Is data the plural of anecdote?

I seem to hear this intriguing quote everywhere these days.

The plural of anecdote is not data.

There is certainly one website that traces it back to Raymond Wolfinger, a political scientist from Berkeley, who claims to have said sometime around 1969 to 1970:

The plural of anecdote is data.

So, which is it?

Anecdote

My Concise Oxford English Dictionary (“COED”) defines “anecdote” as:

Narrative … of amusing or interesting incident.

Wiktionary gives a further alternative definition.

An account which supports an argument, but which is not supported by scientific or statistical analysis.

Edward Jenner by James Northcote.jpg

It’s clear that anecdote itself is a concept without a very exact meaning. It’s a story, not usually reported through an objective channel such as a journalism, or scientific or historical research, that carries some implication of its own unreliability. Perhaps it is inherently implausible when read against objective background evidence. Perhaps it is hearsay or multiple hearsay.

The anecdote’s suspect reliability is offset by the evidential weight it promises, either as a counter example to a cherished theory or as compelling support for a controversial hypothesis. Lyall Watson’s hundredth monkey story is an anecdote. So, in eighteenth century England, was the folk wisdom, recounted to Edward Jenner (pictured), that milkmaids were generally immune to smallpox.

Data

My COED defines “data” as:

Facts or impormation, esp[ecially] as basis for inference.

Wiktionary gives a further alternative definition.

Pieces of information.

Again, not much help. But the principal definition in the COED is:

Thing[s] known or granted, assumption or premise from which inferences may be drawn.

The suggestion in the word “data” is that what is given is the reliable starting point from which we can start making deductions or even inductive inferences. Data carries the suggestion of reliability, soundness and objectivity captured in the familiar Arthur Koestler quote.

Without the little hard bits of marble which are called “facts” or “data” one cannot compose a mosaic …

Yet it is common knowledge that “data” cannot always be trusted. Trust in data is a recurring theme in this blog. Cyril Burt’s purported data on the heritability of IQ is a famous case. There are legions of others.

Smart investigators know that the provenance, reliability and quality of data cannot be taken for granted but must be subject to appropriate scrutiny. The modern science of Measurement Systems Analysis (“MSA”) has developed to satisfy this need. The defining characteristic of anecdote is that it has been subject to no such scrutiny.

Evidence

Anecdote and data, as broadly defined above, are both forms of evidence. All evidence is surrounded by a penumbra of doubt and unreliability. Even the most exacting engineering measurement is accompanied by a recognition of its uncertainty and the limitations that places on its use and the inferences that can be drawn from it. In fact, it is exactly because such a measurement comes accompanied by a numerical characterisation of its precision and accuracy, that  its reliability and usefulness are validated.

It seems inherent in the definition of anecdote that it should not be taken at face value. Happenstance or wishful fabrication, it may not be a reliable basis for inference or, still less, action. However, it was Jenner’s attention to the smallpox story that led him to develop vaccination against smallpox. No mean outcome. Against that, the hundredth monkey storey is mere fantastical fiction.

Anecdotes about dogs sniffing out cancer stand at the beginning of the journey of confirmation and exploitation.

Two types of analysis

Part of the answer to the dilemma comes from statistician John Tukey’s observation that there are two kinds of data analysis: Exploratory Data Analysis (“EDA”) and Confirmatory Data Analysis (“CDA”).

EDA concerns the exploration of all the available data in order to suggest some interesting theories. As economist Ronald Coase put it:

If you torture the data long enough, it will confess.

Once a concrete theory or hypothesis is to mind, a rigorous process of data generation allows formal statistical techniques to be brought to bear (“CDA”) in separating the signal in the data from the noise and in testing the theory. People who muddle up EDA and CDA tend to get into difficulties. It is a foundation of statistical practice to understand the distinction and its implications.

Anecdote may be well suited to EDA. That’s how Jenner successfully proceeded though his CDA of testing his vaccine on live human subjects wouldn’t get past many ethics committees today.

However, absent that confirmatory CDA phase, the beguiling anecdote may be no more than the wrecker’s false light.

A basis for action

Tukey’s analysis is useful for the academic or the researcher in an R&D department where the environment is not dynamic and time not of the essence. Real life is more problematic. There is not always the opportunity to carry out CDA. The past does not typically repeat itself so that we can investigate outcomes with alternative factor settings. As economist Paul Samuelson observed:

We have but one sample of history.

