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Statistical significance on a shoestring budget

alexeymk.com

21–30 of 36 posts

Re: Statistical significance on a shoestring budget

#21
post #19

There's an argument to be made that, so long as your testing fully encompasses all visitors to your site, you aren't sampling the population, you're fully observing it, and statistical significance is irrelevant.

That argument is missing that you are using past users’ behaviour as representative of future users’ preferences. You are not sampling marbles in a jar, but making a lot of assumptions, notably about continuity.

Re: Statistical significance on a shoestring budget

#22

> Gut Check: Especially if you’re off by quite a bit, this is a chance to take a step back and ask whether the company has reached growth scale or not. It could be that there are plenty of obvious 0-1 tactics left. Not everything has to be an experiment. This is a key point, imo. I have a sneaking suspicion that a lot of companies are running "growth teams" that don't have the scale where it actually makes sense to d…

Everything has to be a test early on, but not every test has to rely on random-split-based statistical significance to make a decision. “Would you pay $20 for this?” is a classic way to judge whether your service has product-market fit, and it’s not about sample sizes, not initially.

Some growth teams are trying more exploratory approaches to find something that resonates with simpler approaches. Others rely on A/B tests. Different profiles, but both are “Growth teams”.

Re: Statistical significance on a shoestring budget

#23
post #10
post #9

Earlier quoted context omitted.

> Nooo! First, if one actually works, you’ve massively increased the “noise” for the other experiments I get that a bunch at some of my clients. It's a common misconception. Let's say experiment B is 10% better than control but we're also running experiment C at the same time. Since C's participants are evenly distributed across B's branches, by default they should have no impact on the other experiment. If you do a…

The more experiments you run in parallel, the more likely it becomes that at least one experiment's branches do not have an even distribution across all branches of all (combinations of) other experiments. And the more experiments you run, whether in parallel or sequentially, the more likely you're to get at least one false positive, i.e. p-hacking. XKCD is using "find a subgroup that happens to be positive" to make…

You are confusing:

a. the Family-Wise Error Rate (FWER what xkcd 882 is about) and the many solutions of Multiple Comparison Correction (MCC: Bonferoni, Homes-Sidak, Benjamini-Hochberg, etc.) with

b. Contamination or Interaction: your two variants are not equivalent because one has 52% of its members part of Control from another experiment, while the other variant has 48%.

FWER is a common concern among statisticians when testing, but one with simple solutions. Contamination is a frequent concern among stakeholders, but very rare to observe even with a small sample size, and that even more rarely has a meaningful impact on results. Let’s say you have a 4% overhang, and the other experiment has a remarkably large 2% impact on a key metric. The contamination is only 4% * 2% = 0.08%.

It is a common concern and, therefore, needs to be discussed, but as Lukas Vermeer explained here [0], the solutions are simple and not frequently needed.

[0] https://www.lukasvermeer.nl/publications/2023/04/04/avoiding...

Re: Statistical significance on a shoestring budget

#24
post #10

Earlier quoted context omitted.

The more experiments you run in parallel, the more likely it becomes that at least one experiment's branches do not have an even distribution across all branches of all (combinations of) other experiments. And the more experiments you run, whether in parallel or sequentially, the more likely you're to get at least one false positive, i.e. p-hacking. XKCD is using "find a subgroup that happens to be positive" to make…

Thanks, that is a well reasoned argument! My take is for small n (say 5 experiments at once) with lots of subjects (>10k participants per branch) and a decent hashing algorithm, the risk of uneven bucketing remains negligible. Is my intuition off? False positives for experiments is definitely something to keep an eye on. The question to ask is what is our comfort level for trading-off between false positives and velo…

No, the risk of uneven bucketing of more than 1% is minimal, and even when it’s the case, the contamination is much smaller than other factors. It’s also trivial to monitor at small scales.

False positives do happen (Twyman's law is the most common way to describe the problem: underpowered experiment with spectacular results). The best solution is to ask if the results make sense using product intuition and continue running the experiment if not.

They are more likely to happen with very skewed observations (like how much people spend on a luxury brand), so if you have a goal metric that is skewed at the unit level, maybe think about statistical correction, or bootstrapping confidence intervals.

Re: Statistical significance on a shoestring budget

#25
post #22

> Gut Check: Especially if you’re off by quite a bit, this is a chance to take a step back and ask whether the company has reached growth scale or not. It could be that there are plenty of obvious 0-1 tactics left. Not everything has to be an experiment. This is a key point, imo. I have a sneaking suspicion that a lot of companies are running "growth teams" that don't have the scale where it actually makes sense to d…

Everything has to be a test early on, but not every test has to rely on random-split-based statistical significance to make a decision. “Would you pay $20 for this?” is a classic way to judge whether your service has product-market fit, and it’s not about sample sizes, not initially. Some growth teams are trying more exploratory approaches to find something that resonates with simpler approaches. Others rely on A/B t…

How are A/B tests for non-logged-in users doing these days with all the cookie banners, privacy and ad blockers etc. Is this stuff still working even?

Re: Statistical significance on a shoestring budget

#26
post #13
post #5

First, you really should move away from frequentist statistical testing and use Bayesian statistics instead. It is perfect for such occasions where you want to adjust your beliefs in what UX is best based on empirical data to support your decision. With collecting data you are increasing confidence in your decision rather than trying to meet an arbitrary criterion of a specific p-value. Second, the “run-in-parallel”…

Disagree on using Bayesian statistics. Frequentist statistics are perfect for A/B testing. There are so many strong biases people have about different parts about UI/UX. One of the significant benefits of A/B testing is that it lets you move ahead as a team and make decisions even when there are strongly differing opinions on your team. In these cases you can just "A/B test" and let the data decide. But if you are us…

You have to make almost the exact same choices when you rely on fequentist tools. The main difference is they’re pre-made during the development of the tool, so you don’t get insight into what they are without studying the theory behind the test.

