Data science sold down the Amazon? Jeff Bezos and the culture of rigour

This blog appeared on the Royal Statistical Society website Statslife on 25 August 2015

Jeff Bezos' iconic laugh.jpgThis recent item in the New York Times has catalysed discussion among managers. The article tells of Amazon’s founder, Jeff Bezos, and his pursuit of rigorous data driven management. It also tells employees’ own negative stories of how that felt emotionally.

The New York Times says that Amazon is pervaded with abundant data streams that are used to judge individual human performance and which drive reward and advancement. They inform termination decisions too.

The recollections of former employees are not the best source of evidence about how a company conducts its business. Amazon’s share of the retail market is impressive and they must be doing something right. What everybody else wants to know is, what is it? Amazon are very coy about how they operate and there is a danger that the business world at large takes the wrong messages.

Targets

Targets are essential to business. The marketing director predicts that his new advertising campaign will create demand for 12,000 units next year. The operations director looks at her historical production data. She concludes that the process lacks the capability reliably to produce those volumes. She estimates the budget required to upgrade the process and to achieve 12,000 units annually. The executive board considers the business case and signs off the investment. Both marketing and operations directors now have a target.

Targets communicate improvement priorities. They build confidence between interfacing processes. They provide constraints and parameters that prevent the system causing harm. Harm to others or harm to itself. They allow the pace and substance of multiple business processes, and diverse entities, to be matched and aligned.

But everyone who has worked in business sees it as less simple than that. The marketing and operations directors are people.

Signal and noise

Drawing conclusions from data might be an uncontroversial matter were it not for the most common feature of data, fluctuation. Call it variation if you prefer. Business measures do not stand still. Every month, week, day and hour is different. All data features noise. Sometimes is goes up, sometimes down. A whole ecology of occult causes, weakly characterised, unknown and as yet unsuspected, interact to cause irregular variation. They are what cause a coin variously to fall “heads” or “tails”. That variation may often be stable enough, or if you like “exchangeable“, so as to allow statistical predictions to be made, as in the case of the coin toss.

If all data features noise then some data features signals. A signal is a sign, an indicator that some palpable cause has made the data stand out from the background noise. It is that assignable cause which enables inferences to be drawn about what interventions in the business process have had a tangible effect and what future innovations might cement any gains or lead to bigger prospective wins. Signal and noise lead to wholly different business strategies.

The relevance for business is that people, where not exposed to rigorous decision support, are really bad at telling the difference between signal and noise. Nobel laureate economist and psychologist Daniel Kahneman has amassed a lifetime of experimental and anecdotal data capturing noise misinterpreted as signal and judgments in the face of compelling data, distorted by emotional and contextual distractions.

Signal and accountability

It is a familiar trope of business, and government, that extravagant promises are made, impressive business cases set out and targets signed off. Yet the ultimate scrutiny as to whether that envisaged performance was realised often lacks rigour. Noise, with its irregular ups and downs, allows those seeking solace from failure to pick out select data points and cast self-serving narratives on the evidence.

Our hypothetical marketing director may fail to achieve his target but recount how there were two individual months where sales exceeded 1,000, construct elaborate rationales as to why only they are representative of his efforts and point to purported external factors that frustrated the remaining ten reports. Pairs of individual data points can always be selected to support any story, Don Wheeler’s classic executive time series.

This is where the ability to distinguish signal and noise is critical. To establish whether targets have been achieved requires crisp definition of business measures, not only outcomes but also the leading indicators that provide context and advise judgment as to prediction reliability. Distinguishing signal and noise requires transparent reporting that allows diverse streams of data criticism. It requires a rigorous approach to characterising noise and a systematic approach not only to identifying signals but to reacting to them in an agile and sustainable manner.

Data is essential to celebrating a target successfully achieved and to responding constructively to a failure. But where noise is gifted the status of signal to confirm a fanciful business case, or to protect a heavily invested reputation, then the business is misled, costs increased, profits foregone and investors cheated.

Where employees believe that success and reward is being fudged, whether because of wishful thinking or lack of data skills, or mistakenly through lack of transparency, then cynicism and demotivation will breed virulently. Employees watch the behaviours of their seniors carefully as models of what will lead to their own advancement. Where it is deceit or innumeracy that succeed, that is what will thrive.