History is the only thing that we have any data from. There is no data on the future. Tukey himself recognised the problem and coined the phrase uncomfortable science for inferences from observations whose repetition was not feasible or practical.

In his recent book Strategy: A History (Oxford University Press, 2013), Lawrence Freedman points out the risks of managing by anecdote “The Trouble with Stories” (pp615-618). As Nobel laureate psychologist Daniel Kahneman has investigated at length, our interpretation of anecdote is beset by all manner of cognitive biases such as the availability heuristic and base rate fallacy. The traps for the statistically naïve are perilous.

But it would be a fool who would ignore all evidence that could not be subjected to formal validation. With a background knowledge of statistical theory and psychological biases, it is possible to manage trenchantly. Bayes’ theorem suggests that all evidence has its value.

I think that the rather prosaic answer to the question posed at the head of this blog is that data is the plural of anecdote, as it is the singular, but anecdotes are not the best form of data. They may be all you have in the real world. It would be wise to have the sophistication to exploit them.

Bad Statistics I – the phantom line

I came across this chart on the web recently.

BadScatter01

This really is one of my pet hates: a perfectly informative scatter chart with a meaningless straight line drawn on it.

The scatter chart is interesting. Each individual blot represents a nation state. Its vertical position represents national average life expectancy. I take that to be mean life expectancy at birth, though it is not explained in terms. The horizontal axis represents annual per capita health spending, though there is no indication as to whether that is adjusted for purchasing power. The whole thing is a snapshot from 2011. The message I take from the chart is that Hungary and Mexico, and I think two smaller blots, represent special causes, they are outside the experience base represented by the balance of the nations. As to the other nations the chart suggests that average life expectancy doesn’t depend very strongly on health spending.

Of course, there is much more to a thorough investigation of the impact of health spending on outcomes. The chart doesn’t reveal differential performance as to morbidity, or lost hours, or a host of important economic indicators. But it does put forward that one, slightly surprising, message that longevity is not enhanced by health spending. Or at least it wasn’t in 2011 and there is no explanation as to why that year was isolated.

The question is then as to why the author decided to put the straight line through it. As the chart “helpfully” tells me it is a “Linear Trend line”. I guess (sic) that this is a linear regression through the blots, possibly with some weighting as to national population. I originally thought that the size of the blot was related to population but there doesn’t seem to be enough variation in the blot sizes. It looks like there are only two sizes of blot and the USA (population 318.5 million) is the same size as Norway (5.1 million).

The difficulty here is that I can see that the two special cause nations, Hungary and Mexico, have very high leverage. That means that they have a large impact on where the straight lines goes, because they are so unusual as observations. The impact of those two atypical countries drags the straight line down to the left and exaggerates the impact that spending appears to have on longevity. It really is an unhelpful straight line.

These lines seem to appear a lot. I think that is because of the ease with which they can be generated in Excel. They are an example of what statistician Edward Tufte called chartjunk. They simply clutter the message of the data.

Of course, the chart here is a snapshot, not a video. If you do want to know how to use scatter charts to explain life expectancy then you need to learn here from the master, Hans Rosling.

There are no lines in nature, only areas of colour, one against another.

Edouard Manet

Target and the Targeteers

This blog appeared on the Royal Statistical Society website Statslife on 29 May 2014

DartboardJohn Pullinger, newly appointed head of the UK Statistics Authority, has given a trenchant warning about the “unsophisticated” use of targets. As reported in The Times (London) (“Targets could be skewing the truth, statistics chief warns”, 26 May 2014 – paywall) he cautions:

Anywhere we have had targets, there is a danger that they become an end in themselves and people lose sight of what they’re trying to achieve. We have numbers everywhere but haven’t been well enough schooled on how to use them and that’s where problems occur.

He goes on.

The whole point of all these things is to change behaviour. The trick is to have a sophisticated understanding of what will happen when you put these things out.

Pullinger makes it clear that he is no opponent of targets, but that in the hands of the unskilled they can create perverse incentives, encouraging behaviour that distorts the system they sought to control and frustrating the very improvement they were implemented to achieve.

For example, two train companies are being assessed by the regulator for punctuality. A train is defined as “on-time” if it arrives within 5 minutes of schedule. The target is 95% punctuality.
TrainTargets
Evidently, simple management by target fails to reveal that Company 1 is doing better than Company 2 in offering a punctual service to its passengers. A simple statement of “95% punctuality (punctuality defined as arriving within 5 minutes of timetable)” discards much of the information in the data.

