed by the main terrestrial channels and Sky News in presenting roles but none important contextual information that is necessary to assess how those figures actually relate to what people see on screen.

So, the data itself is of somewhat dubious quality and value, and that’s just the beginning of Harman’s problems.

Older TV presenters, irrespective of gender, do not by and large appear suddenly from nowhere in their 50’s. Although there are some who may make the move into presenting from other careers (e.g. politics, print journalism, acting, etc.) most of the current crop of older TV presenters will have started their career in the broadcast media in their early twenties and will have worked in various on screen and, in some cases, off screen roles for anything up to 25-30 years before they reach the age of fifty.

When we’re looking at TV presenters over the age of fifty – and the effective age range here probably runs from 50 up until 70-75 years of age (Dimbers is currently 74 years of age) – then what we are looking at is a wide cohort (in terms of age) of presenters who originally entered the broadcast industry anything from 25 to 50+ years ago, i.e. at some point between the early-mid 1960’s and the mid-late 1980s.

So, the obvious question we need to ask when looking at the gender balance in that cohort in 2013 is what was the gender balance like when members of that cohort first entered the industry and how does that relate to the gender balance in that cohort today, because its highly likely than any imbalance at the beginning will be, at the very least, be carried forward with the cohort into the present day. In simple terms, if only 18% of the new TV presenters entering the industry in their early 20s during the period from the mid-1960s and mid-1980s were women then it should come as no surprise whatsoever to find that the exact same gender imbalance in that same cohort today, in which case it cannot be said that older women aren’t disappearing from our TV screens when they reach 50 because those ‘missing’ women were never on our TV screens in the first place.

In short, if you want to demonstrate statistically that female TV presenters in the over-50 cohort are getting a rough deal compared to male presenters in the same cohort then you need to look at how the gender balance in that cohort has changed over time and prove that the gender balance has changed in an unfavourable direction so far as women are concerned. If, for example, 40% of the TV presenters who entered the industry between mid 1960’s and mid 1980s were female and you only have 18% left on screen today then you have an argument, although you still have a bit more to do to show that the decline in female number actually occurs at or around the age of 50 and not either later or earlier – and if you look at labour market statistics generally then earlier is a distinct possibility because easily the biggest factor that affects women’s lifetime career progression and earnings is pregnancy and childbirth.

What you cannot legitimately do is compare the gender balance in today’s over 50s cohort with the gender balance in the today’s under 50s cohort, which the figures show to be much more even (52-48 in favour of male presenters). It’s a different cohort of people, one that entered the industry at the different time under very different social, cultural and legal conditions and these two cohorts are not, therefore, automatically comparable.

In order to legitimately make the comparison that Harman is rely on here as ‘proof’ that female TV presenters over 50 are disappearing from our TV screen due to a combination of sexism and ageism, she first has to show that the two cohorts were demographically similar at the outset, i.e. at the point at which members of those cohorts entered the industry. Without that key information, she’s comparing apples and oranges, which is – of course, exactly what she was called out for doing by the then-head of the UK Statistics Authority back in 2009 over misleading claims made in relation to the scale of the gender pay gap.

Moreover, the fact that the overall gender balance in the under 50s cohort appears to close to even does not guarantee that the male-female balance is evenly distributed within that very wide cohort. As is clearly evident in the data relating to the gender pay gap, although on average women earn less than men when you look at the detail you find that, as Tim Worstall puts it:

The pay gap comes and goes dependent upon age cohort. For those 16-21 it’s very definitely a pay gap in favour of women. For those 21-30 it’s around and about equality. Then for those older than 30 it opens up to being in favour of men. Up at the top of the age range it’s still in favour of men.

That last is an effect of undeniable past discrimination. Those born in the 50s did not have equal access to higher education for example: not as it actually worked out at least.

But among the younger cohorts, that pay gap is entirely consistent with the explanation that it’s all about children, not gender per se. 30 is the average age at primagravidae these days.

Despite the appearance of near equality in the overall figures, a similar skew in the gender balance in the current under 50s cohort could very well exist within that cohort if, instead of treating it as a single homogeneous cohort, we break it down into smaller age bands – and if you look at how most official statistics are presented than five-year age bands are standard practice.  Were that to be the case then the most likely internal distribution would, in keeping with the pay gap data and other labour market statistics, be one in which the male-female gender balance is skewed toward women in the younger age bands (i.e. 20-24, 25-29) but which then begins to reverse itself at around the age of 30, leaving men in the majority by the time we get to the 40-44 and 45-49 age bands.

Such a distribution would not only be entirely consistent with the ‘motherhood penalty’ we very clearly see in general labour market and pay data but would also call into serious question Harman’s assertion that female TV presenters disappear from our screens at the age of 50, as such a distribution would show that the decline in the proportion of female presenters on screen actually begins much earlier and is actually associated more closely with motherhood and women taking career breaks in order to have children and raise a family rather than being purely a function of their reaching a particular age (50) at which they fail victim to a combination of sexism and ageism.

It doesn’t rule it out entirely of course – even if female TV presenters do take a hit from the ‘motherhood penalty’ it could still be the case that they begin to disappear from our screens at a faster rate once they reach 50 than was the case for women aged between 30 and 49, but again one would still need to show that was in fact the case by obtaining the same data broken down by 5-year age bands rather than simply lumping everyone aged between 20 and 49 into a single cohort.

To be absolutely clear, none of this disproves the proposition that female TV presenters over 50 are getting a rough deal from broadcasters when compared to their similarly aged male counterparts. That may very well be perfectly true and it may very well be the case that a combination of sexism and ageism within the industry is a significant factor in creating that situation, although it may not be the only factor.

The problem here is not that Harman is necessarily wrong, rather it’s that the evidence she’s put forward in support of that proposition so far, does not support her claim that:

The figures provided by broadcasters show clearly that once female presenters hit 50, their days on-screen are numbered.

There is a combination of ageism and sexism that hits women on TV that doesn’t apply to men in the same way.

Sorry, but the figures do not show that at all.

They are quite simply too crude to support any such assertions and contain far too little contextual information to make any kind of credible analysis possible.

The only thing that is actually clear here is that whoever it was that actually compiled these figures – and it may well have been Harman or she may have dropped the job on an underling – is, in statistical terms, a complete and utter incompetent, which at this stage doesn’t, unfortunately, augur well for the work of this Older Women’s Commission, because if this is the standard of analysis we can expect from it then it will be wasting everyone’s time, especially that of older women.