Alternatives to Hypothesis Testing in R I've been reading a number of articles and blog posts about issues relating to hypothesis testing. While these sources seem to put forth legit problems with hypothesis testing and it's interpretations, I'm not seeing anything in terms of alternatives to it (beyond bayesian hypothesis testing). What are some alternative to hypothesis testing in R?
Problems with the hypothesis testing approach
So-called Bayesian hypothesis testing is just as bad as regular hypothesis testing
Alternatives to Statistical Hypothesis Testing
EDIT:
For example, let's consider the following situation. We have monthly data for one year where 
conversions_a is the control and conversions_b is the experimental data for conversion when using a different headline. 
df = data.frame(year_one_a = 1:12, conversions_a = rnorm(12), 
                year_one_b = 1:12, conversions_b = rnorm(12)+5)

 A: One alternative is to forgo p-values altogether and focus on what the results mean. In many situations, p-values answer a question we are not (or ought not be) interested in:

If, in the population from which this sample was drawn, there is no
  effect, how likely is it that, in a sample of this size, we would get
  a test statistic as big or bigger than the one we got?

Instead, we ought to be interested in what the statistics add to an argument about what is going on. This idea is fully developed in the book "Statistics As Principled Argument" by Robert Abelson (link goes to my review) but, essentially, we ought to be asking these questions about the effects we find:


*

*How big are they?

*How precise are they?

*How widely do they apply?

*How interesting are they?

*How credible are they?


This can only be done if we are also substantive experts or if we work closely with experts. For example, sometimes small effects are quite interesting - so interesting that they are worth discussing. Indeed, sometimes effects are interesting because they are small - if the literature and theory suggests that they ought to be big.
Highly credible claims require less evidence than ones that are not credible, but credibility has non-statistical sources. 
A: This is subjective, and doesn't directly address your question, but I hope it's helpful regardless. 
I think people too often conflate a statistical hypothesis with a scientific one, which leads to problems. Regarding the former, the statistical hypothesis being tested is almost always whether the parameter being estimated is zero or not. But with any deeper thought on the matter, one realizes this is often trivial, for all the reasons Peter stated. But because it's called a hypothesis, and it is falsifiable, it seems to satisfy people that something scientific has been achieved.
It also tends to reduced a complex scientific question to the reporting of one key statistical hypothesis. This is further encouraged by how a lot of scientific research is published - thin-slice the bigger problem and report every slice/p-value in a different paper. 
Where I am going is this, with respect to your question? I am not offended by statistical hypothesis tests per se, as long as they are applied thoughtfully. In other words, the solution is not just about finding a better statistical approach, but rather about applying a better scientific approach; by clearly specifying a complete theory that can be tested, collecting the relevant data, and then ensuring any statistical modelling or testing directly follows from these, rather than the other way around. 
A: Following the ideas put forward here http://robjhyndman.com/working-papers/forecasting-without-significance-tests/, you can formulate two models: with and without a dummy variable. Then you can use AIC-like statistics (and start reading about their own problems and misunderstandings).