Noise and blame

Here is some data of the number of defects caused by production workers last month.

Worker Defects
Al 10
Simone 6
Jose 10
Gabriela 16
Stan 10

What is to be done about Gabriela? Move to an easier job? Perhaps retraining? Or should she be let go? And Simone? Promote to supervisor?

Well, the numbers were just random numbers that I generated. I didn’t add anything in to make Gabriela’s score higher and there was nothing in the way that I generated the data to suggest who would come top or bottom. The data are simply noise. They are the sort of thing that you might observe in a manufacturing plant that presented a “stable system of trouble”. Nothing in the data signals any behaviour, attitude, skill or diligence that Gabriela lacked or wrongly exercised. The next month’s data would likely show a different candidate for dismissal.

Mistaking signal for noise is, like mistaking noise for signal, the path to business under performance and employee disillusionment. It has a particularly corrosive effect where used, as it might be in Gabriela’s case, to justify termination. The remaining staff will be bemused as to what Gabriela was actually doing wrong and start to attach myriad and irrational doubts to all sorts of things in the business. There may be a resort to magical thinking. The survivors will be less open and less willing to share problems with their supervisors. The business itself has the costs of recruitment to replace Gabriela. The saddest aspect of the whole business is the likelihood that Gabriela’s replacement will perform better than did Gabriela, vindicating the dismissal in the mind of her supervisor. This is the familiar statistical artefact of regression to the mean. An extreme event is likely to be followed by one less extreme. Again, Kahneman has collected sundry examples of managers so deceived by singular human performance and disappointed by its modest follow-up.

It was W Edwards Deming who observed that every time you recruit a new employee you take a random sample from the pool of job seekers. That’s why you get the regression to the mean. It must be true at Amazon too as their human resources executive Mr Tony Galbato explains their termination statistics by admitting that “We don’t always get it right.” Of course, everybody thinks that their recruitment procedures are better than average. That’s a management claim that could well do with rigorous testing by data.

Further, mistaking noise for signal brings the additional business expense of over adjustment, spending money to add costly variation while degrading customer satisfaction. Nobody in the business feels good about that.

Target quality, data quality

I admitted above that the evidence we have about Amazon’s operations is not of the highest quality. I’m not in a position to judge what goes on at Amazon. But all should fix in their minds that setting targets demands rigorous risk assessment, analysis of perverse incentives and intense customer focus.

It is a sad reality that, if you set incentives perversely enough,some individuals will find ways of misreporting data. BNFL’s embarrassment with Kansai Electric and Steven Eaton’s criminal conviction were not isolated incidents.

One thing that especially bothered me about the Amazon report was the soi-disant Anytime Feedback Tool that allowed unsolicited anonymous peer appraisal. Apparently, this formed part of the “data” that determined individual advancement or termination. The description was unchallenged by Amazon’s spokesman (sic) Mr Craig Berman. I’m afraid, and I say this as a practising lawyer, unsourced and unchallenged “evidence” carries the spoor of the Star Chamber and the party purge. I would have thought that a pretty reliable method for generating unreliable data would be to maximise the personal incentives for distortion while protecting it from scrutiny or governance.

Kahneman observed that:

… we pay more attention to the content of messages than to information about their reliability, and as a result end up with a view of the world around us that is simpler and more coherent than the data justify.

It is the perverse confluence of fluctuations and individual psychology that makes statistical science essential, data analytics interesting and business, law and government difficult.

Advertisements

#executivetimeseries

ExecTS1OxfordDon Wheeler coined the term executive time series. I was just leaving court in Oxford the other day when I saw this announcement on a hoarding. I immediately thought to myself “#executivetimeseries”.

Wheeler introduced the phrase in his 2000 book Understanding Variation: The Key to Managing Chaos. He meant to criticise the habitual way that statistics are presented in business and government. A comparison is made between performance at two instants in time. Grave significance is attached as to whether performance is better or worse at the second instant. Well, it was always unlikely that it would be the same.

The executive time series has the following characteristics.

