How A/B Tests Lie to Us and How to Drive Genuine Improvement
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Smart marketers know that A/B testing helps take the guesswork out of website optimizations. Often times though, A/B testing doesn't give you a true view of how your site or web page is performing. In this presentation, WP Engine Founder & CTO Jason Cohen covers why tools that show “statistical significance” are often wrong, and how you can correct it, how to use insights from Google Analytics to drive A/B tests and what elements of your marketing campaigns should be A/B tested.
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STATUse the information below to answer Questions 1 through 4..docx
STAT
Use the information below to answer Questions 1 through 4.
Given a sample size of 36, with sample mean 670.3 and sample standard deviation 114.9, we perform the following hypothesis test.
Null Hypothesis
Alternative Hypothesis
1. What is the test statistic?
2. At a 10% significance level (90% confidence level), what is the critical value in this test? Do we reject the null hypothesis?
3. What are the border values between acceptance and rejection of this hypothesis?
4. What is the power of this test if the assumed true mean were 710 instead of 700?.
Questions 5 through 8 involve rolling of dice.
5. Given a fair, six-sided die, what is the probability of rolling the die twice and getting a “1” each time?
6. What is the probability of getting a “1” on the second roll when you get a “1” on the first roll?
7. The House managed to load the die in such a way that the faces “2” and “4” show up twice as frequently as all other faces. Meanwhile, all the other faces still show up with equal frequency. What is the probability of getting a “1” when rolling this loaded die?
8. Write the probability distribution for this loaded die, showing each outcome and its probability. Also plot a histogram to show the probability distribution.
Use the data in the table to answer Questions 9 through 11.
x
3
1
4
4
5
y
1
-2
3
5
9
9. Determine SSxx, SSxy, and SSyy.
10.
Find the equation of the regression line. What is the predicted value when
11. Is the correlation significant at 1% significance level (99% confidence level)? Why or why not?
Use the data below to answer Questions 12 through 14.
A group of students from three universities were asked to pick their favorite college sport to attend of their choice: The results, in number of students, are listed as follows:
Football
Basketball
Soccer
Maryland
60
70
20
Duke
10
75
15
UCLA
35
65
25
Supposed a student is randomly selected from the group mentioned above.
12. What is the probability that the student is from UCLA or chooses football?
13. What is the probability that the student is from Duke, given that the student chooses basketball?
14. What is the probability that the student is from Maryland and chooses soccer?
Use the information below to answer Questions 15 and 17.
There are 3600 apples in a shipment. The weight of the apples in this shipment is normally distributed. It is found that it a mean weight of 14 ounces with a standard deviation of 2.5 ounces.
15. How many of apples have weights between 13 ounces and 15 ounces?
16. What is the probability that a randomly selected mango weighs less than 12.5 ounces?
17. A quality inspector randomly selected 100 apples from the shipment.
a. What is the probability that the 100 randomly selected apples have a mean weight less than 12.5 ounces?
b. Do you come up with the same result in Question 16? Why or why not?
18. A pharmaceutical company has developed a screening test for a rare disease that afflicted 2% of the population. Un.
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The document provides information and questions related to statistics concepts including hypothesis testing, probability, sampling, and data analysis. It includes sample size, means, standard deviations, test statistics, critical values, and confidence levels for hypothesis tests. Questions involve probabilities and distributions for dice rolls, sports preferences among university students, apple weights, disease screening tests, fraud detection using Benford's law, and gemstone hardness tests. Other questions cover seating arrangements, swimming pool contamination sampling, and determining the number of dishes to order for a banquet.
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In the last decade of data analysis, A/B testing and predictive modeling have transitioned from an afterthought to a given in the game industry. Data can be invaluable in understanding the player and making decisions, but it can just as easily lead the industry astray, or worse, narrow the way the industry thinks. When should you be driven by data, and when should you let your imagination roam free? This session will expose common mistakes and pitfalls, both technical and emotional, as well as provide practical guidance on how to improve the rigorousness of your tests and the quality of your data, and how to make sure you don't lose the forest for the trees.
