Making Bayesian statistics accessible

Making Bayesian statistics accessible

So, let us tackle this issue of bringing Bayesian thinking alive for the everyday

market research practitioner, by ¬rst providing an example of how a traditional

statistician, and then, let us call them, statisticians ˜informed by Bayesian think-

ing™, might tackle the same data. The purpose of this exercise is to work towards

explaining the way in which the holistic analyst will establish a broad inter-

pretative boundary by mapping the statistically driven constraints, and then go

beyond this constraint-driven boundary to stretch the interpretation by applying

the enablers.

How a ˜traditional™ and a ˜Bayesian informed™ statistician might

examine the same data

Let us compare the traditional and Bayesian approaches by looking at a sim-

ple example which allows us to quickly draw out the key points of difference

between the two schools of analysis. Figure 10.1 shows a very simple example

of the type of data over which the orthodox and holistic schools would

probably part company. It shows data from a quantitative study into a new

technology targeted at a consumer market. It shows data for a sub-sample

of respondents to whom, for a variety of non-technology-related reasons, the

new technology is appropriate, and it also shows this sample analysed by the

age categories.

60

53

50

43

% very likely to adopt

42

new technology

40

34

30

20

10

0

Total (105) 18 “35 (35 36 “55 (36 56 “ 65 (34

cases) cases) cases)

Age

Figure 10.1 “ Likelihood of adopting new technology by age.

The data in Figure 10.1 would elicit rather different responses to the data from

the following different parties:

144 Establishing the interpretation boundary

• The intelligent non-researcher (a group which includes most of our end clients

for research): to this group, these data seem to indicate that older people are

less likely to adopt the new technology. Everything we know about age and

technology tells us that we can have con¬dence in the particular shape and

pattern in this data. Notwithstanding the trend for lifelong learning, and the

presence of older ˜silver surfers™, it remains the case that, on balance, older

people tend to be less able to acquire new skills and “ as they are more likely

to be established in their chosen careers “ are less likely to move to acquire

new skills.

• The researcher trained in orthodox statistics: these specialists, however, would

point out that the base sizes involved mean that the differences are not

statistically signi¬cant at the 95% level of con¬dence. For example, to be

signi¬cant, the difference between the ¬gure for the 56“65-year-old age

group and that for the 18“35-year-old age group would have to be about

23%, but it is only 19%.

• The holistic analyst: these researchers would want to draw the same conclu-

sion as the intelligent end client (and, left to their own devices, they probably

would, in practice). However, confronted by the orthodox researcher™s objec-

tions to this, they would be unsure how to defend their position, except

to say that the conclusion seems ˜intuitive™, or is what you would ˜expect

to see™. Neither of these forms of defence seems to adequately address

the orthodox researcher™s objections. So what do we do? Do we accept

the strictly statistical interpretation, or go with our prior knowledge, after

taking into account whether there are any special, or unusual, conditions

prevailing that could make older people opt for this particular piece of

new technology?

In sum, the reason why we feel so con¬dent in concluding from the data

in Figure 10.1 that older people will, indeed, be less likely to adopt the new

technology, is that we have a great deal of prior knowledge relating to the attitudes

of older people, in general, to new technology. We tend (quite correctly) to view

older people as being generally, ˜late adopters™ of technology and ˜technophobes™.

Thus, to help us out of this impasse, we can apply some of the principles of

Bayesian statistical thinking to our analysis of the data. In some cases, this

may take the form of a loose application of the notion of prior knowledge, in

other cases, it may require the more detailed application of Bayesian generated

statistical techniques.

Taking the enabler concept forward

We would argue that we urgently need a new conceptualization of how market

research data is interpreted. We believe that to continue with the view that we can

simply apply ˜classic™ statistics to our data ¬‚ies in the face of the way the market

research industry is heading. This would deny the growing trend towards using

145

Taking the enabler concept forward

imperfect evidence drawn from multiple sources. It would also deny the growing

client interest in incorporating prior management knowledge and ˜grounded™

intuition into the data analysis process. In sum, it seems that, over the next

decade, the demand for more clinically correct, methodologically pure, orthodox

statistical interpretations will decline. Surely, in the future, the demand will be for

researchers who can weave the rigour of what we know about statistics together

with what other data sources and management prior knowledge are telling us.

So we think the Bayesian approach is incredibly powerful, and offers commercial

researchers enormous potential.

It provides a methodology for adding rigour and transparency to the pro-

cess of analysing market research data. It provides a clear-cut set of theory,

practice and principles, which allows us to formalize the relationship between

what the survey says, and what we would expect to see. Yet it seems unreal-

istic to expect, after all these years, that commercial researchers will suddenly

embrace Bayesian statistics for the everyday interpretation of statistics. Cer-

tainly, soundings taken among experienced statisticians in the market research

industry show that it is unlikely that pure Bayesian statistics will achieve the

status that orthodox statistics has achieved in the world of evidence-based

decision-making.

So what seems most likely, is that the (Bayesian) thinking behind the notion of

embracing ˜subjective™ prior probability into everyday market research analysis,

will gradually gain more credibility. It seems reasonable to see a day when

decision-makers will begin to see the value in a new approach that makes

current everyday working practices explicit and transparent.

Therefore, it seems realistic to start promoting frameworks that turn com-

mon sense into consistently applied industry-wide common practice. This would

create a situation where both the client and the researcher see the bene¬t of

jointly exploring interpretations of the data, bringing their combined knowl-

edge to the market, thereby adding power to the market research ¬ndings.

However, we accept that this will only be achieved by developing useful heuris-

tics “ general principles “ rather than taking the Bayesian concept forward in its

fullest statistical form.

A simple practical analysis tool

Below, we provide an example of a Bayesian-based model developed for dealing

with statistics derived from smaller base sizes. This provides market researchers

with a practical tool that enables them to estimate Bayesian prior probabilities