Re: Statistical significance on a shoestring budget

#27
post #13
post #5

First, you really should move away from frequentist statistical testing and use Bayesian statistics instead. It is perfect for such occasions where you want to adjust your beliefs in what UX is best based on empirical data to support your decision. With collecting data you are increasing confidence in your decision rather than trying to meet an arbitrary criterion of a specific p-value. Second, the “run-in-parallel”…

Disagree on using Bayesian statistics. Frequentist statistics are perfect for A/B testing. There are so many strong biases people have about different parts about UI/UX. One of the significant benefits of A/B testing is that it lets you move ahead as a team and make decisions even when there are strongly differing opinions on your team. In these cases you can just "A/B test" and let the data decide. But if you are us…

Fixing dysfunctional decision making by delegating it to "data", what could go wrong? Might as well flip a coin and save the money.

Re: Statistical significance on a shoestring budget

#28
post #5

First, you really should move away from frequentist statistical testing and use Bayesian statistics instead. It is perfect for such occasions where you want to adjust your beliefs in what UX is best based on empirical data to support your decision. With collecting data you are increasing confidence in your decision rather than trying to meet an arbitrary criterion of a specific p-value. Second, the “run-in-parallel”…

Thanks for factorial design! I'll update the post to the proper nomenclature. The frequentist/bayesian debate is not one I understand well enough to opine - do you have any reading you'd recommend for this topic?

I myself am a rather recent convert to using Bayesian statistic, for the simple reason, that I was trained and have used frequentist statistics extensively in the past and I had no experience using Bayesian statistics. Once you take the time to master the basic tools, it becomes quite straightforward to use. I am currently away from my computer and resources, which makes it difficult to suggest them. As a somewhat shameless plug, you could check the https://www.frontiersin.org/articles/10.3389/fpsyg.2020.0094... paper and the related R-package https://cran.r-project.org/web/packages/bayes4psy/index.html and GitHub repository https://github.com/bstatcomp/bayes4psy, which were made to be accessible to users with frequentist statistics experience.

To brutaly simplify the distinction. Using frequentist statistics and testing, you are addressing the question, whether based on the results, you can reject the hypothesis that there is no difference between two conditions (e.g., A and B in A/B testing). The p-value broadly gives you the probability that the data from A and B are sampled from the same distribution. If this is really low, then you can reject the null hypothesis and claim that there are statistically significant differences between the two conditions.

In comparison, using Bayes statistic, you can estimate the pobability of a specific hypothesis. E.g. the hypothesis that A is better than B. You start with a prior belief (prior) in your hypothesis and then compute the posterior probability, which is the prior adjusted for the additional empirical evidence that you have collected. The results that you get can help you address a number of questions. For instance, (i) what is the probability that in general A leads to better results than B. Or related (but substantially different), (ii) what is the probability that for any specific case using A you have a higher chance of success than using B. To illustrate the difference, the probability that men in general are taller than women approaches 100%. However, if you randomly pick a man and a woman, the probability that the man will be higher than the woman is substantially lower.

In your A/B testing, if the cost of A is higher, addressing the question (ii) would be more informative than question (i). You can be quite sure that A is in general better than B, however, is the difference big enough to offset the higher cost?

Related to that, in Bayes statistics, you can define the Region of Practical Equivalence (ROPE) - in short the difference between A and B that could be due to measurment error, or that would be in practice of no use. You can then check in what proportion of cases, the difference would fall within ROPE. If the proportion of cases is high enough (e.g. 90%) then you can conclude that in practice it makes no difference whether you use A or B. In frequentist terms, Bayes allows you to confirm a null hypothesis, something that is impossible using frequentist statistic.

In regards to priors - which another person has mentioned - if you do not have specific reason to believe beforehand that A might be better than B or vice versa, you can use a relatively uninformative prior, basically saying, “I don’t really have a clue, which might be better”. So issue of priors should not discourage you to using Bayes statistics.

Re: Statistical significance on a shoestring budget

#29
post #13
post #5

First, you really should move away from frequentist statistical testing and use Bayesian statistics instead. It is perfect for such occasions where you want to adjust your beliefs in what UX is best based on empirical data to support your decision. With collecting data you are increasing confidence in your decision rather than trying to meet an arbitrary criterion of a specific p-value. Second, the “run-in-parallel”…

Disagree on using Bayesian statistics. Frequentist statistics are perfect for A/B testing. There are so many strong biases people have about different parts about UI/UX. One of the significant benefits of A/B testing is that it lets you move ahead as a team and make decisions even when there are strongly differing opinions on your team. In these cases you can just "A/B test" and let the data decide. But if you are us…

We can agree to disagree. My claim is actually quite the reverse. For A/B testing specifically, Bayes is much better suited to address the practical questions you would usually have when running A/B experiments. See my response to AlexeyMK below.

Re: Statistical significance on a shoestring budget

#30
post #22

Earlier quoted context omitted.

Everything has to be a test early on, but not every test has to rely on random-split-based statistical significance to make a decision. “Would you pay $20 for this?” is a classic way to judge whether your service has product-market fit, and it’s not about sample sizes, not initially. Some growth teams are trying more exploratory approaches to find something that resonates with simpler approaches. Others rely on A/B t…

How are A/B tests for non-logged-in users doing these days with all the cookie banners, privacy and ad blockers etc. Is this stuff still working even?

Yes, but it is _rough_. What actually hurts is "browse on mobile, buy on desktop" type behavior.

Still worth doing, but you end up needing more black magic than you'd like (IP-based assignment, Ad Network-sourced assignment, CDN proxies for Analytics tools, etc).

Working on a separate post about that.

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