{"id":32693,"date":"2015-10-06T00:00:09","date_gmt":"2015-10-06T00:00:09","guid":{"rendered":"https:\/\/vwo.com\/blog\/?p=32693"},"modified":"2025-05-05T17:45:31","modified_gmt":"2025-05-05T12:15:31","slug":"smartstats-testing-for-truth","status":"publish","type":"post","link":"https:\/\/vwo.com\/blog\/smartstats-testing-for-truth\/","title":{"rendered":"VWO SmartStats: Testing for Truth Versus Maximizing Revenue"},"content":{"rendered":"\n

In my career I\u2019ve worked in two different worlds. The first is the world of science – clever people running careful experiments and seeking truth. The ultimate goal is to publish papers that reveal truths.<\/p>\n\n\n\n

The second place I\u2019ve worked is the world of finance – clever people trying to make choices in the face of uncertainty that have a high probability of making money. <\/span><\/p>\n\n\n\n

Most A\/B testing tools<\/a> use hypothesis tests designed for the science world. SmartStats is an A\/B testing statistics engine inspired by the financial world and designed to make money even in the face of uncertainty.  <\/span><\/p>\n\n\n\n

Download Free: A\/B Testing Guide<\/span><\/em><\/a><\/h2>\n\n\n\n

As a scientist I\u2019ll formulate a hypothesis – for example, \u2018blue webpages convert more than red ones\u2019. I\u2019ll then design an experiment like exposing visitors to red and blue webpages and measuring conversion rates<\/a>. The experiment is run, and the number of correct guesses (and the number of failures) is tallied. <\/span><\/p>\n\n\n\n

As a scientist, I want to know that the effect I just observed – let\u2019s say blue converts better than blue – is real. So I\u2019ll assume the null hypothesis<\/a> – in this case that red and blue are the same – and try to disprove it. I\u2019ll run a hypothesis test and compute the probability of seeing the experimental results \u2018that I just saw\u2019 assuming the null hypothesis (basically the \u201copposite\u201d of the result I\u2019m looking for) is false. If this probability is low, I\u2019ll conclude that this is strong evidence against the hypothesis<\/a>. If the probability is high, then this is weak  evidence against the null hypothesis. <\/span><\/p>\n\n\n\n

My goal here is to avoid publishing false results. If blue webpages don\u2019t convert more than red ones, I don\u2019t want to publish a paper saying it does. Publishing a lot of papers that can\u2019t be replicated will make me look dumb. Frequentist hypothesis testing  is a great fit for this use case. <\/span><\/p>\n\n\n

Businesses Need Actionable Answers<\/h2>\n\n\n

If I were trading stocks, I don\u2019t necessarily care about truth. If I buy a stock at $10, it stays flat, and then I sell it at $10, I\u2019ve lost nothing (ignoring  transaction costs). If I do this 10 times, and the stock goes up half the time and stays flat the other half the time, I win – I made money 5 times and didn\u2019t lose money the other 5 times.<\/span><\/p>\n\n\n\n

\n

\u201cConversion rate optimization is a lot more like trading stocks than like publishing science papers.\u201d<\/p>\n<\/blockquote>\n\n\n\n

I believe that conversion rate optimization<\/a> is a lot more like trading stocks than like publishing science papers. Coming back to our earlier test of red versus blue webpages, suppose now that I\u2019m 50% certain that blue pages convert better and 50% certain that they are equal to red ones. If I were a scientist, I\u2019d wait for certainty before publishing. <\/span><\/p>\n\n\n\n

When businesses A\/B test, either the red webpage or the blue webpage will be deployed. The only question to answer is, \u2018which one?\u2019 <\/span><\/p>\n\n\n\n

So if I\u2019m 50% certain that the new blue webpage converts 10% more than the current red page, and 50% certain they are both the same, I\u2019ll deploy the blue page right away.<\/span><\/p>\n\n\n\n

The blue webpage is a smart business decision, even if it\u2019s not a proven scientific hypothesis. The blue webpage might be a win, but it\u2019s definitely not a loss. <\/span><\/p>\n\n\n\n