  • It as applied to some statistic, metric, Key Performance Indicator (KPI) or other measure that will be perceived as important by its audience.
  • Two time instants are chosen.
  • The statistic is quoted at each of the two instants.
  • If the latter is greater than the first then an increase is inferred. A decrease is inferred from the converse.
  • Great significance is attached to the increase or decrease.

Why is this bad?

At its best it provides incomplete information devoid of context. At its worst it is subject to gross manipulation. The following problems arise.

  • Though a signal is usually suggested there is inadequate information to infer this.
  • There is seldom explanation of how the time points were chosen. It is open to manipulation.
  • Data is presented absent its context.
  • There is no basis for predicting the future.

The Oxford billboard is even worse than the usual example because it doesn’t even attempt to tell us over what period the carbon reduction is being claimed.

Signal and noise

Let’s first think about noise. As Daniel Kahneman put it “A random event does not … lend itself to explanation, but collections of random events do behave in a highly regular fashion.” Noise is a collection of random events. Some people also call it common cause variation.

Imagine a bucket of thousands of beads. Of the beads, 80% are white and 20%, red. You are given a paddle that will hold 50 beads. Use the paddle to stir the beads then draw out 50 with the paddle. Count the red beads. Repeat this, let us say once a week, until you have 20 counts. The data might look something like this.

RedBeads1

What we observe in Figure 1 is the irregular variation in the number of red beads. However, it is not totally unpredictable. In fact, it may be one of the most predictable things you have ever seen. Though we cannot forecast exactly how many red beads we will see in the coming week, it will most likely be in the rough range of 4 to 14 with rather more counts around 10 than at the extremities. The odd one below 4 or above 14 would not surprise you I think.

But nothing changed in the characteristics of the underlying process. It didn’t get better or worse. The percentage of reds in the bucket was constant. It is a stable system of trouble. And yet measured variation extended between 4 and 14 red beads. That is why an executive time series is so dangerous. It alleges change while the underlying cause-system is constant.

Figure 2 shows how an executive time series could be constructed in week 3.

RedBeads2

The number of beads has increase from 4 to 10, a 150% increase. Surely a “significant result”. And it will always be possible to find some managerial initiative between week 2 and 3 that can be invoked as the cause. “Between weeks 2 and 3 we changed the angle of inserting the paddle and it has increased the number of red beads by 150%.”

But Figure 2 is not the only executive time series that the data will support. In Figure 3 the manager can claim a 57% reduction from 14 to 6. More than the Oxford banner. Again, it will always be possible to find some factor or incident supposed to have caused the reduction. But nothing really changed.

RedBeads3

The executive can be even more ambitious. “Between week 2 and 17 we achieved a 250% increase in red beads.” Now that cannot be dismissed as a mere statistical blip.

RedBeads4

#executivetimeseries

Data has no meaning apart from its context.

Walter Shewhart

Not everyone who cites an executive time series is seeking to deceive. But many are. So anybody who relies on an executive times series, devoid of context, invites suspicion that they are manipulating the message. This is Langian statistics. par excellence. The fallacy of What you see is all there is. It is essential to treat all such claims with the utmost caution. What properly communicates the present reality of some measure is a plot against time that exposes its variation, its stability (or otherwise) and sets it in the time context of surrounding events.

We should call out the perpetrators. #executivetimeseries

Techie note

The data here is generated from a sequence of 20 Bernoulli experiments with probability of “red” equal to 0.2 and 50 independent trials in each experiment.

Soccer management – signal, noise and contract negotiation

Some poor data journalism here from the BBC on 28 May 2015, concerning turnover in professional soccer managers in England. “Managerial sackings reach highest level for 13 years” says the headline. A classic executive time series. What is the significance of the 13 years? Other than it being the last year with more sackings than the present.

The data was purportedly from the League Managers’ Association (LMA) and their Richard Bevan thought the matter “very concerning”. The BBC provided a chart (fair use claimed).

MgrSackingsto201503

Now, I had a couple of thoughts as soon as I saw this. Firstly, why chart only back to 2005/6? More importantly, this looked to me like a stable system of trouble (for football managers) with the possible exception of this (2014/15) season’s Championship coach turnover. Personally, I detest multiple time series on a common chart unless there is a good reason for doing so. I do not think it the best way of showing variation and/ or association.

