{"id":1564,"date":"2012-02-17T00:32:47","date_gmt":"2012-02-17T07:32:47","guid":{"rendered":"http:\/\/qpr.ca\/blogs\/?p=1564"},"modified":"2012-02-17T00:32:47","modified_gmt":"2012-02-17T07:32:47","slug":"silly-questions","status":"publish","type":"post","link":"https:\/\/qpr.ca\/blogs\/2012\/02\/17\/silly-questions\/","title":{"rendered":"Silly Questions?"},"content":{"rendered":"

Statistical pundit William M. Briggs has written a piece for ‘Significance’ on\u00a0Why Do Statisticians Answer Silly Questions That No One Ever Asks?<\/a>.<\/p>\n

Briggs is right to object to instances where statisticians (or more often users of statistics) respond to silly questions with the answers to different (and often equally silly) ones without making it clear enough that they are not answering the original question. But he is wrong in his presumption that the questions asked usually make sense.<\/p>\n

In fact it is common to talk of probability in quantitative terms in situations where it is by no means clear what a specific numerical probability would mean. \u00a0Such talk is what gives rise to many well known “paradoxes”\u00a0which can only be resolved by clarifying the interpretation.<\/p>\n

But although Briggs alludes to recent advances in Bayesian analysis, he doesn’t seem to understand them well enough himself \u00a0– at least not well enough to answer a simple question about what he means when he says\u00a0\u00a0<\/span>\u201ca civilian needs little or no maths to understand what \u2018the probability that A is better than B is 80%\u2019 means\u201d.\u00a0<\/span><\/p>\n

Briggs response to the question of what that understanding might be is just “It means the evidence is such that the probability ‘A is better than B’ is 80%. Which is greater than 0% but less than 100%. Nothing more.<\/span>”<\/p>\n

When challenged that this is like claiming to\u00a0explain what \u201cthe hoy is gerflumptive\u201d means by saying that it means \u201cthe evidence is such that the hoy is gerflumptive\u201d, he responds with “<\/span>I wasn\u2019t being glib. Probability (see above) is a measure of truth, or closeness to truth. 80% is closer than 70% and less close than 90% to being true. What you do with this number is different than what the number is.<\/span>“<\/span><\/p>\n

Well, I\u2019m sorry, but giving \u201ccloseness to truth\u201d as a definition of probability *is* glib.<\/p>\n

(It\u2019s also more than 75% wrong in that I can think of at least three measures of closeness to truth that are more common than anything to do with probability.)<\/p>\n

He asks for examples and I say:<\/p>\n

For example, in common language (as per my claim):<\/span><\/p>\n

1. an approximate answer is often referred to as close to the truth<\/span><\/p>\n

2. a false statement is sometimes referred to as close to the truth if its error arises from a fairly common misuse of terminology<\/span><\/p>\n

3. a detective may be said to be getting close to the truth if he has a good idea of where to look for the deciding piece of evidence<\/span><\/p>\n

etc.<\/span><\/p>\n

Briggs responds to these with:<\/p>\n

But two of these examples are non-probabilistic.<\/p>\n

1. Given our background knowledge, an approximate answer is likely true
3. Ditto<\/p>\n

2. You\u2019ll have to clarify this. A falsity is not close to a truth; a mistake is still a mistake.<\/p>\n

Cooper:<\/p>\n

They were intended to be non-probabilistic as I was giving them as examples of why \u201ccloseness to truth\u201d is not a good definition of probability.<\/span>
1. The statement that the circumference of a circle is six times its radius has zero probability of being true but it is close to the truth.<\/span>
3. Knowledge of the fact that the murdered duke wrote a deathbed note which will tell me whether it was Colonel Mustard or Professor Plum who poisoned him brings me closer to the truth without increasing the probability of either hypothesis.<\/span>
2. Your attempt to define probability as \u201ccloseness to the truth\u201d may be close to the truth but it has zero probability of actually providing a useful definition.<\/span><\/p>\n