WEEK 5 HOMEWORK 5THIS WEEK INVOLVES READING NEW TABLES, THE t-TA.docx
WEEK 5 HOMEWORK 5
THIS WEEK INVOLVES READING NEW TABLES, THE t-TABLES. BUT, UNLIKE THE Z-TABLES WHERE YOU JUST NEEDED TO CALCULATE A Z-VALUE TO FIND THE PROBABILITY IN THE TABLE, WITH THE t-TABLE YOU NEED THE t-VALUE AND THE DEGREES OF FREEDOM, WHICH IS SIMPLY N – 1. THE t-VALUES DEPEND ON THE SIZE OF THE SAMPLE. THE t-DISTRIBUTION SHAPE CAN BE A “SKINNY” BELL CURVE, SYMETRICAL JUST LIKE THE NORMAL DISTRIBTION; BUT, AS YOU CAN SEE, THE LARGER THE SAMPLE SIZE THE MORE THE t-DISTRIBUTION SHAPE LOOKS LIKE THE NORMAL DISTRIBUTION SHAPE.
THE t-TABLES ARE IN OUR COURSE CONTENT > COURSE RESOURCES (NEAR THE BOTTOM OF CONTENT) > STATISTICAL RESOURCES. I SUGGEST YOU PRINT IT OUT AND REVIEW IT AS YOU READ THESE INSTRUCTIONS:
LET’S SAY YOU WANT TO BE 99% CONFIDENT (LEVEL OF CONFIDENCE) IN YOUR CONFIDENCE INTERVAL. THIS LEAVES A 1% CHANCE YOUR SAMPLE STATISTIC LIKE THE MEAN IS NOT IN THAT INTERVAL. KEEP IN MIND THAT THE CI HAS AN UPPER LIMIT AND A LOWER LIMIT SO THIS 1% COVERS BOTH ENDS. THIS MEANS THAT THE PROBABILITY THAT OUR RESULT IS IN ONE OR THE OTHER TAIL IS 1% / 2 = 0.5% (OR 0.005). THINK ABOUT IT. NOTE THAT IN THE TABLE THE 99% CI (BOTTOM LINE) EQUATES TO 0.005 ON THE TOP LINE. ALL WE NEED NOW IS THE DEGREES OF FREEDOM, WHICH IS N – 1, TO GET OUR CRITICAL t-VALUE FROM THE BODY OF THE TABLE. IN THIS EXAMPLE THE df IS 14, SO THE t-VALUE IS 2.977. THIS t-VALUE IS A CRITICAL VALUE LIKE A Z-VALUE.
THE t-TABLES ARE DIFFERENT FROM THE z-TABLES IN THAT WITH THE “t” WE SPECIFY THE PROBABILITY WE WANT AND THEN FIND THE CRITICAL t-VALUE. WITH THE NORMAL DISTRIBUTION, WE CALCULTE THE z-VALUE FIRST AND THEN COMPARE IT TO THE CRITICAL z-VALUE OF OUR DESIRED LEVEL OF SIGNIFICANCE (90%, 95%, OR 99%) TO SEE IF OUR CALCULATED z-VALUE IS FURTHER OUT IN EITHER TAIL, HENCE “UNUSUAL”.
THE NORMAL DISTRIBUTION CURVE IS ONE CURVE AND DOES NOT CHANGE WITH SAMPLE SIZE, HENCE WE CAN HAVE THE SAME CRITICAL z-VALUES FOR EVERY PROBLEM (99%, 95%, AND 90%). THE t-DISTRIBTUTION CURVE STARTS OUT A SKINNY BELL CURVE AND SLOWLY WIDENS AS THE SAMPLE SIZE (THE df) INCREASES. YOU CAN SEE FROM THE t-TABLE THAT WHEN THE df APPROACHES 1000, WE ARE VERY CLOSE TO THE NORMAL DISTRIBUTION’S BELL SHAPE. BUT, SINCE THE t-SHAPE CHANGES, THERE ARE DIFFERENT CRITICAL t-VALUES DEPENDING ON THE df (SAMPLE SIZES) INVOLVED.
