## Speed vs. Certainty in A/B Testing

A/B testing is a great tactical tool for studying customer behavior on the web. But like any randomized trial there's some chance that the improvement we measure is just statistical noise.

How worried should we be that the feature we thought improved our product actually does nothing, or worse, hurts our bottom line? How can we ever really know that we're making the correct decision? And is it better to run tests more quickly or more accurately?

The answers to these questions depend on the cost of a bad decision. If mistakes are cheap then it's better to make 1,000 decisions and get only 60% of them right than to make 100 decisions and get 100% of them right.

One way to achieve this balance in the context of A/B testing is to tune the confidence level.

### Tuning the Confidence Level

Intuitively, the confidence level of an A/B test tells you how certain you can be of the result of the A/B test. For example, a confidence level of 95% means that there's a 5% chance that a statistically significant result is actually random variation, i.e., there is a 5% chance of a false positive.

Of course, we're free to choose some other confidence level besides 95%. We could choose 80%, 90%, or 99.999%. A higher confidence level requires more data before reaching statistical significance, but we will be more certain of the result.

If you're not comfortable with the nuts and bolts of statistical analysis, confidence levels, and A/B testing I recommend reading my article about statistical analysis and A/B testing, which explains exactly how one "chooses" a confidence level.

In short, the confidence level acts as a dial between speed and certainty, and we're free to choose where to set that dial depending on the priorities of our business or product.

### Speed vs. Certainty

So where on the speed-certainty spectrum should you, as a product manager or startup entrepreneur, sit?

Mike Cassidy has a great presentation where he argues that speed is the primary business startegy for startups.

Why is speed great for startups? Because mistakes are cheap and calculated risks are rewarded. Most product decisions can be undone, and important early tests can be redone at a higher confidence level when the product has more traction.

But mistakes aren't always cheap. Here are some factors that increase the cost of a mistake.

#### Volume

Volume is leverage. If you have millions of customers, like Google or Amazon, a 1% improvement to the bottom line is a huge win. Conversely, a 1% mistake is a huge hit.

Fortunately this problem helps mitigate itself. Increased volume affords you the luxury of running A/B tests at a higher confidence level in the same amount of time.

#### Reversibility

Most product decisions in a consumer technology startup can be undone, for a price. For example, it's easy to undo a bad decision for a web-based product, slightly harder to undo a decision for desktop software, and very difficult (and costly) to undo a decision for a physical product.

The less reversible a decision is the more certain you should be before you make it. In the context of A/B testing a product feature this means a higher confidence level, even if it takes longer to run the test.

#### Real Money

Imagine you're an ad network. You're constantly A/B testing formatting, positioning, offers, etc. to see which performs best. Making a mistake in this regard costs your publishers money.

Like volume, money creates leverage. But it is more complicated than that: publishers don't just want increased revenues, they want reliable cash flow. That is, when money is involved, not only do you have to perform better but you have to perform more consistently because of phenomena like the peak-end rule.

In this case a "three steps forward one step back" strategy might actually be worse than going step-by-step in the right direction, even if the former averages out to better performance.

### Conclusions

Maintaining momentum in a startup isn't about making *only* correct decisions — it's about making *enough* correct decisions. This presents a continuum from speed to certainty. At one extreme you run the business with a magic eight-ball; at the other you agonize over every detail until you're 100% certain that you've made the correct choice.

This thought process extends naturally to A/B testing where the idea of "certainty" and "cost" can be quantified. To recap:

- A/B testing is a great tactical tool for testing
*specific*hypotheses about your customers. - However, there is a tradeoff between speed and certainty, controlled by the confidence level of the A/B test.
- The cost of doing A/B tests quickly is that you will make more wrong decisions, but that is ok if mistakes are cheap.
- For example, it's better to make 1,000 decisions and get only 60% of them right than to make 100 decisions and get 100% of them right, all else being equal.

### A Spreadsheet Model

Below is a little spreadsheet model that illustrates all my points above.

The two independent variables are the gain from a good decision and the cost of a bad decision. The spreadsheet assumes a fixed time period, so a higher confidence level means more certainty but **fewer tests**. The ideal confidence level is highlighted as you change the parameters of the model.

You can download the A/B testing confidence model here.

For the statistically inclined this model assumes that traffic increases linearly over time, that the sample statistic is normally distributed, and that a one-tailed t-test is the appropriate statistical test.

### Credits

This article was inspired by a conversation with Sean Ellis and edited by my wonderful girlfriend, who is probably going to yell at me for linking to her Twitter account.