Hypothesis Testing

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Hypothesis Testing
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What is a Hypothesis?

• Claim Average Weekly Entertainment Spending is
  55?
• How would you test that claim?

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How to Test a Hypothesis
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Hypothesis Testing

• Statistical hypothesis testing represents a
  formal, systematic approach to evaluating data,
  and deciding whether the results from an observed
  sample of data can be generalized to a larger
  population, or if instead the results might just
  be due to chance.

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Who Likes Wallace and Gromit?

• Potential Hypothesis about the Wallace and Gromit
  (WG)
• Males prefer WG to Females

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Who Likes Wallace and Gromit?

• Potential Hypothesis about the Wallace and Gromit
  (WG)
• Males prefer WG to Females
• Greeks prefer the WG over independents

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Who Likes Wallace and Gromit?

• Potential Hypothesis about the Wallace and Gromit
  (WG)
• Males prefer WG to Females
• Greeks prefer the WG over independents
• If you have heard about WG you will prefer them
  over people who have not heard of the WG

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Who Likes Wallace and Gromit?

• Potential Hypothesis about the Wallace and Gromit
  (WG)
• Males prefer WG to Females
• Greeks prefer the WG over independents
• If you have heard about WG you will prefer them
  over people who have not heard of the WG
• If you have watched the WG you will prefer them
  over people who have not watched the WG

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Who Likes Wallace and Gromit?

• Potential Hypothesis about the Wallace and Gromit
  (WG)
• Males prefer WG to Females
• Greeks prefer the WG over independents
• If you have heard about WG you will prefer them
  over people who have not heard of the WG
• If you have watched the WG you will prefer them
  over people who have not watched the WG
• If you have lived outside the USA for more than 6
  months you will prefer WG over people who have
  lived in the USA

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Who Likes Wallace and Gromit?

• Potential Hypothesis about the Wallace and Gromit
  (WG)
• Males prefer WG to Females
• Greeks prefer the WG over independents
• If you have heard about WG you will prefer them
  over people who have not heard of the WG
• If you have watched the WG you will prefer them
  over people who have not watched the WG
• If you have lived outside the USA for more than 6
  months you will prefer WG over people who have
  lived in the USA
• A greater percentage of people who have lived
  outside of the USA have watched WG previously

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Checking out Wallace and Gromit
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Wallace and Gromit Questionnaire

• Survey is Anonymous

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Wallace and Gromit Questionnaire

• Survey is Anonymous
• Age
• Gender
• Member of a fraternity or sorority
• Ever lived out side of the USA for more than 6
  months

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Wallace and Gromit Questionnaire

• Survey is Anonymous
• Age
• Gender
• Member of a fraternity or sorority
• Ever lived out side of the USA for more than 6
  months
• Ever heard of Wallace and Gromit
• Ever watched Wallace and Gromit
• If so, when was last time watched

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Wallace and Gromit Questionnaire

• Survey is Anonymous
• Age
• Gender
• Ever lived out side of the USA for more than 6
  months
• Member of a fraternity or sorority
• Ever heard of Wallace and Gromit
• Ever watched Wallace and Gromit
• If so, when was last time watched
• Rate on scale from 1 to 5 (1 strongly disagree
  5 strongly agree)
• Wallace and Gromit is clever comedy
• Wallace and Gromit is my kind of entertainment
• Would watch Wallace and Gromit again at home

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Hypothesis Testing Structure

• 1. Business question
• 2. Null hypothesis (H0)
• 3. Alternative hypothesis (Ha)
• 4. Test statistic
• 5. Rejection region
• 6. Observed test statistic
• 7. p-value
• 8. Statistical conclusion
• 9. Business conclusion

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• Example 1 Over a period of years, a toothpaste
  has received a mean customer satisfaction rating
  of 5.9 out of 7. Because of a change in
  suppliers, there is concern that customer
  satisfaction may have decreased. In a sample of
  60 customers, the mean rating is found to be
  5.60, with a standard deviation of 0.87.

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Hypothesized Mean
Hypothesized Mean
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Toothpaste Example

• 1. Business question
• 2. Null hypothesis (H0)
• 3. Alternative hypothesis (Ha)
• 4. Test statistic
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Decreased?
• 2. Null hypothesis (H0)
• 3. Alternative hypothesis (Ha)
• 4. Test statistic
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Decreased?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  
• 3. Alternative hypothesis (Ha)
• 4. Test statistic
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong! m0
  m True Mean equals the Hypothesized Mean
• 3. Alternative hypothesis (Ha)
• 4. Test statistic
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  m0 m True Mean equals the Hypothesized
  Mean 5.9 m True Average Equals 5.9
• 3. Alternative hypothesis (Ha)
• 4. Test statistic
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  m0 m True Mean equals the Hypothesized
  Mean 5.9 m True Average Equals 5.9
• 3. Alternative hypothesis (Ha) What We Really
  Think!
• 4. Test statistic
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  m0 m True Mean equals the Hypothesized
  Mean 5.9 m True Average Equals 5.9
• 3. Alternative hypothesis (Ha) What We Really
  Think! m0 ? m Something Has Changed
• 4. Test statistic
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  m0 m True Mean equals the Hypothesized
  Mean 5.9 m True Average Equals 5.9
• 3. Alternative hypothesis (Ha) What We Really
  Think! m0 ? m Something Has Changed True
  Average Not Equal to 5.9
• 4. Test statistic
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  m0 m True Mean equals the Hypothesized
  Mean 5.9 m True Average Equals 5.9
• 3. Alternative hypothesis (Ha) What We Really
  Think! m0 ? m Something Has Changed True
  Average Not Equal to 5.9
• 4. Test statisticTest using a Z-score
• 5. Rejection region