Signal and noise

The first task of any analyst looking at data is to seek to separate signal from noise. Nate Silver made this point powerfully in his book The Signal and the Noise: The Art and Science of Prediction. As Don Wheeler put it: all data has noise; some data has signal.

Noise is typically the irregular aggregate of many causes. It is predictable in the same way as a roulette wheel. A signal is a sign of some underlying factor that has had so large an effect that it stands out from the noise. Signals can herald a fundamental unpredictability of future behaviour.

If we find a signal we look for a special cause. If we start assigning special causes to observations that are simply noise then, at best, we spend money and effort to no effect and, at worst, we aggravate the situation.

The Championship data

In any event, I wanted to look at the data for myself. I was most interested in the Championship data as that was where the BBC and LMA had been quick to find a signal. I looked on the LMA’s website and this is the latest data I found. The data only records dismissals up to 31 March of the 2014/15 season. There were 16. The data in the report gives the total number of dismissals for each preceding season back to 2005/6. The report separates out “dismissals” from “resignations” but does not say exactly how the classification was made. It can be ambiguous. A manager may well resign because he feels his club have themselves repudiated his contract, a situation known in England as constructive dismissal.

The BBC’s analysis included dismissals right up to the end of each season including 2014/15. Reading from the chart they had 20. The BBC have added some data for 2014/15 that isn’t in the LMA report and not given the source. I regard that as poor data journalism.

I found one source of further data at website The Sack Race. That told me that since the end of March there had been four terminations.

Manager Club Termination Date
Malky Mackay Wigan Athletic Sacked 6 April
Lee Clark Blackpool Resigned 9 May
Neil Redfearn Leeds United Contract expired 20 May
Steve McClaren Derby County Sacked 25 May

As far as I can tell, “dismissals” include contract non-renewals and terminations by mutual consent. There are then a further three dismissals, not four. However, Clark left Blackpool amid some corporate chaos. That is certainly a termination that is classifiable either way. In any event, I have taken the BBC figure at face value though I am alerted as to some possible data quality issues here.

Signal and noise

Looking at the Championship data, this was the process behaviour chart, plotted as an individuals chart.

MgrSackingsto201503

There is a clear signal for the 2014/15 season with an observation, 20 dismissals,, above the upper natural process limit of 19.18 dismissals. Where there is a signal we should seek a special cause. There is no guarantee that we will find a special cause. Data limitations and bounded rationality are always constraints. In fact, there is no guarantee that there was a special cause. The signal could be a false positive. Such effects cannot be eliminated. However, signals efficiently direct our limited energy for, what Daniel Kahneman calls, System 2 thinking towards the most promising enquiries.

Analysis

The BBC reports one narrative woven round the data.

Bevan said the current tenure of those employed in the second tier was about eight months. And the demand to reach the top flight, where a new record £5.14bn TV deal is set to begin in 2016, had led to clubs hitting the “panic button” too quickly.

It is certainly a plausible view. I compiled a list of the dismissals and non-renewals, not the resignations, with data from Wikipedia and The Sack Race. I only identified 17 which again suggests some data quality issue around classification. I have then charted a scatter plot of date of dismissal against the club’s then league position.

MgrSackings201415

It certainly looks as though risk of relegation is the major driver for dismissal. Aside from that, Watford dismissed Billy McKinlay after only two games when they were third in the league, equal on points with the top two. McKinlay had been an emergency appointment after Oscar Garcia had been compelled to resign through ill health. Watford thought they had quickly found a better manager in Slavisa Jokanovic. Watford ended the season in second place and were promoted to the Premiership.

There were two dismissals after the final game on 2 May by disappointed mid-table teams. Beyond that, the only evidence for impulsive managerial changes in pursuit of promotion is the three mid-season, mid-table dismissals.

