Or you can decide the maximum number of conversions that you'll spendWhat are "conversions" in this context?
 Whatever you want them to be.People signing up for your service. People buying. Whatever you're trying to optimize for in the A/B test.
 I'm sorry, but this is entirely unfair, especially points 1 and 3.First, addressing #3:>People who know statistics can't interpret results to laymen.This doesn't match my experience. Stats experts can sometimes be terrible at communicating their work, but no more so than the security expert at explaining why we have to jump through these hoops, or the web dev explaining why the site went down. Some technical experts are good at communicating to lay people, some aren't. Stats is no outlier.But for learning and using statistics:> Go google how to do basic significance calculations in, say, Excel. The first paragraph of the resulting articles will dive into t-test and twin-tales and P-values and on down the lines.This seems to really be saying Using statistics requires you to understand statistics. Which seems sensible.The big issue is that uncertainty is a different kind of thinking. To put it at its simplest, if you want a yes or no answer and I keep saying "Well, probably yes, but maybe no" you're going to be really frustrated that I keep using the language of uncertainty. "I just want excel to give me a yes or no answer, but the articles keep trying to teach me about 'maybe' in the first paragraph!" Uncertainty involves new kinds of statements. No way around it. The software and the concepts require it, and there's no (correct) way to reduce it to "I just want excel to tell me whether this effect is real." When you say most people know how to ask the basic question, I disagree. Most people want to know "Is this effect real, yes or no?" But no matter what tools you use, that's not enough of a question to have a single correct answer."You'll probably see some nasty formulas and opining about which PhD-level approach is better." That's just untrue. It sounds anti-intellectual and a lot like the defeatist "I'm just not a math person." The formulas you'll see in those 'Intro to NHST' tutorials require high school math and are covered in the first stats class you'd take in undergrad.Edit: Sorry for the rant. I'm going to leave it up, but I'm just really turned off by "I consider myself analytically-minded, and statistics still gives me a headache," followed by 'here are the problems with statistics.' It's not hard, but you have to learn the foundation to use it. Do that before criticizing how we use it.
 In his defense (and admitting your points are all completely right):I consider my self analytically minded (i hope I am to some degree since its how I make my living).Statistics during university also gave me a headache. Still does.10 years later though: I've now worked for the national statistics body. I put my head down and said "Screw this, every time I don't get something, I'm going to try to implement it from first principals until I do. I'm going to code it up. Every time I don't understand the paradigm/language, i'm going to try to do everything in that mindset until I do."I worked for several years in the stats methodology division until I moved on.I am now of the not uncontroversial opinion admittedly, but ever increasing in popularity, that the reason I didn't understand stats in university stems from:1) It is taught badly.2) Often what is taught IS wrong.3) In practice it is used wrong: sig testing is the most overused technique I've seen in any field i've had experience with, except perhaps linear models (another stats baby) and in my experience, once one has internalised the lessons/mindset of variance/sampling/etc rather than "correct/not-correct", statistical significance is almost always tangential to the actual analytical question, yet it is often treated as the goal. I think its popularity is partly due to the fact that it does provide someone a framework for yes/no decision making, negating the very mindset change needed to properly understand statistics. Frequentist techniques were the focus in university stat level classes, and such a framework and models are often forced into very non-frequentist type situations where a bayesian/subjective interpretation is, in my subjective opinion, more rational and justified. My stats classes had almost no material on computation, logic, falsifiability, experiment and data design, etc, which, subjectively I view as much more important to real statistical work than rote learning what a regression, least squares, or R^2 measure is.A great deal of the time, analysts have trouble explaining the methods they use because its obvious (to me) that they don't really understand the methods they're using (if they did, they often wouldn't be using them).
 The more I study (halfway through a tough PhD now), the more I realise there's an obsesion with making hard things harder, sometimes just because you were taugh that way, other times because hey, "it's post-graduate education! it´s suposed to be hard".And the many times me and the research group I work with have sat, read things from the basics upwards, doing an effort to explain everything as simple as posible, while not hiding complexity, it took a lot of effort, but our work was highly praised and moved back into the courses we teach. And students are happier (or at least not miserable as they used to be when teaching hard things was done "the classical way").So I agree with (1), and all I can say is that, when in a position of teaching, it's best to take the time, work our material from the ground up, and teach it in the simplest posible way.
 > ... taught badly [and educators are] often [incorrect]Yes, but this may also be the case with many other topics. I had the dismaying experience of TAing a class at a highly respected university where a tenured professor was using lecture notes that were factually incorrect and in my mind glaringly so. Not just a bit of errata, but consistently wrong.