Further, when presented with a train that has slipped outside the 5 minute tolerance, a manager held solely to the target of 95% has no incentive to stop the late train from slipping even further behind. Certainly, if it puts further trains at risk of lateness, there will always be a temptation to strip it of all priority. Here, the target is not only a barrier to effective measurement and improvement, it is a threat to the proper operation of the railway. That is the point that Pullinger was seeking to make about the behaviour induced by the target.

And again, targets often provide only a “snapshot” rather than the “video” that discloses the information in the data that can be used for planning and managing an enterprise.

I am glad that Pullinger was not hesitant to remind users that proper deployment of system measurement requires an appreciation of psychology. Nobel Laureate psychologist Daniel Kahneman warns of the inherent human trait of thinking that What you see is all there is (WYSIATI). On their own, targets do little to guard against such bounded rationality.

In support of a corporate programme of improvement and integrated in a culture of rigorous data criticism, targets have manifest benefits. They 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. What is important is that the targets do not become a shield to weak managers who wish to hide their lack of understanding of their own processes behind the defence that “all targets were met”.

However, all that requires some sophistication in approach. I think the following points provide a basis for auditing how an organisation is using targets.

Risk assessment

Targets should be risk assessed, anticipating realistic psychology and envisaging the range of behaviours the targets are likely to catalyse.

Customer focus

Anyone tasked with operating to a target should be periodically challenged with a review of the Voice of the Customer and how their own role contributes to the organisational system. The target is only an aid to the continual improvement of the alignment between the Voice of the Process and the Voice of the Customer. That is the only game in town.

Borrowed validation

Any organisation of any size will usually have independent data of sufficient borrowing strength to support mutual validation. There was a very good recent example of this in the UK where falling crime statistics, about which the public were rightly cynical and incredulous, were effectively validated by data collection from hospital emergency departments (Violent crime in England and Wales falls again, A&E data shows).

Over-adjustment

Mechanisms must be in place to deter over-adjustment, what W Edwards Deming called “tampering”, where naïve pursuit of a target adds variation and degrades performance.

Discipline

Employees must be left in no doubt that lack of care in maintaining the integrity of the organisational system and pursuing customer excellence will not be excused by mere adherence to a target, no matter how heroic.

Targets are for the guidance of the wise. To regard them as anything else is to ask them to do too much.

Deconstructing Deming III – Cease reliance on inspection

3. Cease dependence on inspection to achieve quality. Eliminate the need for massive inspection by building quality into the product in the first place.

W Edwards Deming Point 3 of Deming’s 14 Points. This at least cannot be controversial. For me it goes to the heart of Deming’s thinking.

The point is that every defective item produced (or defective service delivered) has taken cash from the pockets of customers or shareholders. They should be more angry. One day they will be. Inputs have been purchased with their cash, their resources have been deployed to transform the inputs and they will get nothing back in return. They will even face the costs of disposing of the scrap, especially if it is environmentally noxious.

That you have an efficient system for segregating non-conforming from conforming is unimpressive. That you spend even more of other people’s money reworking the product ought to be a matter of shame. Lean Six Sigma practitioners often talk of the hidden factory where the rework takes place. A factory hidden out of embarrassment. The costs remain whether you recognise them or not. Segregation is still more problematic in service industries.

The insight is not unique to Deming. This is a common theme in Lean, Six Sigma, Theory of Constraints and other approaches to operational excellence. However, Deming elucidated the profound statistical truths that belie the superficial effectiveness of inspection.

Inspection is inefficient

When I used to work in the railway industry I was once asked to look at what percentage of signalling scheme designs needed to be rechecked to defend against the danger of a logical error creeping through. The problem requires a simple application of Bayes’ theorem. I was rather taken aback at the result. There were only two strategies that made sense: recheck everything or recheck nothing. I didn’t at that point realise that this is a standard statistical result in inspection theory. For a wide class of real world situations, where the objective is to segregate non-conforming from conforming, the only sensible sampling schemes are 100% or 0%.

Where the inspection technique is destructive, such as a weld strength test, there really is only one option.