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  m0 m True Mean equals the Hypothesized
  Mean 5.9 m True Average Equals 5.9
• 3. Alternative hypothesis (Ha) What We Really
  Think! m0 ? m Something Has Changed True
  Average Not Equal to 5.9
• 4. Test statisticTest using a Z-score
• 5. Rejection region If Z-score,

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  m0 m True Mean equals the Hypothesized
  Mean 5.9 m True Average Equals 5.9
• 3. Alternative hypothesis (Ha) What We Really
  Think! m0 ? m Something Has Changed
  True Average Not Equal to 5.9
• 4. Test statisticTest using a Z-score
• 5. Rejection region If Z-score, based on m0,

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Toothpaste Example

• 1. Business question Has Customer
  Satisfaction Changed?
• 2. Null hypothesis (H0) Try to Prove Wrong!
  m0 m True Mean equals the Hypothesized
  Mean 5.9 m True Average Equals 5.9
• 3. Alternative hypothesis (Ha) What We Really
  Think! m0 ? m Something Has Changed True
  Average Not Equal to 5.9
• 4. Test statisticTest using a Z-score
• 5. Rejection region If Z-score, based on m0, is
  unusual -- far away from 0, reject Null
  Hypothesis

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Toothpaste Example

• Example 1 Over a period of years, a toothpaste
  has received a mean customer satisfaction rating
  of 5.90 out of 7. Because of a change in
  suppliers, there is concern that customer
  satisfaction may have decreased. In a sample of
  60 customers, the mean rating is found to be
  5.60, with a standard deviation of 0.87.
• The Z-score

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How Unusual is Z -2.67?
Hypothesized Mean
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(No Transcript)
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Toothpaste Example

• 5. Rejection region Depends on Confidence Level
• 6. Observed test statistic
• 7. p-value
• 8. Statistical conclusion
• 9. Business conclusion

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Toothpaste Example

• 5. Rejection region Depends on Confidence
  Level 95 Confidence Level, if Z gt 1.96 or
  Z lt -1.96, Reject Null
• 6. Observed test statistic
• 7. p-value
• 8. Statistical conclusion
• 9. Business conclusion

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95 Rejection Region
Reject
Reject
Accept
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Other Rejection Regions
Reject
Reject
90 Region
-1.645
1.645
99 Region
Reject
Reject
-2.57
2.57
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Toothpaste Example

• 5. Rejection region Depends on Confidence
  Level 95 Confidence Level, if Z gt 1.96 or
  Z lt -1.96, Reject Null
• 6. Observed test statistic Already
  Calculated z -2.67
• 7. p-value
• 8. Statistical conclusion
• 9. Business conclusion

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Toothpaste Example

• 5. Rejection region Depends on Confidence
  Level 95 Confidence Level, if Z gt 1.96 or
  Z lt -1.96, Reject Null
• 6. Observed test statistic Already
  Calculated z -2.67
• 7. p-value
• 8. Statistical conclusion Reject Null Hypothesis
• 9. Business conclusion

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Toothpaste Example

• 5. Rejection region Depends on Confidence
  Level 95 Confidence Level, if Z gt 1.96 or
  Z lt -1.96, Reject Null
• 6. Observed test statistic Already
  Calculated z -2.67
• 7. p-value
• 8. Statistical conclusion Reject Null Hypothesis
• 9. Business conclusion Average Customer
  Satisfaction Has Changed In Particular,
  Decreased.

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Toothpaste Example

• 5. Rejection region Depends on Confidence
  Level 95 Confidence Level, if Z gt 1.96 or
  Z lt -1.96, Reject Null
• 6. Observed test statistic Already
  Calculated z -2.67
• 7. p-value pr(zlt-2.67 or zgt2.67)
• 8. Statistical conclusion Reject Null Hypothesis
• 9. Business conclusion Average Customer
  Satisfaction Has Changed In Particular,
  Decreased

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p-value

• The p-value is a measure of the evidence against
  H0 it is the probability of observing the test
  statistic z given that H0 is true.

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p-value

• The p-value is a measure of the evidence against
  H0 it is the probability of observing the test
  statistic z given that H0 is true.
• Small p-value ? (accept/reject) H0
• Large p-value ? (accept/reject) H0

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p-value
pr(zlt-2.67) pr(zgt2.67)
2 x pr(zgt2.67)
2 x (0.0038)
p-value (0.0076)