HERE IS WHAT THE CONFIDENCE INTERVAL MEANS GRAPHICALLY: IN THIS SAMPLE PROBLEM WE WANTED A 95% CONFIDENCE LEVEL CONFIDENCE INTERVAL BASED ON A SAMPLE WITH A MEAN OF 3.26, A STD DEV OF 1.019 AND A SAMPLE SIZE OF 39 (df = 39-1 =38). THE CRITICAL t-VALUE FROM THE TABLE IS 2.023 (WE DON’T HAVE 39 df IN THE TABLE SO WE APPROXIMATED USING THE df FOR 39 AND 40). USE THE TABLE AND NOT SOFTWARE FOR THESE PROBLEMS. NOTE THAT THE 95% LEVEL MEANS 2.5% OF THE AREA UNDER THE t-CURVE IS IN EACH TAIL AS THE LIMITS.
NOW WE HAVE OUR t-VALUE = 2.023. REMEMBER WHEN WE STANDARDIZED OUR RAW DATA POINTS (THE X-VALUES) USING: Z = (X –MEAN)/STD DEV. IF WE WERE GIVEN T.
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The WordPress REST API, in conjunction with a JavaScript MVC framework such as AngularJS, opens up endless opportunities for developers to build new types of plugins and customize user experiences. This webinar goes in-depth into how to use AngularJS with the WordPress REST API. Together, these tools help you tie systems together to customize user experiences, build plugins, and advance your business in new, innovative ways that are only limited by your imagination!
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Chapter 29
The Fourfold Pattern
Whenever you form a global evaluation of a complex object—a car you may buy, your son-in-law, or an uncertain situation—you assign weights to its characteristics. This is simply a cumbersome way of saying that some characteristics influence your assessment more than others do. The weighting occurs whether or not you are aware of it; it is an operation of System 1. Your overall evaluation of a car may put more or less weight on gas economy, comfort, or appearance. Your judgment of your son-in-law may depend more or less on how rich or handsome or reliable he is. Similarly, your assessment of an uncertain prospect assigns weights to the possible outcomes. The weights are certainly correlated with the probabilities of these outcomes: a 50% chance to win a million is much more attractive than a 1% chance to win the same amount. The assignment of weights is sometimes conscious and deliberate. Most often, however, you are just an observer to a global evaluation that your System 1 delivers. Changing Chances One reason for the popularity of the gambling metaphor in the study of decision making is that it provides a natural rule for the assignment of weights to the outcomes of a prospect: the more probable an outcome, the more weight it should have. The expected value of a gamble is the average of its outcomes, each weighted by its probability. For example, the expected value of “20% chance to win $1,000 and 75% chance to win $100” is $275. In the pre-Bernoulli days, gambles were assessed by their expected value. Bernoulli retained this method for assigning weights to the outcomes, which is known as the expectation principle, but applied it to the psychological value of the outcomes. The utility of a gamble, in his theory, is the average of the utilities of its outcomes, each weighted by its probability. The expectation principle does not correctly describe how you think about the probabilities related to risky prospects. In the four examples below, your chances of receiving $1 million improve by 5%. Is the news equally good in each case? A. From 0 to 5% B. From 5% to 10% C. From 60% to 65% D. From 95% to 100% The expectation principle asserts that your utility increases in each case by exactly 5% of the utility of receiving $1 million. Does this prediction describe your experiences? Of course not. Everyone agrees that 0 5% and 95% 100% are more impressive than either 5% 10% or 60% 65%. Increasing the chances from 0 to 5% transforms the situation, creating a possibility that did not exist earlier, a hope of winning the prize. It is a qualitative change, where 5 10% is only a quantitative improvement. The change from 5% to 10% doubles the probability of winning, but there is general agreement that the psychological value of the prospect does not double. The large impact of 0 5% illustrates the possibility effect, which causes highly unlikely outcomes to be weighted disproportionately more than they “deserve.” People wh ...
STATUse the information below to answer Questions 1 through 4..docx
STAT
Use the information below to answer Questions 1 through 4.
Given a sample size of 36, with sample mean 670.3 and sample standard deviation 114.9, we perform the following hypothesis test.