Inspection is ineffective

All inspection methods are imperfect. There will be false-positives and false-negatives. You will spend some money scrapping product you could have sold for cash. Some defective product will escape onto the market. Can you think of any examples in your own experience? Further, some of the conforming product will be only marginally conforming. It won’t delight the customer.

So build quality into the product

… and the process for producing the product (or delivering the service). Deming was a champion of the engineering philosophy of Genechi Taguchi who put forward a three-stage approach for achieving, what he called, off-line quality control.

  1. System design – in developing a product (or process) concept think about how variation in inputs and environment will affect performance. Choose concepts that are robust against sources of variation that are difficult or costly to control.
  2. Parameter design – choose product dimensions and process settings that minimise the sensitivity of performance to variation.
  3. Tolerance design – work out the residual sources of variation to which performance remains sensitive. Develop control plans for measuring, managing and continually reducing such variation.

Is there now no need to measure?

Conventional inspection aimed at approving or condemning a completed batch of output. The only thing of interest was the product and whether it conformed. Action would be taken on the batch. Deming called the application of statistics to such problems an enumerative study.

But the thing managers really need to know about is future outcomes and how they will be influenced by present decisions. There is no way of sampling the future. So sampling of the past has to go beyond mere characterisation and quantification of the outcomes. You are stuck with those and will have to take the consequences one way or another. Sampling (of the past) has to aim principally at understanding the causes of those historic outcomes. Only that enables managers to take a view on whether those causes will persist in the future, in what way they might change and how they might be adjusted. This is what Deming called an analytic study.

Essential to the ability to project data into the future is the recognition of common and special causes of variation. Only when managers are confident in thinking and speaking in those terms will their organisations have a sound basis for action. Then it becomes apparent that the results of inspection represent the occult interaction of inherent variation with threshold effects. Inspection obscures the distinction between common and special causes. It seduces the unwary into misguided action that exacerbates quality problems and reputational damage. It obscures the sad truth that, as Terry Weight put it, a disappointment is not necessarily a surprise.

The programme

  1. Drive out sensitivity to variation at the design stage.
  2. Routinely measure the inputs whose variation threatens product performance.
  3. Measure product performance too. Your bounded rationality may have led you to get (2) wrong.
  4. No need to measure every unit. We are trying to understand the cause system not segregate items.
  5. Plot data on a process behaviour chart.
  6. Stabilise the system.
  7. Establish capability.
  8. Keep on measuring to maintain stability and improve capability.

Some people think they have absorbed Deming’s thinking, mastered it even. Yet the test is the extent to which they are able to analyse problems in terms of common and special causes of variation. Is that the language that their organisation uses to communicate exceptions and business performance, and to share analytics, plans, successes and failures?

There has always been some distaste for Deming’s thinking among those who consider it cold, statistically driven and paralysed by data. But the data are only a means to getting beyond the emotional reaction to those two impostors: triumph and disaster. The language of common and special causes is a profound tool for building engagement, fostering communication and sharing understanding. Above that, it is the only sound approach to business measurement.

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.

Music is silver but …

The other day I came across a report on the BBC website that non-expert listeners could pick out winners of piano competitions more reliably when presented with silent performance videos than when exposed to sound alone. In the latter case they performed no better than chance.

The report was based on the work of Chia-Jung Tsay at University College London, in a paper entitled Sight over sound in the judgment of music performance.

The news report immediately leads us to suspect that the expert evaluating a musical performance is not in fact analysing and weighing auditory complexity and aesthetics but instead falling under the subliminal influence of the proxy data of the artist’s demeanour and theatrics.

That is perhaps unsurprising. We want to believe, as does the expert critic, that performance evaluation is a reflective, analytical and holistic enterprise, demanding decades of exposure to subtle shades of interpretation and developing skills of discrimination by engagement with the ascendant generation of experts. This is what Daniel Kahneman calls a System 2 task. However, a wealth of psychological study shows only too well that System 2 is easily fatigued and distracted. When we believe we are thinking in System 2, we are all too often loafing in System 1 and using simplistic learned heuristics as a substitute. It is easy to imagine that the visual proxy data might be such a heuristic, a ready reckoner that provides a plausible result in a wide variety of commonly encountered situations.

