Most mar­ket­ing peo­ple have only a pass­ing inter­ac­tion with sta­tis­tics, and often times only under­stand it as a mea­sure of how it has impacted their daily life. One of the funny things peo­ple don’t real­ize is that there are two com­pletely dif­fer­ent com­pet­ing schools of thought when it comes to sta­tis­tics. Most peo­ple are famil­iar with fre­quen­tist sta­tis­tics, hav­ing dealt with things like nor­mal dis­tri­b­u­tion, bell curves, and estab­lished prob­a­bil­i­ties. The other school, Bayesian sta­tis­tics, is a realm that fewer peo­ple are famil­iar with, but just as applic­a­ble. In fact, the move over the last few years is for more peo­ple to change from the fre­quen­tist model to Bayesian techniques.

So what is Bayesian sta­tis­tics? To put sim­ply, Bayesian analy­sis is the use of con­di­tional or evi­den­tial prob­a­bil­i­ties. It looks at what you know of the envi­ron­ment and past knowl­edge, and allows you to infer prob­a­bil­i­ties based off of that data. It asks what is the like­li­hood of some­thing hap­pen­ing based on our knowl­edge of past con­di­tions and the con­text of them in the world. Where fre­quin­tist sta­tis­tics can be viewed as much more of a eval­u­a­tion of the larger data col­lec­tion and judg­ing the chances of some­thing hap­pen­ing again based off of those results, Baysian is about the like­li­hood a set of results reflects the larger real­ity and about mak­ing infer­ence based on the lim­ited data set.

Whereas a fre­quen­tist model looks at an absolute basis for chances, some­thing like the pop­u­la­tion of females is 52%, so that means that if I select some­one at ran­dom from my office, I have a 52% chance of pick­ing a female. The chances are purely based on the total prob­a­bil­ity. The Bayesian approach is to rely on past knowl­edge and then adjust accord­ingly. If I know that 75% of my office is male, and I grab a per­son, then I know that I have a 25% chance of pick­ing a female.

So is it 52% or 25%? Both are cor­rect answers depend­ing on what ques­tion you are really ask­ing, but both look at things dif­fer­ently. Fre­quen­tists look at the larger per­spec­tive of all chances, and base things off that ideal look at the world. Bayesian users use much more per­sonal or past knowl­edge to infer infor­ma­tion. Bayesian thinkers would much rather answer what are the chances that the total pop­u­la­tion is 52% female based on the fact that only 25% are female in this office. The risk with using Bayesian logic is that you are allow­ing for bias and poor data col­lec­tion to dra­mat­i­cally later how you view things. The gain is that while fre­quen­tist will often be right in a con­trolled set­ting and over time, Bayesian has the chance to give you bet­ter infor­ma­tion based on what you know. Bayesian logic also allows you to do con­di­tional logic state­ments, like based on the office sce­nario before and a lit­tle bit more con­tex­tual knowl­edge, you can answer “what is the like­li­hood that if you choose a women that she would have blond hair?”. Bayesian tech­niques are often used for logic rea­sons, because it allows you to make a con­clu­sion about the like­li­hood some­thing is the best answer based on what you know. Both tech­niques are at risk for black swan type of analy­sis, though Bayesian analy­sis can be even more influ­enced by only focus­ing on the known.

So why is this impor­tant? All test­ing tools and mod­els are almost always rely­ing on fre­quen­tist tech­niques to give you the global view of some­thing as to how often it fits into a pat­tern. This is why you see things like 92% con­fi­dence when eval­u­at­ing things, we know that under sim­i­lar cir­cum­stances, 92% of the sam­ple means will fit into that win­dow. Those tech­niques give you answers in an ideal sit­u­a­tion and over time, but that may not be true of spe­cific peri­ods or non nor­mal events. They don’t take into account the con­text of this spe­cific sit­u­a­tion, nor prior his­tory rel­e­vant specif­i­cally to the sit­u­a­tion. They often times don’t take into account even the con­tex­tual knowl­edge of the other recipes and infor­ma­tion con­tained in that same test. They might be true of nor­mal cir­cum­stances, but not of a spe­cial sale or sea­sonal activ­ity. Bayesian tech­niques rely on prior knowl­edge that for test­ing is rarely avail­able, and for ana­lyt­ics is prob­lem­atic at best. They might reflect spe­cial cir­cum­stances, but not give a good long term view due to those same mit­i­gat­ing circumstances.

In all cases, noth­ing will replace under­stand­ing the con­text of what your data tells you, the pat­terns of it, and know­ing how and when to act. You have to appre­ci­ate what the sta­tis­tics are telling you, but also appre­ci­ate what they aren’t telling you. Any overt belief in a mea­sure, by itself is always going to be prob­lem­atic. Just get­ting a sta­tis­ti­cal answer is not a replace­ment for the con­text and the envi­ron­ment by which you are gath­er­ing data, nor mak­ing a deci­sion. You can not have blind faith in stats to replace your own abil­ity to rea­son, nor can you you blindly believe that all lab­o­ra­tory sta­tis­tics prop­erly reflect real world situations.

No mat­ter what tech­niques you use, no mat­ter which camp you are in for the cor­rect way to look at things, there is never a time when you can ignore the prob­lems of any sin­gle type of analy­sis. You can not replace using dis­ci­pline and logic in your actions. Sta­tis­tics are just a tool, they can not replace proper rea­son­ing, yet too many peo­ple look at it as a mag­i­cal panacea to remove respon­si­bil­ity for action. Always remem­ber that there are mul­ti­ple ways to look at a prob­lem, let alone hun­dreds of ways to solve it. Fig­ur­ing out the effi­cient and best way for you is the real key.

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