The tradeoff we made while designing SmartStats<\/a> is that instead of trying to find the absolute truth, SmartStats looks for the better choice. The benefit of this is that we can get results in much less time. We risk getting more false positives, but only false positives that won\u2019t hurt the bottom line. SmartStats is designed to give you more intelligent answers quickly so that you get more time to increase your conversions and more time to test more ideas. Also, if you want to be really, really sure, there\u2019s also a High Certainty mode that takes longer and tests more samples to get really accurate.<\/span><\/p>\n\n\n

Reducing your Potential Loss<\/h2>\n\n\n

The way we deal with false positives is by ensuring that we minimize the cost of any mistake. The potential loss of page A is the lift you would lose by deploying A when in fact B was better<\/a>. <\/span><\/p>\n\n\n\n

For example, suppose there is a 50% chance that A is 10% better than B, and a 50% chance that B is 10% better than A. The potential loss from choosing A is 50% x 10% = 5%, and the potential loss from choosing B is 50% x 10% = 5%. This is pretty high, so your best bet is to continue testing.<\/span><\/p>\n\n\n\n

Potential loss can become small (very close to zero) in two ways. The first way, and most common, is for one variation to be not worse (but possibly not better) than the other variation. The second is for both variations to be identical, and thus nothing is lost by choosing one or the other. If one variation is known to be definitively better than the other, this case also applies. <\/span><\/p>\n\n\n\n

Download Free: A\/B Testing Guide<\/span><\/em><\/a><\/h2>\n\n\n

More Accurate Calculations<\/h2>\n\n\n

Our new calculations are also more accurate than our old ones. Our old method used a common trick the <\/span>Central Limit Theorem  <\/a><\/span>and approximated the true statistical distribution by a normal distribution. This approximation works very well if you have a lot of samples. That\u2019s not possible for all customers, so it became clear to us that we needed to find a better way to get more accurate answers.<\/span><\/p>\n\n\n\n

Let\u2019s look at a couple of graphs that illustrate the problem. We\u2019ll consider an A\/B test with a 5% conversion rate. When we have 10,000 visitors, the true distribution and the normal approximation line up perfectly:<\/span><\/p>\n\n\n

\n
\"True<\/figure>\n<\/div>\n\n\n

That\u2019s great for anyone who has tens of thousands of visitors reaching the end of their funnel every week. <\/span><\/p>\n\n\n\n

In contrast, as you can see in the graph below, when we have only 100 visitors the green and the blue line differ significantly.<\/span><\/p>\n\n\n\n

\"True<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\n

\u201cThe true calculations are more difficult for both our math geeks and our computers, but it gives more accurate and faster results.\u201d<\/p>\n<\/blockquote>\n\n\n\n

Our old method used the approximation (the green line) in our calculations whereas our new method uses the true distribution (blue line) itself. (For the more technically inclined, the true posterior is a beta distribution<\/span>) It\u2019s more work for us – the true calculations are more difficult for both our math geeks and our computers – but it gives more accurate and faster results. <\/span><\/p>\n\n\n\n

Fun fact: A lot of statistical techniques tell you something like \u201cthis method is only accurate<\/a> if number of conversions > 3 sqrt(num_conversions x ctr<\/a> x (1-ctr))\u201d or something along those lines. This kind of \u2018rule of thumb\u2019 is there to ensure that the green and blue lines agree with each other. As a result of using exact calculations, SmartStats does not require any such rules. <\/span><\/i><\/p>\n\n\n

Take a Fresh Approach to Testing with SmartStats<\/h2>\n\n\n

SmartStats doesn\u2019t change your fundamental testing process. You still need to identify a good hypothesis<\/a>, run tests and wait for the results. <\/span><\/p>\n\n\n\n

SmartStats just cuts down your waiting time, drastically. Finding intelligent answers quickly can widen your pipeline. You can run more tests, learn faster and improve conversions quickly. That\u2019s a certainty which many will value.<\/span><\/p>\n\n\n\n

Note: The author owns screenshots in the blog.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

In my career I\u2019ve worked in two different worlds. The first is the world of science – clever people running careful experiments and seeking truth. The ultimate goal is to publish papers that reveal truths. 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