I agree. There must be subjectivity. And as to math itself, there is the old question of whether it is created or discovered.

Models (including tool to establish such models) are always and neccesarily subjective. In the beginning, it is mostly dirven by one or few subjects, and if it is successful, it will be adoped by more data, modified, and confirmed by a growing amount of data. Thereby it will become a more and more inter-subjective consensus.

Of course. In fact the measuring procedure produces infected data (either caused by "shaking hands", or by some unprecise instruments, or both); sometimes there is no need for high precision measurements, so the data "almost exact". The statistical hypotheses testing controls the system data by the concept of the degrees of freedom: if you don't know the exact value of a parameter in the statistical distribution you assumed in the testing procedure, you have to estimate the parameters' value from the sample (which could be infected), therefore the dergees of freedom decreases for the number of parameters estimated from the input sample.

The Researchgate's "answer-processor" is pretty slow and skips some words of mine - please, interpolate and correct my answer's grammar.

The only way to come around the subjectivity in data analysis is to make it pre-planned, i.e. plan the analysis and document it before you collect the data (at least as far as I know). That is obviously only in some scenarios possible, e.g. clinical studies.

Another way to come around this, is to make sure, that the results are somehow robust when the data is analyzed in different ways. (and yes - this editor is really slow :-(((...

In some way the answer is yes! let see a research project where we are looking to model some process, let say a rainfall-runoff process. Starting from the choice of the model type we are introducing our personal preference. Several problems admit deterministic and stochastic solutions at the same time, choosing wich want to implement imposes our favorite research flavour. Nevertheless, research protocols, modelling protocol can help avoiding such subjectivity, but, it can raise againg when trying to conclude is it our model validated enough or not! it becomes of special importance when modelling non stationary and unstable systems. It can sound weird but in such kind of situation some subjectivity can improve your research results, specially with living or complex systems.

A quotation from E. T. Jaynes:

"In most real problems, the only prior information we have about the noise is its mean square value because it has maximum entropy for a given mean square noise level, the independent "white" Gaussian distribution will be the safest, most conservative one we can use; i.e. it protects us most strongly from drawing erroneous conclusions. In other words, it most honestly describes our state of knowledge".

So even the least-square modeling is subjective because it is chosen to fit a model under the awgn assumption, isn't it?

Hello Katharina Anna Zweig, I don't think this really answers your question at all, but just a quirky finding / thought given what you are asking. Take for example giftedness, an array of tests to determine this and calculate an IQ. But then I find some people who are gifted so highly intelligent and academically clever are subjectively in my mind rude ! Just a thought don't give too many tests, help them to learn that other people have feelings and that sometimes the clever exclude others horrendously. As I said not really an answer, just a thought for what it is worth. Maths is important to calculate scores, but sometimes it ends up clouding the obvious if you know what I mean.

Thanks

Deborah Hilton Statistics Online

http://sites.google.com/site/deborahhilton/

The beauty of math models is in the usefulness of the model. Whether the model is subjectively influenced really does not matter--what matters is the reproducibility and predictability of the function of the model. The math models I have worked with, however, are most useful for those subjects that are colse to the norm. Outliers rarely fit the model. That being said, expansion of the model which would include the outliers should eventually encompass a larger population base. The constant revision of the model using objective methods as possible should make the model more useful, functional, reproducible, and trustworthy.

At the moment that you picked up a model then your scientific research has become subjective. Why did you choose that model and not another one? A typical answer is that "I chose that model because it optimizes something'.Yes, but then why did you choose that specific 'norm' to be optimized and not another one?

I think that we have to establish methods that do not need to pre-assume a model.

My work in finding the inflection point of a convex/concave curve is a typical example.

I didn't assume any kind of functional form in order to find the inflection point via regression, but I examined the geometrical properties that follow the existence of an inflection point.

Your question is excellent and I hope a nice conversation to start from it.

