As predicted, there were cigars. But I missed them. The smoking party left without me while I listed to Ireland’s version of the Mr Wizard brothers. A science experiment involving a syringe, 100 meters of day-glo green tubing, a reservoir of water, and a rush of explanation. And something to do with oxygen dimers. And multimers.
So no cigars, but whisky (not whiskey) there was. And plenty of good food. After an excellent meal, with plenty of sauce, everybody was juiced and raring to go.
The only negative is the Washington Court Hotel. The wall “art” is festooned about, like troops ready to attack. It’s ugly like most “art” is these days. But it’s worse. It’s aggressively ugly. This “art” hates you. I can only imagine it won some sort of award.
Anyway, while trying to explain that no statistical model or test is necessary when looking at time series to discover whether there was a “trend”, I hit upon the following simplification.
I don’t have the facilities, so draw for yourself a standard x-y plot, with x the time and y the measure of interest, say temperature. At some early time point, place a dot for the first “temperature”. And at some later point, place a second dot higher than the first.
Now I ask you: was there a trend in the data?
This question causes distress in anybody who has had classical statistic training. They want to answer, but feel—and I do mean feel, not think—they cannot. The objections will be “There’s not enough data to tell” or “I can’t fit a model to that” and the like.
It is very difficult, almost impossible, for people with training in classical statistics to look at data without reflexively wondering what model “best explains” the data. This is why classical statistics, especially hypothesis testing, has to go. Put it in the same place as the Hotel’s “art.”
Firstly, the probability models in the classical quiver do not say word one about what caused the data. If we knew what caused the data, we would not need probability models. We would just point to the cause! Probability models are used in the absence of knowledge of cause. And they should never be used to say what happened.
Let me repeat that, and let me shout it: probability models should never be used to say what happened. We can simply look at the data and it can tell us what happened.
So why does everybody think “fitting” a, say, straight line to time series data think that straight line explains the data? Well, that’s what they’re taught. Sort of. The concept of causality is vague in probability and statistics. So vague that people are allowed to take away from any analysis whatever they want.
This is why hypothesis testing is so toxic. Once a wee p-value is spotted, “randomness” or “chance” are rejected as causes and whatever other idea the researcher had in mind is said to be the cause. This is wrong in every possible way. Randomness and chance are never causes, and to assume a cause is not a proof this was the sole correct cause.
Secondly, the answer to our question is: there is no way to tell because there is no definition of trend.
We’ve talked about this many times. Trend is analogical. My idea of the word might not match yours. Thus in order to say whether there is a “trend”, we need a definition. If that is “any increase” then, yes, unambiguously, there was a trend. If the definition is “at least three increased in a row”, then there was no trend.
If the definition was “the slope of a regression line fit to the data is greater than 0” then there was no trend. Frequentist statistics in particular often fails when the data are not plentiful.
That’s it. All typos today free on charge. When this thing publishes, I’ll already been in today’s meetings. I speak tomorrow morning. They whole thing will be streamed: click here.