Null Hypothesis
Alternative Hypothesis
1. What is the test statistic?
2. At a 10% significance level (90% confidence level), what is the critical value in this test? Do we reject the null hypothesis?
3. What are the border values between acceptance and rejection of this hypothesis?
4. What is the power of this test if the assumed true mean were 710 instead of 700?.
Questions 5 through 8 involve rolling of dice.
5. Given a fair, six-sided die, what is the probability of rolling the die twice and getting a “1” each time?
6. What is the probability of getting a “1” on the second roll when you get a “1” on the first roll?
7. The House managed to load the die in such a way that the faces “2” and “4” show up twice as frequently as all other faces. Meanwhile, all the other faces still show up with equal frequency. What is the probability of getting a “1” when rolling this loaded die?
8. Write the probability distribution for this loaded die, showing each outcome and its probability. Also plot a histogram to show the probability distribution.
Use the data in the table to answer Questions 9 through 11.
x
3
1
4
4
5
y
1
-2
3
5
9
9. Determine SSxx, SSxy, and SSyy.
10.
Find the equation of the regression line. What is the predicted value when
11. Is the correlation significant at 1% significance level (99% confidence level)? Why or why not?
Use the data below to answer Questions 12 through 14.
A group of students from three universities were asked to pick their favorite college sport to attend of their choice: The results, in number of students, are listed as follows:
Football
Basketball
Soccer
Maryland
60
70
20
Duke
10
75
15
UCLA
35
65
25
Supposed a student is randomly selected from the group mentioned above.
12. What is the probability that the student is from UCLA or chooses football?
13. What is the probability that the student is from Duke, given that the student chooses basketball?
14. What is the probability that the student is from Maryland and chooses soccer?
Use the information below to answer Questions 15 and 17.
There are 3600 apples in a shipment. The weight of the apples in this shipment is normally distributed. It is found that it a mean weight of 14 ounces with a standard deviation of 2.5 ounces.
15. How many of apples have weights between 13 ounces and 15 ounces?
16. What is the probability that a randomly selected mango weighs less than 12.5 ounces?
17. A quality inspector randomly selected 100 apples from the shipment.
a. What is the probability that the 100 randomly selected apples have a mean weight less than 12.5 ounces?
b. Do you come up with the same result in Question 16? Why or why not?
18. A pharmaceutical company has developed a screening test for a rare disease that afflicted 2% of the population. Un.
STATUse the information below to answer Questions 1 through 4..docx
The document provides information and questions related to statistics concepts including hypothesis testing, probability, sampling, and data analysis. It includes sample size, means, standard deviations, test statistics, critical values, and confidence levels for hypothesis tests. Questions involve probabilities and distributions for dice rolls, sports preferences among university students, apple weights, disease screening tests, fraud detection using Benford's law, and gemstone hardness tests. Other questions cover seating arrangements, swimming pool contamination sampling, and determining the number of dishes to order for a banquet.
Unit 11.2 theoretical probability
This document provides an overview of theoretical probability concepts including:
- Theoretical probability is calculated as the number of favorable outcomes divided by the total number of equally likely outcomes.
- Experiments are considered "fair" if all outcomes are equally likely.
- The probability of an event occurring plus the probability of it not occurring equals 1.
- Complement probability refers to outcomes not included in the main event.
- Odds can be used to express likelihood and converted to and from probabilities using ratios of favorable to total outcomes.
Classification in data mining
This course is all about the data mining that how we get the optimized results. it included with all types and how we use these techniques.This course is all about the data mining that how we get the optimized results. it included with all types and how we use these techniques.This course is all about the data mining that how we get the optimized results. it included with all types and how we use these techniques.This course is all about the data mining that how we get the optimized results. it included with all types and how we use these techniques.This course is all about the data mining that how we get the optimized results. it included with all types and how we use these techniques
Emily Greer at GDC 2018: Data-Driven or Data-Blinded?