I completely agree with Demetris!! The approach to have the model "discovered" objectively and then analyzed for it's usefulness is truly the best approach. My research has used the multiple regression approach that encompasses all of the independent variables. Those variables that reach statistical significance are then considered to be a part of the model and the coefficients of each of those variables are then used as the coefficients within the model. The model is then been chosen based on statistical signficance and the onlyu subjective aspect would be within the original research design during the choosing of the independent variables that are studied. Otherwise, I feel that this approach eliminates most of the subjectivity in the model.

Wayne, although we are in different fields, I see that we have similar scientific approach.

If you want just to find an inflection point in your noisy S-shape data you can install and use the new package: inflection

You can find it on CRAN or you can simply install it via R or RStudio.

Have an efficient research!

http://cran.r-project.org/web/packages/inflection/index.html

In a model or in a result, the newly introduced parameters are sometime subjectively used (artificial generalization, extension, unification etc.). Then, specifying the parameters value we arrive at already proved classical findings, but sometimes it turns out that the new parameters are helpful and the generalization is OK. Let me give an example. Assume that the inequality $f(x) \le g(x)$ holds for some subset of positive reals. Considering $e^{-\alpha x}f(x) \le g(x)$, $\alpha>0$ we get a redundant result, since the LHS of the new inequality it is obviously not an improvement , but for $\alpha=0$ we get the already known relation. However, proving $f(x) \le e^{-\alpha x}g(x)$, we interpolate the input inequality, establishing new stronger upper bound for $f(x)$. In both cases we take subjectively the new factor $e^{-\alpha x}$ (the reason to introducing it was may be only the academic curiosity), but in the first case it is senseless artificial manipulation, and in the second case it is a nice contribution.

Hi Katharina, I am not completely sure that I would use the word subjective, but I would say there are a lot of bad practices among quantative researchers. For high-stakes research, such as clinical trials, I think that the analyses should be pre-specified and the primary analyses confined within those specifications with limited exceptions. For example, in a recent article we just submitted we discovered that there was a more rigorous (and probably not necessary in our case) way to handle the fact that there was stratification in our trial, so we applied it. I think there a lot of bad practices, such as performing significance tests for correlation matrices to see what's significant, or things like stepwise regression that performs countless statistical tests even though the researcher doesn't see them. I don't do either or those things. Left to my own devices I perform a pretty liminted set of sequential models. I admit that pushed by colleagues I will do models of variations they want to see, or I have a better, usually more intricate idea as compared to my initial idea. I think you can see the integrity of certain researchers who use the certain classes of models over time consistent techniques and presentations as opposed to what might appear to be capitalizing on a chance finding. Unfortunately, even though an official statement of the American Psychlogical Association pointed to the inherent troubles with the routine step of statistical testing in a correlation matrix, many still rely on such chance methods to guide their research. Relying on chance to come up with publishable findings isn't quite subjective to me, but it also isn't very scientific. It also isn't always going to be possible to tweak findings to finding what you want without literally faking something, but there is definitely a gray area where you could prune items from your measures or something like that, but an honest academic would report everything and leave it to peer reviewers to determine the integrity. My integrity is certainly more important to me than getting a desired finding. Despite almost any competent expert saying that adhering religiously to the .05 level of significance for decades now, we still tend to report anything even slightly on the high side as "not significant." I bring this up, because although we can try an aresenal of different statisitcs on one problem, assuming they fit the problem at all, they are rarely off by a huge amount, so someone might tweak something to force something under the .05 barrier using one test rather than another (and again they face peer reviewers over their choice), they are not changing the larger reality of what is going on, just some conclusion of the likelihood of that finding in a population based on one of several standard distribtuions.

What we measure and how we measure it are, indeed, huge choices. If there is one leg the whole enterprise stands on it's that. Anyone who spends much time in this and doesn't think about measurment really should get out. Sometimes we have measured something for so long and in a certain way that the measure has taken on a life of its own, such as IQ. We have hardly agreed what intelligence might be, but IQ has been around so long that pretty much everyone knows what it is. The choices made about what to measure and how to measure it are definitely very human choices. Once in place, I don't know if I would call the measures themselves subjective, but the choices about measures can very much affect the research, more so than anything else.

Bob