These behaviours are difficult to identify, even for the most mindful individual. Kahneman notes:

… all of us live much of our lives guided by the impressions of System 1 – and we do not know the source of these impressions. How do you know that a statement is true? If it is strongly linked by logic or association to other beliefs or preferences you hold, or comes from a source you trust and like, you will feel a sense of cognitive ease. The trouble is that there may be other causes for your feeling of ease … and you have no simple way of tracing your feelings to their source”

Thinking, Fast and Slow, p64

The problem is that what Kahneman describes is exactly what I was doing in finding my biases confirmed by this press report. I have had a superficial look at the statistics in this study and I am now less persuaded than when I read the press item. I shall maybe blog about this later and the difficulties I had in interpreting the analysis. Really, this is quite a tentative and suggestive study on a very limited frame. I would certainly like to see more inter-laboratory studies in psychology. The study is open to multiple interpretations and any individual will probably have difficulty making an exhaustive list.  There is always a danger of falling into the trap of What You See Is All There Is (WYSIATI).

That notwithstanding, even anecdotally, the story is another reminder of an important lesson of process management that, even though what we have been doing has worked in the past, we may not understand what it is that has been working.

Late-night drinking laws saved lives

That was the headline in The Times (London) on 19 August 2013. The copy went on:

“Hundreds of young people have escaped death on Britain’s roads after laws were relaxed to allow pubs to open late into the night, a study has found.”

It was accompanied by a chart.

How death toll fell

This conclusion was apparently based on a report detailing work led by Dr Colin Green at Lancaster University Management School. The report is not on the web but Lancaster were very kind in sending me a copy and I extend my thanks to them for the courtesy.

This is very difficult data to analyse. Any search for a signal has to be interpreted against a sustained fall in recorded accidents involving personal injury that goes back to the 1970s and is well illustrated in the lower part of the graphic (see here for data). The base accident data is therefore manifestly not stable and predictable. To draw inferences we need to be able to model the long term trend in a persuasive manner so that we can eliminate its influence and work with a residual data sequence amendable to statistical analysis.

It is important to note, however, that the authors had good reason to believe that relaxation of licensing laws may have an effect so this was a proper exercise in Confirmatory Data Analysis.

Reading the Lancaster report I learned that The Times graphic is composed of five-month moving averages. I do not think that I am attracted by that as a graphic. Shewhart’s Second Rule of Data Presentation is:

Whenever an average, range or histogram is used to summarise observations, the summary must not mislead the user into taking any action that the user would not take if the data were presented in context.

I fear that moving-averages will always obscure the message in the data. I preferred this chart from the Lancaster report. The upper series are for England, the lower for Scotland.

Drink Drive scatter

Now we can see the monthly observations. Subjectively there looks to be, at least in some years, some structure of variation throughout the year. That is unsurprising but it does ruin all hope of justifying an assumption of “independent identically distributed” residuals. Because of that alone, I feel that the use of p-values here is inappropriate, the usual criticisms of p-values in general notwithstanding (see the advocacy of Stephen Ziliak and Deirdre McCloskey).

As I said, this is very tricky data from which to separate signal and noise. Because of the patterned variation within any year I think that there is not much point in analysing other than annual aggregates. The analysis that I would have liked to have seen would have been a straight line regression through the whole of the annual data for England. There may be an initial disappointment that that gives us “less data to play with”. However, considering the correlation within the intra-year monthly figures, a little reflection confirms that there is very little sacrifice of real information. I’ve had a quick look at the annual aggregates for the period under investigation and I can’t see a signal. The analysis could be taken further by calculating an R2. That could then be compared with an R2 calculated for the Lancaster bi-linear “change point” model. Is the extra variation explained worth having for the extra parameters?

I see that the authors calculated an R2 of 42%. However, that includes accounting for the difference between English and Scottish data which is the dominant variation in the data set. I’m not sure what the Scottish data adds here other than to inflate R2.

There might also be an analysis approach by taking out the steady long term decline in injuries using a LOWESS curve then looking for a signal in the residuals.

What that really identifies are three ways of trying to cope with the long term declining trend, which is a nuisance in this analysis: straight line regression, straight line regression with “change point”, and LOWESS. If they don’t yield the same conclusions then any inference has to be treated with great caution. Inevitably, any signal is confounded with lack of stability and predictability in the long term trend.

I comment on this really to highlight the way the press use graphics without explaining what they mean. I intend no criticism of the Lancaster team as this is very difficult data to analyse. Of course, the most important conclusion is that there is no signal that the relaxation in licensing resulted in an increase in accidents. I trust that my alternative world view will be taken constructively.