Why should you want to test normality? Why should a particular real-world probability distribution be (close to) a normal distribution?

Remember George Box's famous statement "all models are wrong but some are useful". https://en.wikiquote.org/wiki/George_E._P._Box

Life is hard, especially the life of an honest statistician. Who said it was going to be easy?

Thanks Richard for your remarks. Humans can not live without interpreting our reality with models expressed in some language. It is our past and our destin. Normal distributions were the answer adopted by several generations; they have a place in history and deserve recognition as the product of highly creative people in their context. Eduardo Galeano -a latinoamerican writer- wrote some years ago: Why are utopies useful if we advance one step toward them while they go two steps far from us? The answer was something like: "Just for that, to walk and decide the road in our lives".

Dear Emilio

As Fausto before, I do not see why the Pareto distribution may be related to control on the ethical practices of statistics and sampling.

May be that you are saying that this model is better always than a normal model for the same problem, and that it would be more ethical to use it instead of the usual parametric (or normal), but I do not believe this. I may be forgetting something here, then I would like that you specify better what you are saying.

Guillermo, statistical models are not ethical by theirselves. They are only mathematical constructs to interpret collected data by researchers and we assume datasets are made with rigour and honesty. Some models may fit and interpret a particular dataset better than others. The task is that obtained model fits dataset, not that dataset follows model -unless you use the model for simulations where you generate artifitial datasets-. Now, if you predefine a model as "an apriori" truth, then you may simulate and build datasets of any size to observe them, and to analize them by other methods.

In some cases datasets may be, and have been changed to favour the hypothesis advanced by researchers; this is an ethical problem related to truth and human freedom to act well or not. Fausto has mentioned many cases where managers lied -by choosing a convenient parameter - to prove results of their convenience, or to save expenses derived from quality control replications, etc. Those are practical examples of the ethical point.

When random samples are built from controlled experiments and interpreted with the Laplace criterion there may be some distorsions in the structural function obtained, mainly if the dataset has few points; eventhough, you may recognize the basic distributive structure behind it. Pareto´s distribution is only a particular model useful and convenient as a tool to prove the point; it is not a universal distribution recipe.

I consider normal distributions as an old model that had an important roll in the history of statistics and science, but it needs to be overcome and replaced as soon as possible by better methods. This implies a mindset change in textbooks, teachers, students, researchers and it will probably ask the replication of many researches of the past. But what would happen if the replication also contains the same or different errors and lies of the original research? Only a clean ethical behaviour will free us from distorted conclusions.

I know this may produce heavy resistance from some sectors because it is harder to accept deep truth than to accept unintentional errors. Thanks for your feedback and welcome to new ideas and comments to treat these points. emilio

Kenneth, your question seems to be a bit off-topic ... if you give me the data (or give me a link to a place where I can get the data myself, easily, and draw this graph myself) then I could try to answer it.

The graph looks like pure noise. (Not a random walk: a random walk is the cumulative sums of pure noise). However if we would compute from the noise the corresponding walk, we would see that it keeps coming back close to zero. Because over many years, the average temperature computed over those years and over those years shifted by one month can hardly differ.

So I think your conclusion is wrong. But I don't see what the scientific interest in the question should be, nor the relevance to ethics in statistics.

Keneth and Richard, indeed sampling is both a technical and ethical task. Have you tried to represent the same data using absolute temperatures -adding 273 centigrades- in Kelvin degrees? I assume that your data is among the best available ones and it may be interpreted such as it comes for the particular context studied; even if it does not represent the planet it contains useful information. If results show some tendence or regularity it means that its behaviour is structural, but not random, and this brings new questions to answer. OK, welcome to your work and contribution, emilio

Keneth, I sent an answer yesterday, it did not arrive there: probably I made a typing mistake. It said that working only positive values of variable produces graphs where it is easier to observe the trends and mathematics are easier to handle, like your Maunaloa CO2 graph. In the case of De Bilt temperatures I think that its cyclical shape is enough to accept that distribution is not random, but it is structural and perhaps it contains other tendences. Thanks, emilio

Keneth. Sorry if I caused your confusion. You sent two graphs, in one of them -to Richard- you say "Of course, de Bilt is a very small place, but the northern hemisphere temperatures show the same thing. (Chart attached)." I thought the chart referred to de BIlt, where you show seasonal temperatures which are cyclical. The second one -to me- is about Maunaloa about CO2, made of positive values. My comment was based in the two posts you made, and the two graphs. Does this help to understand what happened? Regards, emilio