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WEEK 5 HOMEWORK 5THIS WEEK INVOLVES READING NEW TABLES, THE t-TA.docx
WEEK 5 HOMEWORK 5
THIS WEEK INVOLVES READING NEW TABLES, THE t-TABLES. BUT, UNLIKE THE Z-TABLES WHERE YOU JUST NEEDED TO CALCULATE A Z-VALUE TO FIND THE PROBABILITY IN THE TABLE, WITH THE t-TABLE YOU NEED THE t-VALUE AND THE DEGREES OF FREEDOM, WHICH IS SIMPLY N – 1. THE t-VALUES DEPEND ON THE SIZE OF THE SAMPLE. THE t-DISTRIBUTION SHAPE CAN BE A “SKINNY” BELL CURVE, SYMETRICAL JUST LIKE THE NORMAL DISTRIBTION; BUT, AS YOU CAN SEE, THE LARGER THE SAMPLE SIZE THE MORE THE t-DISTRIBUTION SHAPE LOOKS LIKE THE NORMAL DISTRIBUTION SHAPE.
THE t-TABLES ARE IN OUR COURSE CONTENT > COURSE RESOURCES (NEAR THE BOTTOM OF CONTENT) > STATISTICAL RESOURCES. I SUGGEST YOU PRINT IT OUT AND REVIEW IT AS YOU READ THESE INSTRUCTIONS:
LET’S SAY YOU WANT TO BE 99% CONFIDENT (LEVEL OF CONFIDENCE) IN YOUR CONFIDENCE INTERVAL. THIS LEAVES A 1% CHANCE YOUR SAMPLE STATISTIC LIKE THE MEAN IS NOT IN THAT INTERVAL. KEEP IN MIND THAT THE CI HAS AN UPPER LIMIT AND A LOWER LIMIT SO THIS 1% COVERS BOTH ENDS. THIS MEANS THAT THE PROBABILITY THAT OUR RESULT IS IN ONE OR THE OTHER TAIL IS 1% / 2 = 0.5% (OR 0.005). THINK ABOUT IT. NOTE THAT IN THE TABLE THE 99% CI (BOTTOM LINE) EQUATES TO 0.005 ON THE TOP LINE. ALL WE NEED NOW IS THE DEGREES OF FREEDOM, WHICH IS N – 1, TO GET OUR CRITICAL t-VALUE FROM THE BODY OF THE TABLE. IN THIS EXAMPLE THE df IS 14, SO THE t-VALUE IS 2.977. THIS t-VALUE IS A CRITICAL VALUE LIKE A Z-VALUE.
THE t-TABLES ARE DIFFERENT FROM THE z-TABLES IN THAT WITH THE “t” WE SPECIFY THE PROBABILITY WE WANT AND THEN FIND THE CRITICAL t-VALUE. WITH THE NORMAL DISTRIBUTION, WE CALCULTE THE z-VALUE FIRST AND THEN COMPARE IT TO THE CRITICAL z-VALUE OF OUR DESIRED LEVEL OF SIGNIFICANCE (90%, 95%, OR 99%) TO SEE IF OUR CALCULATED z-VALUE IS FURTHER OUT IN EITHER TAIL, HENCE “UNUSUAL”.
THE NORMAL DISTRIBUTION CURVE IS ONE CURVE AND DOES NOT CHANGE WITH SAMPLE SIZE, HENCE WE CAN HAVE THE SAME CRITICAL z-VALUES FOR EVERY PROBLEM (99%, 95%, AND 90%). THE t-DISTRIBTUTION CURVE STARTS OUT A SKINNY BELL CURVE AND SLOWLY WIDENS AS THE SAMPLE SIZE (THE df) INCREASES. YOU CAN SEE FROM THE t-TABLE THAT WHEN THE df APPROACHES 1000, WE ARE VERY CLOSE TO THE NORMAL DISTRIBUTION’S BELL SHAPE. BUT, SINCE THE t-SHAPE CHANGES, THERE ARE DIFFERENT CRITICAL t-VALUES DEPENDING ON THE df (SAMPLE SIZES) INVOLVED.
