Sum Mistake, Probably

Statistics is not just for Christmas, it’s for life.

‘Be a little wiser’ Two Become One, Spice Girls

Number Shy

I often say that statisticians will apply statistics to anything except what they do themselves. Designing an experiment? You’d better see the statisticians first. Statisticians running a simulation? Let’s just start and make it up as we go along. Screening for a disease? The statisticians have a theory all about that. Statisticians checking their models? Let’s just test this and that and come up with something.

Merging two statistical societies? What could figures have to do with that? Figures, as the Royal Statistical Society motto is rumoured to say, are for others to thresh. They are certainly noticeably absent from the PSI/RSS Joint Assessment Committee (JAC) report.

What could the societies have done better? Well, the RSS has a number of sections and intends the PSI to be one. Did they call on their expertise? The Social Statistics and Official Statistics sections could have advised them on surveying the membership and establishing a simple basic fact that would be quite important to the decisions to merge: how many statisticians in the RSS but not in the PSI work in the pharmaceutical industry? If none, the merger adds little of interest to RSS fellows not in the PSI. They could have consulted the Business and Finance section on financial issues. They could have consulted the Quality Improvement section on management matters. The JAC assures us that the, ‘PSI would be the largest and most active section’. It is to be hoped so, since the activity of the sections in advising the JAC on what must be one of the most important current issues facing the RSS is noticeably absent.

And what of PSI itself? The society is full of statisticians who make their living by doing detailed calculations in support of decisions to invest millions of pounds but nothing in the way of decision analysis is offered by the JAC.

Instead, we got a report that shows a preference for words over numbers that would not shame The Alliance of Literary Societies.

In my opinion, a very little statistical analysis would not be amiss and, although I am well aware that there are many in both societies better qualified to deliver it than I am, I am going to make a start here in order to encourage others to do better.

Who benefits?

Let us start first of all with trying to establish ‘who is the merger for?’

Figure 1. Approximate numbers in the two societies

Figure 1 shows the approximate situation in terms of numbers of persons in the two societies. These are based on rough estimates, which suggest that there is a total of 6675 statisticians in the two societies, with 225 being in both. (Wikipedia gives 7200 for the RSS but 6000 is the figure given in the annual report of 31 December 2014.)  I propose to first consider the merger from the perspective of four categories of statistician: 1) members of PSI & RSS, 2) members of PSI only, 3) members of RSS only and 4) members of neither. In doing so I shall also consider category by category things from the point of view of the two societies, un-merged as they are and merged as they may be.

I shall look at the matter first of all from the financial side and then consider ‘value’.

Money matters

Statisticians in both societies

The 225 statisticians who are members of both societies (excluding a very few honorary life members of PSI, for example, a category in which I fall myself), currently pay £135 for their RSS membership and will soon pay £95 for their PSI membership. On the costs side (ignoring any effects on deliverables) the merger will present them with a gift of £95. (Statisticians who are also graduate statisticians or chartered statisticians pay an additional fee but this is not really relevant here since the £95 is still saved.) So for this category of statistician, there is nothing, on the cost side, not to like in the merger.

Of course this is a loss to PSI plus RSS of 225 x £95=£21,375 and this, in turn, raises the question. How is this shortfall to be made good? There are four obvious answers

1. The income lost is absorbed by the RSS from its operating profit.
2. The income lost is taken from the PSI’s current operating profit.
3. The income lost is cross-subsidised by increased funding from other categories of statistician.
4. The income lost is compensated by efficiency savings.

Of the above, 1) can be dismissed right away, since it would be irresponsible of the RSS to take on a loss-making activity.  It is hard to represent 2) as being a benefit generally to the PSI, although recouping the income this way may be what the RSS has in mind. I shall consider 3) in the next section. 4) can only be the answer if the following is the case. a) The marginal cost of each PSI member to the PSI is much more than the membership fee b) getting the RSS to handle memberships for the PSI will reduce this cost considerably. Suppose for example, it currently costs PSI £200 per year to handle memberships (profits from annual conference covering the shortfall) but the RSS can do it for £100 there is a £5 net benefit for getting the RSS to handle these cases and remit their membership.  In fact, it seems from PSI accounts that all of the administrative services currently provided commercially to PSI are done so at a total cost of just under £108,000 or about £120 a member. However, it would be wrong to suppose that these are just membership costs since they also include handling of courses. It is likely that the cost of just handling membership is much less.