Club league position
Manager Club On dismissal At end of season
Nigel Adkins Reading 16 19
Bob Peeters Charlton Athletic 14 12
Stuart Pearce Nottingham Forrest 12 14

A table that speaks for itself. I am not impressed by the argument that there has been the sort of increase in panic sackings that Bevan fears. Both Blackpool and Leeds experienced chaotic executive management which will have resulted in an enhanced force of mortality on their respective coaches. That along with the data quality issues and the technical matter I have described below lead me to feel that there was no great enhanced threat to the typical Championship manager in 2014/15.

Next season I would expect some regression to the mean with a lower number of dismissals. Not much of a prediction really but that’s what the data tells me. If Bevan tries to attribute that to the LMA’s activism them I fear that he will be indulging in Langian statistical analysis. Will he be able to resist?

Techie bit

I have a preference for individuals charts but I did also try plotting the data on an np-chart where I found no signal. It is trite service-course statistics that a Poisson distribution with mean λ has standard deviation √λ so an upper 3-sigma limit for a (homogeneous) Poisson process with mean 11.1 dismissals would be 21.1 dismissals. Kahneman has cogently highlighted how people tend to see patterns in data as signals even where they are typical of mere noise. In this case I am aware that the data is not atypical of a Poisson process so I am unsurprised that I failed to identify a special cause.

A Poisson process with mean 11.1 dismissals is a pretty good model going forwards and that is the basis I would press on any managers in contract negotiations.

Of course, the clubs should remember that when they look for a replacement manager they will then take a random sample from the pool of job seekers. Really!

Anecdotes and p-values

JellyBellyBeans.jpgI have been feeling guilty ever since I recently published a p-value. It led me to sit down and think hard about why I could not resist doing so and what I really think it told me, if anything. I suppose that a collateral question is to ask why I didn’t keep it to myself. To be honest, I quite often calculate p-values though I seldom let on.

It occurred to me that there was something in common between p-values and the anecdotes that I have blogged about here and here. Hence more jellybeans.

What is a p-value?

My starting data was the conversion rates of 10 elite soccer penalty takers. Each of their conversion rates was different. Leighton Baines had the best figures having converted 11 out of 11. Peter Beardsley and Emmanuel Adebayor had the superficially weakest, having converted 18 out of 20 and 9 out of 10 respectively. To an analyst that raises a natural question. Was the variation between the performance signal or was it noise?

In his rather discursive book The Signal and the Noise: The Art and Science of Prediction, Nate Silver observes:

The signal is the truth. The noise is what distracts us from the truth.

In the penalties data the signal, the truth, that we are looking for is Who is the best penalty taker and how good are they? The noise is the sampling variation inherent in a short sequence of penalty kicks. Take a coin and toss it 10 times. Count the number of heads. Make another 10 tosses. And a third 10. It is unlikely that you got the same number of heads but that was not because anything changed in the coin. The variation between the three counts is all down to the short sequence of tosses, the sampling variation.

In Understanding Variation: The Key to Managing ChaosDon Wheeler observes:

All data has noise. Some data has signal.

We first want to know whether the penalty statistics display nothing more than sampling variation or whether there is also a signal that some penalty takers are better than others, some extra variation arising from that cause.

The p-value told me the probability that we could have observed the data we did had the variation been solely down to noise, 0.8%. Unlikely.

p-Values do not answer the exam question

The first problem is that p-values do not give me anything near what I really want. I want to know, given the observed data, what it the probability that penalty conversion rates are just noise. The p-value tells me the probability that, were penalty conversion rates just noise, I would have observed the data I did.

The distinction is between the probability of data given a theory and the probability of a theory give then data. It is usually the latter that is interesting. Now this may seem like a fine distinction without a difference. However, consider the probability that somebody with measles has spots. It is, I think, pretty close to one. Now consider the probability that somebody with spots has measles. Many things other than measles cause spots so that probability is going to be very much less than one. I would need a lot of information to come to an exact assessment.

In general, Bayes’ theorem governs the relationship between the two probabilities. However, practical use requires more information than I have or am likely to get. The p-values consider all the possible data that you might have got if the theory were true. It seems more rational to consider all the different theories that the actual data might support or imply. However, that is not so simple.