Briggs:<\/p>\n

Alan,<\/p>\n

I assume you meant your \u201c2\u2033 as a joke, but it has backfired on you. In a useful way, however. Let\u2019s see.<\/p>\n

1. A = \u201cThe circumference of a circle is six times is radius.\u201d Now, there is no such thing as<\/p>\n

\u00a0\u00a0\u00a0 Pr(A).<\/p>\n

But we can calculate:<\/p>\n

\u00a0\u00a0\u00a0 Pr(A | E) = 0<\/p>\n

where E = \u201cMy knowledge of geometry as might be found in any high school or higher text\u201d. Notice that this is completely different than B = \u201cA is a good approximation\u201d. We still cannot calculate<\/p>\n

\u00a0\u00a0\u00a0 Pr(B).<\/p>\n

But we can calculate:<\/p>\n

\u00a0\u00a0\u00a0 Pr(B | E & F) = 1<\/p>\n

where we have the same E plus information F = \u201cA good approximation is being within plus or minus 20% of the radius\u201d or some other F (different F might change the probability, of course).<\/p>\n

3. A = \u201cDuke says M or P killed him\u201d. If B = \u201cM killed the Duke\u201d then<\/p>\n

\u00a0\u00a0\u00a0 Pr(B | A) = 1\/2<\/p>\n

and similarly for C = \u201cP killed the Duke.\u201d The probability<\/p>\n

\u00a0\u00a0\u00a0 Pr(Duke was murdered | evidence of dead body & foul play) = 1<\/p>\n

which is the same as<\/p>\n

\u00a0\u00a0\u00a0 Pr(Duke was murdered by somebody | evidence of dead body & foul play) = 1.<\/p>\n

But we cannot compute<\/p>\n

\u00a0\u00a0\u00a0 Pr(Duke was murdered by M | evidence of dead body & foul play) = unknown,<\/p>\n

unless we condition on something more, namely a list of suspects.<\/p>\n

2. I could write this out, but you\u2019ll get the idea. The probability that I have provided you the true definition, given all this (and other information on the blog) is 1.<\/p>\n

Cooper:<\/p>\n

All I can say is that I think you must have missed my point \u2013 which was that there are common language senses of \u201ccloseness to truth\u201d which have nothing to do with probability, and so that \u201ccloseness to truth\u201d is not a good definition of probability.<\/p>\n

This all started when I asked you what you would say \u2018the probability that A is better than B is 80%\u2019 means, and so far I haven\u2019t seen anything not glib in response.<\/p>\n

Briggs:<\/p>\n

Alan,<\/p>\n

I haven\u2019t; you have failed to make yours. In order to disprove my thesis, you need to show an example that can\u2019t be written in the forms (for example) that I\u2019ve given.<\/p>\n

\n

Cooper:<\/p>\n

Thanks for trying, but I don\u2019t understand what you are saying. If you have given an intelligible answer to my question about the meaning of probability then I guess I\u2019ll just have to accept that the subject is beyond me.<\/span><\/p>\n

\n

Seriously, am I nuts or is this guy cuckoo?<\/p>\n","protected":false},"excerpt":{"rendered":"

Statistical pundit William M. Briggs has written a piece for ‘Significance’ on\u00a0Why Do Statisticians Answer Silly Questions That No One Ever Asks?. Briggs is right to object to instances where statisticians (or more often users of statistics) respond to silly … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1564","post","type-post","status-publish","format-standard","hentry","category-general"],"_links":{"self":[{"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/posts\/1564","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/comments?post=1564"}],"version-history":[{"count":1,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/posts\/1564\/revisions"}],"predecessor-version":[{"id":1565,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/posts\/1564\/revisions\/1565"}],"wp:attachment":[{"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/media?parent=1564"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/categories?post=1564"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/tags?post=1564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}