Optimizely Stats EngineLeo Pekelis

Darwish Gani Robin Pam

Housekeeping notes

• Chat box is available for questions • There will be time for Q&A at the end • We will be recording the webinar for future viewing • All attendees will receive a copy of slides after the webinar

Your speakers

Darwish Gani Product manager

Robin Pam Product marketing

Leo Pekelis Statistician

Objectives

Understand why Optimizely built Stats Engine

Introduce the methods Stats Engine uses to calculate results

Get practical recommendations for how to test with Stats Engine

Why make a new Stats Engine?

Meet Joe: A farmer who uses a traditional t-test

Joe wants to try a new fertilizer this year

With his original fertilizer, 10% of plants survive the winter

He thinks that this new fertilizer might helpmore survive.

Joe has a hypothesis

Joe calculates a sample size for his experiment in advance, given how much better he thinks the new fertilizer might be

He waits through the winter…

10% of plants survive the winter

15% of plants survive

96% statistical significance!

…and he is rewarded for his patience

Does that work today?

Meet Kyle: Head of Optimization at Optimizely

Kyle doesn’t know what improvement to expect

Kyle also gets data from Optimizely all the time

Kyle wants to test many goals and variations at once, instead of just one hypothesis

vs.

Actually that’s a lot of work. It’s cumbersome and error-prone.

What’s your chance of making incorrect decision?

30%

Objectives

Understand why Optimizely built Stats Engine

Introduce the methods Stats Engine uses to calculate results

Get practical recommendations for how to test with Stats Engine

Introducing Stats Engine

How we did it

• Partnered with Stanford statisticians

• Talked with customers • Examined historical experiments

• Found the best methods for real-time data

What does Stats Engine do?

Provides a principled and mathematical way to calculate your chance of making an incorrect decision.

Sequential Testing False Discovery Rate• First used in 1940s for military weapons testing

• Sample size is not fixed in advance

• Data is evaluated as it’s collected

• First used in 1990s in genetics

• Correct error rates for multiple goals and variations

• Expected number of false discoveries

Sequential Testing

False Discovery Rate control

+

=

Statistical Significance for Digital Experimentation

Statistical Significance for Digital ExperimentationContinuously Evaluate Test Results

Run many goals and variations

Don’t worry about estimating a MDE upfront

Sequential Testing Finding the right stopping rule

Variation #1

Variation #2

Declare a winner?

500

Visitors

50%

65%

Is this lift big enough for the visitors I saw?

?

Desired Stopping Rule: I will be “wrong” only 5% of the time.

Variation #1

Variation #2

1000

Visitors

55%

59%

Traditional Error Rates 5%

Find a stopping rule, so I declare a winner incorrectly <5% of the

time

Variation #1

Variation #2

Traditional Error Rates

Visitors

500

50%

65%

5%

1000

55%

59%

5%

5000

52%

57%

5%

10000

54%

59%

5%

Variation #1

Variation #2

Traditional Error Rates

500 1000 5000 10000

Visitors

50% 55% 52% 54%

65% 59% 57% 59%

5% 5% 5% 5%

Look only once: 5% Error rate

Variation #1

Variation #2

Traditional Error Rates

500 1000 5000 10000

Visitors

50% 55% 52% 54%

65% 59% 57% 59%

5% 5% 5% 5%

Look only once: 5% Error rate

Look more than once: >5% Error rate

Variation #1

Variation #2

Traditional Error Rates

500 1000 5000 10000

Visitors

50% 55% 52% 54%

65% 59% 57% 59%

5% 5% 5% 5%

<5% Error rate for the entire test!

Sequential Testing Error Rate 1% .5% 1.5% 1.5% < 5%

“P-Hacking” “Continuous Monitoring”

“Repeated Significance Testing”

These are not new problems!

Steven Goodman, Stanford Physician & Statistician, nature.com

“The P value was never meant to be used the way it's used today.”