A dumb question

In any event, I know the answer to the question of whether some penalty takers are better than others. Of course they are. In that sense p-values fail to answer a question to which I already know the answer. Further, collecting more and more data increases the power of the procedure (the probability that it dodges a false negative). Thus, by doing no more than collecting enough data I can make the p-value as small as I like. A small p-value may have more to do with the number of observations than it has with anything interesting in penalty kicks.

That said, what I was trying to do in the blog was to set a benchmark for elite penalty taking. As such this was an enumerative study. Of course, had I been trying to select a penalty taker for my team, that would have been an analytic study and I would have to have worried additionally about stability.

Problems, problems

There is a further question about whether the data variation arose from happenstance such as one or more players having had the advantage of weather or ineffective goalkeepers. This is an observational study not a designed experiment.

And even if I observe a signal, the p-value does not tell me how big it is. And it doesn’t tell me who is the best or worst penalty taker. As R A Fisher observed, just because we know there had been a murder we do not necessarily know who was the murderer.

E pur si muove

It seems then that individuals will have different ways of interpreting p-values. They do reveal something about the data but it is not easy to say what it is. It is suggestive of a signal but no more. There will be very many cases where there are better alternative analytics about which there is less ambiguity, for example Bayes factors.

However, in the limited case of what I might call alternative-free model criticism I think that the p-value does provide me with some insight. Just to ask the question of whether the data is consistent with the simplest of models. However, it is a similar insight to that of an anecdote: of vague weight with little hope of forming a consensus round its interpretation. I will continue to calculate them but I think it better if I keep quiet about it.

R A Fisher often comes in for censure as having done more than anyone to advance the cult of p-values. I think that is unfair. Fisher only saw p-values as part of the evidence that a researcher would have to hand in reaching a decision. He saw the intelligent use of p-values and significance tests as very different from the, as he saw it, mechanistic practices of hypothesis testing and acceptance procedures on the Neyman-Pearson model.

In an acceptance procedure, on the other hand, acceptance is irreversible, whether the evidence for it was strong or weak. It is the result of applying mechanically rules laid down in advance; no thought is given to the particular case, and the tester’s state of mind, or his capacity for learning is inoperative. By contrast, the conclusions drawn by a scientific worker from a test of significance are provisional, and involve an intelligent attempt to understand the experimental situation.

“Statistical methods and scientific induction”
Journal of the Royal Statistical Society Series B 17: 69–78. 1955, at 74-75

Fisher was well known for his robust, sometimes spiteful, views on other people’s work. However, it was Maurice Kendall in his obituary of Fisher who observed that:

… a man’s attitude toward inference, like his attitude towards religion, is determined by his emotional make-up, not by reason or mathematics.

Deconstructing Deming XI B – Eliminate numerical goals for management

11. Part B. Eliminate numerical goals for management.

W. Edwards Deming.jpgA supposed corollary to the elimination of numerical quotas for the workforce.

This topic seems to form a very large part of what passes for exploration and development of Deming’s ideas in the present day. It gets tied in to criticisms of remuneration practices and annual appraisal, and target-setting in general (management by objectives). It seems to me that interest flows principally from a community who have some passionately held emotional attitudes to these issues. Advocates are enthusiastic to advance the views of theorists like Alfie Kohn who deny, in terms, the effectiveness of traditional incentives. It is sad that those attitudes stifle analytical debate. I fear that the problem started with Deming himself.

Deming’s detailed arguments are set out in Out of the Crisis (at pp75-76). There are two principle reasoned objections.

  1. Managers will seek empty justification from the most convenient executive time series to hand.
  2. Surely, if we can improve now, we would have done so previously, so managers will fall back on (1).

The executive time series

I’ve used the time series below in some other blogs (here in 2013 and here in 2012). It represents the anual number of suicides on UK railways. This is just the data up to 2013.
RailwaySuicides2

The process behaviour chart shows a stable system of trouble. There is variation from year to year but no significant (sic) pattern. There is noise but no signal. There is an average of just over 200 fatalities, varying irregularly between around 175 and 250. Sadly, as I have discussed in earlier blogs, simply selecting a pair of observations enables a polemicist to advance any theory they choose.

