This document discusses hypothesis testing and p-values. It defines a hypothesis as a proposition or prediction about the outcome of an experiment. Hypotheses are tested to evaluate their credibility against observed data. There are two main types of hypotheses: the null hypothesis, which corresponds to a default or general position, and the alternative hypothesis, which asserts a relationship different from the null. Errors in hypothesis testing can occur if the decision to reject or fail to reject the null hypothesis is wrong. The p-value indicates how likely the observed or more extreme results would be if the null hypothesis were true. A lower p-value provides stronger evidence against the null hypothesis.

1. Hypothesis Testing and P Value
BY DR ZAHID KHAN
SENIOR LECTURER KING FAISAL UNIVERSITY, KSA

2. Two ways to learn
about a population

Confidence intervals

Hypothesis testing

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Any Questions !!!!
Thank
You.