Source: Evan Miller, How not to Run an A/B Test

Sample Size + Power Calculations Focus on creating and running tests

Sequential Testing

• Continuously Evaluate Test Results

• Don’t worry about estimating a MDE upfront

Framework of hypothesis testing that was created to allow the experimenter to evaluate test results as they come in

False discovery rate control Error rates for a world with many goals and

variations

Variations Goal 1 Goal 2 Goal 3 Goal 4 Goal 5

Control

Variation 1

Variation 2

Variations Goal 1 Goal 2 Goal 3 Goal 4 Goal 5

Control

Variation 1

Variation 2

Significance Level 90 (False Positive Rate 10%)

Variations Goal 1 Goal 2 Goal 3 Goal 4 Goal 5

Control

Variation 1

Variation 2

Significance Level 90 (False Positive Rate 10%)

1 False Positive!

Variations Goal 1 Goal 2 Goal 3 Goal 4 Goal 5

Control

Variation 1

Variation 2

1 False Positive!

Significance Level 90 (False Positive Rate 10%)

1 other variation x goal has a large improvement.

Variations Goal 1 Goal 2 Goal 3 Goal 4 Goal 5

Control

Variation 1

Variation 2

1 False Positive!

Significance Level 90 (False Positive Rate 10%)

1 other variation x goal has a large improvement.

1 True Positive!

My Report

• Variation 2 is improving on Goal 1

• Variation 1 is improving on Goal 4

“10% of what I

report could be wrong.”X50%

• Variation 2 is improving on Goal 1• Variation 1 is improving on Goal 4

Furthermore, I found the following results.This leads me to conclude that …

Statistical Significance:

The chance that any variation on any goal

that is reported as a winner or loser

is correct.

• “New York Times has a feature in its Tuesday science section, Take a Number … Today’s column is in error … This is the old, old error of confusing p(A|B) with p(B|A).”

• Andrew Gelman, Misunderstanding the p-value

• “If I were to randomly select a drug out of the lot of 100, run it through my tests, and discover a p<0.05 statistically significant benefit, there is only a 62% chance that the drug is actually effective.”

• Alex Reinhart, The p value and the base rate fallacy

• “In this article I’ll show that badly performed A/B tests can produce winning results which are more likely to be false than true. At best, this leads to the needless modification of websites; at worst, to modification which damages profits.”

• Martin Goodson, Most Winning A/B Test Results are Illusory

• “An unguarded use of single-inference procedures results in a greatly increased false positive (significance) rate”

• Benjamini, Yoav, and Yosef Hochberg. "Controlling the false discovery rate: a practical and powerful approach to multiple testing." Journal of the Royal Statistical Society. Series B (Methodological) (1995): 289-300. APA

• “New York Times has a feature in its Tuesday science section, Take a Number … Today’s column is in error … This is the old, old error of confusing p(A|B) with p(B|A).”

• Andrew Gelman, Misunderstanding the p-value

• “If I were to randomly select a drug out of the lot of 100, run it through my tests, and discover a p<0.05 statistically significant benefit, there is only a 62% chance that the drug is actually effective.”

• Alex Reinhart, The p value and the base rate fallacy

• “In this article I’ll show that badly performed A/B tests can produce winning results which are more likely to be false than true. At best, this leads to the needless modification of websites; at worst, to modification which damages profits.”

• Martin Goodson, Most Winning A/B Test Results are Illusory

• “An unguarded use of single-inference procedures results in a greatly increased false positive (significance) rate”

• Benjamini, Yoav, and Yosef Hochberg. "Controlling the false discovery rate: a practical and powerful approach to multiple testing." Journal of the Royal Statistical Society. Series B (Methodological) (1995): 289-300. APA

False Discovery Rate controlFramework for controlling errors that arise from running multiple

experiments at once.

Run many goals & variations

What Stats Engine means for you

• You see fewer, but more accurate conclusive results.

• You can implement winners as soon as significance is reached.

• You get • easy experiment workflow. • reduced unforeseen, and hidden errors.

Objectives

Understand why Optimizely built Stats Engine

Introduce the methods Stats Engine uses to calculate results

Get practical recommendations for how to test with Stats Engine

And now, for some practical guidance

First, some vocabulary• Baseline conversion rate

The control group’s expected conversion rate.