In Railway Suicides in the UK: risk factors and prevention strategies, Kamaldeep Bhui and Jason Chalangary of the Wolfson Institute of Preventive Medicine, and Edgar Jones of the Institute of Psychiatry, King’s College, London quoted the Rail Safety and Standards Board (RSSB) in the following two assertions.

  • Suicides rose from 192 in 2001-02 to a peak 233 in 2009-10; and
  • The total fell from 233 to 208 in 2010-11 because of actions taken.

Each of these points is what Don Wheeler calls an executive time series. Selective attention, or inattention, on just two numbers from a sequence of irregular variation can be used to justify any theory. Deming feared such behaviour could be perverted to justify satisfaction of any goal. Of course, the process behaviour chart, nowhere more strongly advocated than by Deming himself in Out of the Crisis, is the robust defence against such deceptions. Diligent criticism of historical data by means of process behaviour charts is exactly what is needed to improve the business and exactly what guards against success-oriented interpretations.

Wishful thinking, and the more subtle cognitive biases studied by Daniel Kahneman and others, will always assist us in finding support for our position somewhere in the data. Process behaviour charts keep us objective.

If not now, when?

If I am not for myself, then who will be for me?
And when I am for myself, then what am “I”?
And if not now, when?

Hillel the Elder

Deming criticises managerial targets on the grounds that, were the means of achieving the target known, it would already have been achieved and, further, that without having the means efforts are futile at best. It’s important to remember that Deming is not here, I think, talking about efforts to stabilise a business process. Deming is talking about working to improve an already stable, but incapable, process.

There are trite reasons why a target might legitimately be mandated where it has not been historically realised. External market conditions change. A manager might unremarkably be instructed to “Make 20% more of product X and 40% less of product Y“. That plays in to the broader picture of targets’ role in co-ordinating the parts of a system, internal to the organisation of more widely. It may be a straightforward matter to change the output of a well-understood, stable system by an adjustment of the inputs.

Deming says:

If you have a stable system, then there is no use to specify a goal. You will get whatever the system will deliver.

But it is the manager’s job to work on a stable system to improve its capability (Out of the Crisis at pp321-322). That requires capital and a plan. It involves a target because the target captures the consensus of the whole system as to what is required, how much to spend, what the new system looks like to its customer. Simply settling for the existing process, being managed through systematic productivity to do its best, is exactly what Deming criticises at his Point 1 (Constancy of purpose for improvement).

Numerical goals are essential

… a manager is an information channel of decidedly limited capacity.

Kenneth Arrow
Essays in the Theory of Risk-Bearing

Deming’s followers have, to some extent, conceded those criticisms. They say that it is only arbitrary targets that are deprecated and not the legitimate Voice of the Customer/ Voice of the Business. But I think they make a distinction without a difference through the weasel words “arbitrary” and “legitimate”. Deming himself was content to allow managerial targets relating to two categories of existential risk.

However, those two examples are not of any qualitatively different type from the “Increase sales by 10%” that he condemns. Certainly back when Deming was writing Out of the Crisis most OELs were based on LD50 studies, a methodology that I am sure Deming would have been the first to criticise.

Properly defined targets are essential to business survival as they are one of the principal means by which the integrated function of the whole system is communicated. If my factory is producing more than I can sell, I will not work on increasing capacity until somebody promises me that there is a plan to improve sales. And I need to know the target of the sales plan to know where to aim with plant capacity. It is no good just to say “Make as much as you can. Sell as much as you can.” That is to guarantee discoordination and inefficiency. It is unsurprising that Deming’s thinking has found so little real world implementation when he seeks to deprive managers of one of the principle tools of managing.

Targets are dangerous

I have previously blogged about what is needed to implement effective targets. An ill judged target can induce perverse incentives. These can be catastrophic for an organisation, particularly one where the rigorous criticism of historical data is absent.

The future of p-values

Another attack on p-values. This time by Regina Nuzzo in prestigious science journal Nature. Nuzzo advances the usual criticisms clearly and trenchantly. I hope that this will start to make people think hard about using probability to make decisions.

However, for me, the analysis still does not go deep enough. US baseball commentator Yogi Berra is reputed once to have observed that:

It’s tough to make predictions, especially about the future.