Of course, it may be argued, that such members of PSI already being fellows of the RSS, the membership handling costs of PSI are zero since there will only be one fellowship but this presupposes that nothing is provided by PSI that the RSS has to provide that costs anything, an admission, in my opinion that the Yes campaign would not like to make.

However, I maintain an open mind on the matter. To know if efficiency savings are the answer, we need to have the figures. No such figures are given by the JAC.

Statisticians in PSI only

To maintain their membership of PSI these statisticians will now have to pay £40 more. They will then become fellows of the RSS. The 675 statisticians in this category currently value RSS fellowship at less than £135 per annum, otherwise they would join, but, it is of course possible that they value it at more than £40. In that case the merger will be a benefit to them. It may also be the case, of course, that statisticians who place no value whatsoever on membership of the RSS value their current PSI membership at £135 or more. Such statisticians will not welcome the merger but will absorb the loss. This is a disadvantage to them but I suppose the merged societies could take the cynical view that this does not matter.

If all of them choose to join, then the extra income is 675 x £40= £27,000. The difference to the loss from gifting PSI membership to those already in both societies is then £27,000-£21,375=£5,625. On the other hand, if 1 in 5 such statisticians decides not to join the merged society then the merger is neutral as regards revenue.

In fact, 40% of PSI statisticians, that is to say about 360, are not based in the UK. Even if (which is improbable) they are just as likely to be in the RSS as not, this would make about 270 statisticians not in the RSS and not based in the UK. Even if 1 in 2 of these decides to pay the extra £40 we get the position that 1 in 2 of 40% = 20% do not join the merged society. So we would then have the situation discussed above that the merger is neutral as regards revenue. Personally, I find this unlikely and think a loss is probable.

However, these statisticians do bring an increase in costs to the merged societies. It is at this point that it would be useful to know something about the marginal costs of membership of the Royal Statistical Society. The JAC report is silent on this issue but there is an alarming possibility.

It could be that the marginal revenue of one new fellow exceeds the marginal cost. In that case, increasing numbers joining increases operating profit. However, much of the current income of the RSS comes from journals. Thus, it is also possible, that the marginal revenue does not exceed the marginal cost. In that case increasing the fellowship reduces net revenue. I am not saying that this is the case. I am saying that if the JAC knows whether this is the case or not they have not shared the figures.

RSS Fellows only

These are by far the largest group considered so far, some 5775 making up more than 85% of the total. It is hard to believe that many of these will gain much benefit from the merger. The sort of statistician who might benefit would be one who was an RSS fellow only but worked in the pharmaceutical industry. I doubt that there are many in this category. Of course, the JAC could have tried to find out but they didn’t.

Statisticians in neither society

One would have to suppose a class of statistician who currently finds the RSS not worth the £135 and the PSI not worth the £95 but that a two for one deal would be attractive. Such a statistician would almost certainly also have to be in the pharmaceutical industry, feel that £95 was too much for PSI membership but if the RSS were thrown in as well it would become attractive.

I find it hard to believe that there are many such statisticians.

Value Added?

So the commercial case seems shaky to me. Of course, my analysis may be wrong but the JAC analysis is simply absent. It does not exist.

What about value, however? Can the merged societies deliver more in the way of value?

I am not going to go through the list of benefits supposed or real provided by the JAC. I invite any member of either society to read them and consider how convincing they are and also to consider Nigel Howitt's excellent discussion of them and Jame's Matcham's careful comparison of the two societies. However, I will say that many of them depend on a trade-off that many organisations face when increasing size (whether through mergers, take-overs or whatever) between benefits of pooled resources on the one hand and loss of flexibility on the other. Many pharmaceutical companies have been so concerned about the disadvantages of increased size that they have created semi-independent business units or even spun off companies altogether. Bigger is not necessarily better.

There is another point about which all PSI members should be quite clear. This is not a merger of societies. It is a take-over of the PSI by the RSS. I readily concede that it is not a hostile take-over but the PSI will cease to exist once it happens and the RSS will carry on largely as before. It is my firm opinion that the PSI will have less influence within the RSS not more by being absorbed in it.

Finally, those members of PSI that value Pharmaceutical Statistics should not assume that in the long term the journal will survive a merger. When the Institute of Statisticians merged with the RSS in 1993 its journal, The Statistician, became JRSS D. Ten years later it was abandoned to make way for the magazine Significance. This is an interesting publication but not a substitute for The Statistician.

Due Diligence?

In summary, what we are offered in the JAC report are words. Calculations and consideration of consequences are absent. They claim to have carried out a due diligence assessment. For me, due diligence involves calculation. Is it too much to ask of a working party of statisticians that they share their calculations with us?