HERE IS WHAT THE CONFIDENCE INTERVAL MEANS GRAPHICALLY: IN THIS SAMPLE PROBLEM WE WANTED A 95% CONFIDENCE LEVEL CONFIDENCE INTERVAL BASED ON A SAMPLE WITH A MEAN OF 3.26, A STD DEV OF 1.019 AND A SAMPLE SIZE OF 39 (df = 39-1 =38). THE CRITICAL t-VALUE FROM THE TABLE IS 2.023 (WE DON’T HAVE 39 df IN THE TABLE SO WE APPROXIMATED USING THE df FOR 39 AND 40). USE THE TABLE AND NOT SOFTWARE FOR THESE PROBLEMS. NOTE THAT THE 95% LEVEL MEANS 2.5% OF THE AREA UNDER THE t-CURVE IS IN EACH TAIL AS THE LIMITS.
NOW WE HAVE OUR t-VALUE = 2.023. REMEMBER WHEN WE STANDARDIZED OUR RAW DATA POINTS (THE X-VALUES) USING: Z = (X –MEAN)/STD DEV. IF WE WERE GIVEN T.
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How A/B Tests Lie to Us and How to Drive Genuine Improvement
- 1. SIX PUZZLES How A/B tests lie to us, and how to drive genuine improvement Jason Cohen, founder & CTO http://wpengine.com
- 3. 654 out of 24,483 visits 85% chance-to-beat
- 4. What do stats really tell us?
- 6. 654 out of 24,483 visits 85% chance-to-beat
- 7. Finding the Cheaters 105 athletes. 100 are clean. 5 are juicing. Test is 95% accurate.
- 8. Finding the Cheaters IN REALITY Clean (100) Juicing (5) TEST RESULT (95% accuracy) Clean Juicing 5 095 5
- 9. Insight: Rare events are indistinguishable from random noise
- 10. 758 out of 24,483 visits 85% chance-to-beat
- 11. Easy significance testing with hamsters Trust in the Hamster. bit.ly/abhamster
- 12. Easy significance testing N = A+B = total # of conversions. D = (A–B)/2 = half the difference. Significant if D2 > N. bit.ly/abhamster N = 758 + 685 = 1443 D = ( 758 — 685 ) / 2 = 37 1369 > 1443? No! Not significant.
- 13. Final Result: As predicted Wasted another month
- 14. 30 40 50 60 70 12/2/09 12/16/09 1/5/10 1/13/10 2/2/10 4/9/10 4/27/10 9/24/10 9/14/11 11/8/11 OtherInbox Splash Page
- 16. Lesson #1 Beware the Rare
- 17. Lesson #2 Trust the Hamster
- 19. 41 Shades of Blue
- 20. 41 Shades of Blue Does this... ...get more clicks than this?
- 21. 2 Shades of Blue with 1 winner at a 95% confidence level, chance of a false-positive: 5%
- 22. 3 Shades of Blue with 1 winner at a 95% confidence level, chance of a false-positive: 9%
- 23. 10 Shades of Blue with 1 winner at a 95% confidence level, chance of a false-positive: 40%
- 24. 41 Shades of Blue with 1 winner at a 95% confidence level, chance of a false-positive: 88%
- 26. Oops, you’re doing this.
- 28. Lesson #3 Test theories, not headlines
- 30. Bible Code!
- 31. Bible Code!
- 33. War and Peace
- 35. GA reveals ideas, not facts
- 36. Lesson #4 Exploration yields new theories, not new truth.
- 38. Headwinds to improvement significance → huge N → N/A high failure rate → many tests → false-positives rare events → worse on both!
- 39. Summary: Subtly is the Enemy
- 40. Insight: You don’t want “Subtle” anyway!
- 41. Lesson #5 Seek Huge Effects
- 42. Can you A/B test your way to big results?
- 44. Wisdom of the Crowd “I’m as clueless as you, but in the equal and opposite direction.”
- 45. What’s the funniest joke?
- 46. And the winner is…
- 47. Jokes, Pizza, Design, Features, Voice, Values, Culture
- 48. Lesson #6 Crowds find objective truth but kill creativity and greatness
- 49. Think for yourself. Test theories. Seek big effects. Jason Cohen, founder & CTO http://wpengine.com
- 50. Register now for our next webinar! “Your Workflow, Your Way, with WP Engine” Register now: http://wpeng.in/ywyw
- 51. Q & A Jason Cohen, founder & CTO http://wpengine.com