• Minimum detectable effect The smallest conversion rate difference it is possible to detect in an A/B Test.

• Statistical significance The likelihood that the observed difference in conversion rates is not due to chance.

• Minimum sample size The smallest number of visitors required to reliably detect a given conversion rate difference

Sample size calculators and statistical power

How many visitors do you need to see significant results?

Visitors needed to reach significance with Stats Engine

Improvement

5% 10% 25%

Baseline conversion rate

1% 458,900 101,600 13,000

5% 69,500 15,000 1,800

10% 29,200 6,200 700

25% 8,100 1,700 200

Lower conversion rate, lower effects = more visitors

One example of calculating your opportunity cost

12% minimum detectable effect

Original

Variation

Should you stop or continue a test?

Should you stop or continue a test?

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

Should you stop or continue a test?

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

Difference intervals

Difference intervals

15.4

11.6 Middle Ground

Best Case

Worst case

7.3

Seasonality• We DO take into account seasonality while a test is running.

• We DO NOT take into account future seasonality after an experiment is stopped.

Should you stop or continue a test?

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

• Use Difference Intervals to understand the types of lifts you could see.

Should you stop or continue a test?

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

A reasonable number of visitors left, relative to your traffic?

Visitors Remaining Explained

Improvement Increases in Magnitude

Improvement Stays the Same

Improvement Decreases in Magnitude

A good idea to wait

5761 + 3200 Note!

Should you stop or continue a test?

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

• Use Visitors Remaining to evaluate if waiting makes sense.

Should you stop or continue a test?

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

If you’re an organization that can

• Iterate quickly on new variations • Run lots of experiments • Have little downside risk of implementing non-winning variations

then you can likely tolerate a higher error rate.

Difference intervals can guide your decision

Should you stop or continue a test?

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes • Use Difference Intervals to measure risk you take on

> 100,000 visitors? What next?

Time to move on to the next idea

Should you stop or continue a test?

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

• Use Visitors Remaining to evaluate if waiting makes sense.

Recap

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

• Use Difference Intervals to understand the types of lifts you could see.

Recap

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

• Use Difference Intervals to understand the types of lifts you could see.

Can I afford to wait?

Continue

Stop

Concede inconclusive

Yes

NoNo

• Use Visitors Remaining to evaluate if waiting makes sense.

Recap

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

• Use Difference Intervals to understand the types of lifts you could see.

Can I afford to wait?

Continue

Stop

Concede inconclusive

Yes

NoNo

• Use Visitors Remaining to evaluate if waiting makes sense.

Stop

Accept lowersignificance

Concede inconclusive

Yes

No

Can I afford to wait?

• Use Difference Intervals to measure risk you take on

Recap

Is my test significant?

Congrats

Can I afford to wait?

Continue

Stop

Accept lowersignificance

Concede inconclusive

Yes

NoNo

Yes

• Use Difference Intervals to understand the types of lifts you could see.

Can I afford to wait?

Continue

Stop

Concede inconclusive

Yes

NoNo

• Use Visitors Remaining to evaluate if waiting makes sense.

Stop

Accept lowersignificance

Concede inconclusive

Yes

No

Can I afford to wait?

• Use Difference Intervals to measure risk you take on

• Use Visitors Remaining to evaluate if waiting makes sense.

Tuning your testing strategy for your traffic and business

1%6% 4% 3% inconclusive inconclusive inconclusiveinconclusive 18%

Looking for small effects?

• Tests take longer to reach significance

• Might find more winners, if you are willing to wait long enough

inconclusive

Testing for larger effects?

• Run more tests, faster

• Know when it’s time to move on to the next idea

Frequently asked questions

Do I need to re-run my historical tests?

Is this a one-tailed or two-tailed test? Why did you switch?

Why does Stats Engine report 0% Statistical Significance when other tools

report higher values?

Why does Statistical Significance increase step-wise?

If I take the results I see in Optimizely and plug them into any other statistics

calculator, the statistical significance is different. Why?

How does Stats Engine handle revenue calculations?

Questions?