The fact that scientists work with confidence intervals, whereas if society is interested in such things it is interested in prediction intervals, belies the proper recognition of the future in much scientific writing.

The principal reason for doing statistics is to improve the reliability of predictions and forecasts. But the foundational question is whether the past is even representative of the future. Unless the past is representative of the future then it is of no assistance in forecasting. Many statisticians have emphasised the important property that any process must display to allow even tentative predictions about its future behaviour. Johnson and de Finetti called the property exchangeability, Shewhart and Deming called it statistical control, Don Wheeler coined the more suggestive term stable and predictable.

Shewhart once observed:

Both pure and applied science have gradually pushed further and further the requirements for accuracy and precision. However, applied science, particularly in the mass production of interchangeable parts, is even more exacting than pure science in certain matters of accuracy and precision.

Perhaps its unsurprising then that the concept is more widely relied upon in business than in scientific writing. All the same, statistical analysis begins and ends with considerations of stability. An analysis in which p-values do not assist.

At the head of this page is a tab labelled “Rearview” where I have surveyed the matter more widely. I would like to think of this as supplementary to Nuzzo’s views.

Adoption statistics for England – signals of improvement?

I am adopted so I follow the politics of adoption fairly carefully. I was therefore interested to see this report on the BBC, claiming a “record” increase in adoptions. The quotation marks are the BBC’s. The usual meaning of such quotes is that the word “record” is not being used with its usual meaning. I note that the story was repeated in several newspapers this morning.

The UK government were claiming a 15% increase in children adopted from local authority care over the last year and the highest total since data had been collected on this basis starting in 1992.

Most people will, I think, recognise what Don Wheeler calls an executive time series. A comparison of two numbers ignoring any broader historical trends or context. Of course, any two consecutive numbers will be different. One will be greater than the other. Without the context that gives rise to the data, a comparison of two numbers is uninformative.

I decided to look at the data myself by following the BBC link to the GOV.UK website. I found a spreadsheet there but only with data from 2009 to 2013. I dug around a little more and managed to find 2006 to 2008. However, the website told me that to find any earlier data I would have to consult the National Archives. At the same time it told me that the search function at the National Archives did not work. I ended up browsing 30 web pages of Department of Education documents and managed to get figures back to 2004. However, when I tried to browse back beyond documents dated January 2008, I got “Sorry, the page you were looking for can’t be found” and an invitation to use the search facility. Needless to say, I failed to find the missing data back to 1992, there or on the Office for National Statistics website. It could just be my internet search skills that are wanting but I spent an hour or so on this.

Gladly, Justin Ushie and Julie Glenndenning from the Department for Education were able to help me and provided much of the missing data. Many thanks to them both. Unfortunately, even they could not find the data for 1992 and 1993.

Here is the run chart.

Adoption1

Some caution is needed in interpreting this chart because there is clearly some substantial serial correlation in the annual data. That said, I am not able to quite persuade myself that the 2013 figure represents a signal. Things look much better than the mid-1990s but 2013 still looks consistent with a system that has been stable since the early years of the century.

The mid 1990s is a long time ago so I also wanted to look at adoptions as a percentage of children in care. I don’t think that that is automatically a better measure but I wanted to check that it didn’t yield a different picture.

Adoption2

That confirms the improvement since the mid-1990s but the 2013 figures now look even less remarkable against the experience base of the rest of the 21st century.

I would like to see these charts with all the interventions and policy changes of respective governments marked. That would then properly set the data in context and assist interpretation. There would be an opportunity to build a narrative, add natural process limits and come to a firmer view about whether there was a signal. Sadly, I have not found an easy way of building a chronology of intervention from government publications.

Anyone holding themselves out as having made an improvement must bring forward the whole of the relevant context for the data. That means plotting data over time and flagging background events. It is only then that the decision maker, or citizen, can make a proper assessment of whether there has been an improvement. The simple chart of data against time, even without natural process limits, is immensely richer than a comparison of two selected numbers.

Properly capturing context is the essence of data visualization and the beginnings of graphical excellence.

One my favourite slogans:

In God we trust. All else bring data.

W Edwards Deming

I plan to come back to this data in 2014.