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Hypothesis Testing and P Value
BY DR ZAHID KHAN
SENIOR LECTURER KING FAISAL UNIVERSITY, KSA
Two ways to learn
about a population


Confidence intervals



Hypothesis testing
HYPOTHESIS
What do you mean by a Hypothesis?
A hypothesis is a proposition that is –


assumed as a premise in an argumen...
Why do we make hypotheses?


The practice of science traditionally involves
formulating and testing hypotheses



Hypoth...
TYPES OF HYPOTHESIS
Null Hypothesis



The null hypothesis typically corresponds to a
general or default position
Making...
Dependant and independent
variables


Shoppers in a store playing music shop spend
more.



Independent Variable:
 Musi...
Example -- Continued
1.

Obtain a random sample of shoppers who go
to stores with music

2.

Check shop spending

3.

Comp...
TYPES OF ERRORS
What are errors in Hypothesis
Testing?
The purpose of Hypothesis Testing is to reject or not
reject the Nu...
TYPES OF ERRORS
Actual State of Affairs
Belief

Decision

H0 is True

H0 is False

H0 is False

Reject H0

Type I Error
Fa...
Statistical Power
1.

Probability that the test will correctly reject a
false null hypothesis.

2.

When a treatment effec...
α, β AND THE INTER-RELATIONSHIP
During the Hypothesis Testing,
α – is the probability of occurrence of a Type-I Error
β – ...
INTERPRETING RESULTS
Interpreting the weight of evidence against the Null
Hypothesis for rejecting / not rejecting Ho
If t...
Jury’s Decision
Did Not Commit Crime

Committed Crime

Guilty

Type I Error
Convict Innocent
Person

Correct Verdict
Convi...
Level of Significance
1. Alpha: probability of committing a Type I
error
1.

Reject H0 although it is true

2.

Symbolized...
One Sided & Two Sided Tests


Consider two means A & B.



One sided test only tells you that A > B.



Two sided tests...
Any Questions !!!!

Thank

You.
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Hypothesis testing and p values 06

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Hypothesis testing and p values 06

  1. 1. Hypothesis Testing and P Value BY DR ZAHID KHAN SENIOR LECTURER KING FAISAL UNIVERSITY, KSA
  2. 2. Two ways to learn about a population  Confidence intervals  Hypothesis testing
  3. 3. HYPOTHESIS What do you mean by a Hypothesis? A hypothesis is a proposition that is –  assumed as a premise in an argument / claim  set forth as an explanation for the occurrence of some specified group of phenomena  A hypothesis is a prediction about the outcome of an experiment. In market research this could be the result of the out come of a focus or field study
  4. 4. Why do we make hypotheses?  The practice of science traditionally involves formulating and testing hypotheses  Hypotheses are assertions that are capable of being proven false using a test of observed data  Hypothesis testing is a procedure through which sample data is used to evaluate the credibility of a hypothesis
  5. 5. TYPES OF HYPOTHESIS Null Hypothesis   The null hypothesis typically corresponds to a general or default position Making this assertion will make no difference and hence cannot be proven positively Alternate Hypothesis  An alternate hypothesis asserts a rival relationship between the phenomena measured by the null hypothesis  It need not be a logical negation of the null hypothesis as it only helps in rejecting or not rejecting the null hypothesis
  6. 6. Dependant and independent variables  Shoppers in a store playing music shop spend more.  Independent Variable:  Music  in the store Dependent Variable:  Amount spent in store
  7. 7. Example -- Continued 1. Obtain a random sample of shoppers who go to stores with music 2. Check shop spending 3. Compare sample data to hypothesis 4. Make decision: 1. Reject the hypothesis 2. Fail to reject the hypothesis
  8. 8. TYPES OF ERRORS What are errors in Hypothesis Testing? The purpose of Hypothesis Testing is to reject or not reject the Null Hypothesis based on statistical evidence Hypothesis Testing is said to have resulted in an error when the decision regarding treatment of the Null Hypothesis is wrong
  9. 9. TYPES OF ERRORS Actual State of Affairs Belief Decision H0 is True H0 is False H0 is False Reject H0 Type I Error False Positive Correct Rejection 1Power H0 is True Fail to Reject H0 Correct Failure to Reject 1- Type II Error False Negative
  10. 10. Statistical Power 1. Probability that the test will correctly reject a false null hypothesis. 2. When a treatment effect exists 1. A study may fail to discover it (Type II error, fail to reject a false null hypothesis) 2. A study may discover it (reject a false null hypothesis)
  11. 11. α, β AND THE INTER-RELATIONSHIP During the Hypothesis Testing, α – is the probability of occurrence of a Type-I Error β – is the probability of occurrence of a Type-II Error Relationship between α and β   For a fixed sample size, the lower we set value of α, the higher is the value of β and vice-versa In many cases, it is difficult or almost impossible to calculate the value of β and hence we usually set only α
  12. 12. INTERPRETING RESULTS Interpreting the weight of evidence against the Null Hypothesis for rejecting / not rejecting Ho If the p-value for testing Ho is less than –  < 0.05, we have strong evidence that Ho is false  < 0.01, we have very strong evidence that Ho is false  < 0.001, we have extremely strong evidence that Ho is false  P value is taken as 0.05 or 5% because it is a standard icon & it nearly corresponds to the difference of two standard errors.
  13. 13. Jury’s Decision Did Not Commit Crime Committed Crime Guilty Type I Error Convict Innocent Person Correct Verdict Convict Guilty Person Not Guilty Correct Acquittal Type II Error Fail to Convict Innocent Fail to Convict Person Guilty Person
  14. 14. Level of Significance 1. Alpha: probability of committing a Type I error 1. Reject H0 although it is true 2. Symbolized by 2. Obtained result attributed to: 1. 2. Real effect (reject H0) Chance
  15. 15. One Sided & Two Sided Tests  Consider two means A & B.  One sided test only tells you that A > B.  Two sided tests tells you that either A>B or A <B so leaving you with two options.  Mostly Two sided tests are used except in cases of equivalence tests like Lumpectomy done for Breast surgery as well as radical Mastectomy.  One sided test would be whether Lumpectomy is worst for survival than Radical Mastectomy and we don't bother about better survival results.
  16. 16. Any Questions !!!! Thank You.

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