 `````` It's not hard, but you have to learn the foundation to use it. Do that before criticizing how we use it. `````` Here's the crux of the problem: we disagree on your first phrase here! I think statistics is hard to learn. I (clearly) don't have the foundation to use it. I'm not criticizing how you use it, I'm criticizing my inability to do so.Sounds like a personal problem, dunnit?What's frustrating is that I do "consider myself analytically-minded". I have a Bachelor's in CS; I took two (?) stat classes in college. And it's still like pounding my head against a wall. I find opportunities to use statistics to solve business problems, but finding resources to help me solve those problems with statistics is challenging without, in effect, going "back to school". (Incidentally, this is how I learn: concepts through examples.)I find that answers to what I think should—should—be simple questions to involve academic digressions into, in effect, the "different kind of thinking" you mention. I find them academic because they don't help me solve my immediate problem. That's not anti-intellectual: but by virtue of statistics being intellectual, it's exclusionary.I don't think I'm alone in that. From observation, I'm ahead of the curve in even trying. Maybe what I'm asking for is impossible. I hope not, because it the alternative is continued non-use of statistics. I'm bullish because I see opportunity for software to bridge the gap. Software may not be mature enough to do all the heavy lifting required of the user today, but it'll get there.
 What’s a good way of learning statistics for someone who is more into pure mathematics?I always avoided stats as much as possible because I found the classes extremely un-rigorous. I couldn’t get to grips with what the notation really meant, and there seemed to be a lot of hand waving on the way to results.I’m not doubting that stats is rigorous, just my exposure to it so far hasn’t been.
 My recommendation depends on what you'd like to do with it/what problems you are trying to solve. Huge field and all. Whatcha looking for?One resource I've started recommending to people is this little book http://bayes.cs.ucla.edu/PRIMER/ It's not going to teach you a lot of the practical tools, but there's a weird feature of statistics that the answers to most questions aren't just functions of the data. They're functions of how the data was gathered and what assumptions are fair to make too.So I've started to point people to this first, and only after that to what's usually stats 1. Once you finish that little book, any intro to mathematical statistics should suffice, but is probably overkill on the practical side. Hence my original question.
 > 1. (...) Go google how to do basic significance calculations in, say, Excel. The first paragraph of the resulting articles will dive into t-test and twin-tales and P-values and on down the lines.Understanding significance calculations and performing them in Excel are completely different things, and it's perfectly reasonable for a learning resource to cover one of them but not the other. Software developers, the primary target audience of this website, should know this as “separation of concerns”.> 2. (...) Software needs to bridge the gap between users' intent and their ability to do the analysis.All statistical software can do for you is perform calculations. The meaning of the results or even the calculations themselves is completely up to you. You can even decide it's meaningless!> 3. (...) Your c-suite doesn't care about that: it cares about the so-what.This is exactly the problem. People want to make the right decisions, but they don't want to take the trouble to understand how reality's complexity affects the outcomes of these decisions.
 Learning statistics is like learning anything else. Kids who want to make a video game are often dismayed when they realise how much they'd have to learn. If they ask how you put a walking character controlled by the mouse and keyboard on the screen, you'd have to explain about 3d graphics, the game loop, input devices. For 3d graphics you need vectors, transformation matrices, etc. Eventually you get down to basic programming constructs like loops. Like with statistics it can seem like an infinite fractally expanding amount of knowledge. A simple question such as how you draw a moving character or how you calculate whether the difference is statistically significant, has a complicated answer. The knowledge required isn't infinite or tautological or circular. With statistics it eventually bottoms out, but to really understand a t test you need at least probability theory and calculus. College students spend a year studying that.
 Probability theory requires a solid grounding in real analysis. Undergraduate real analysis alone is one year worth of material, and this is assuming that you already know how to write basic proofs. If all you know is some calculus tricks, as taught to engineering students, then you can probably compute probabilities, but you aren't ready to understand probability theory.Fortunately, most users of statistical tests don't really need to know probability theory anyway. This even includes some statisticians.
 With today's computers you can get a lot done without knowing t distribution and p-values, just using bootstrap and Monte-Carlo. See 93 conversions in test and 87 in control and want to know if this is just noise? Pull 10,000 bootstrap samples and look at the distribution. You can even do it in Excel if you want, but writing a loop in any programming language is not that difficult either.
 Yea, but I wouldn't trust someone's bootstrap estimator if they don't know how to interpret a t-test.
 At least a partial antidote for #1: https://www.amazon.com/Cartoon-Guide-Statistics-Larry-Gonick...For #2: In my experience, it takes a long time to go from "the basic question" to a well-founded statistical question for which analysis is appropriate.For #3: The best managers and analysts will find ways to ask questions and meet in the middle between technical complexity and the business/science problem at hand.
 Re point 2.. I am a bit of an Evan Miller fanboy, but would like to make a shoutout to Wizard anyway. https://www.wizardmac.com/ is a fantastic piece of software.
 "I consider myself analytically-minded, and statistics still gives me a headache""... blah blah etc."I suspect you do yourself a disservice. I think you instinctively know how to interpret and analyse discussions that involve statistics. That will include seriously complex and probably abstruse (to the layman) discourse. You are probably not a bleeding edge exponent and probably not in the habit of dropping papers on the world.However, I think you might be able to mess around with equations involving mu 'n' sigma (int al) without breaking a sweat.

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