grweergrerdeer

1. HYPOTHESIS TESTING

2. A hypothesis is an assumption about the
population parameter.
A parameter is characteristic of the population,
like its mean or variance.
© 1984-1994 T/Maker Co.
WHAT IS A HYPOTHESIS?

3. T
ESTING OF HYPOTHESIS
For testing of hypothesis we collect sample data , then we
calculate sample statistics (say sample mean) and then use this
information to judge/decide whether hypothesized value of
population parameter is correct or not.
Then we judge whether the difference is significant or not(difference
between hypothesized value and sample value)
The smaller the difference ,the greater the chance that our
hypothesized value for the mean is correct.

4. THE NULL HYPOTHESIS, H0
The null hypothesis H0 represents a theory that has been put
forward either because it is believed to be true or because it
is used as a basis for an argument and has not been proven.
Forexample, in a clinical trial ofa newdrug, the null
hypothesis might be thatthe newdrug is nobetter, on
average, than the current drug. We would write
H0: there is no difference between the two drugs on an
average.

5. ALTERNATIVE HYPOTHESIS
new drug has a different effect, on average, compared to that of the
current drug. We would write
HA: the two drugs have different effects, on average.
or
HA: the new drug is better than the current drug, on average.
The result of a hypothesis test:
‘Reject H0 in favour of HA’ OR ‘Do not reject H0’
The alternative hypothesis, HA, is a statement of what a statistical
hypothesis test is set up to establish. For example, in the clinical
trial of a new drug, the alternative hypothesis that the

6. SELECTING AND INTERPRETING
SIGNIFICANCE LEVEL
1. Deciding on a criterion for accepting or rejecting the null
hypothesis.
2. Significance level refers to the percentage of the means that is
outside certain prescribed limits. E.g testing a hypothesis at 5%
level of significance means
 that we reject the null hypothesis if it falls in the two regions of
area 0.025.
 Do not reject the null hypothesis if it falls within the region of
area 0.95.
3. The higher the level of significance, the higher is the probability
of rejecting the null hypothesis when it is true.
(acceptance region narrows)

7. Critical value
Critical value
If our sample statistic(calculated value) fall in the non-
shaded region( acceptance region), then it simply means
that there is no evidence to reject the null hypothesis.
(Confidence
interval)

8. A type I error, also known as an error of the first kind,
occurs when the null hypothesis (H0) is true, but is rejected.
A type I error may be compared with a so called false positive.
Denoted by the Greek letter α (alpha).
It is usually equals to the significance level of a test.
If type I error is fixed at 5 %, it means that there are about 5
chances in 100 that we will reject H0 when H0 is true.

9. Type II error, also known as an error of the second kind, occurs when the null
hypothesis is false, but incorrectly fails to be rejected.
Type II error means accepting the hypothesis which should have been rejected.
A type II error may be compared with a so-called False Negative.
A type II error occurs when one rejects the alternative hypothesis (fails to reject
the null hypothesis) when the alternative hypothesis is true.
The rate of the type II error is denoted by the Greek letter β (beta) and related to
the power of a test (which equals 1-β ).

11. EXAMPLE 1-COURT ROOM TRIAL
In court room, a defendant is considered not guilty as
long as his guilt is not proven. The prosecutor tries to
prove the guilt of the defendant. Only when there is
enough charging evidence the defendant is condemned.
In the start of the procedure, there are two hypotheses
H0: "the defendant is not guilty", and H1: "the
defendant is guilty". The first one is called null
hypothesis, and the second one is called alternative
(hypothesis).

12. Suppose the null hypothesis, H0, is: Frank's rock climbing equipment is safe.
Type I error: Frank thinks that his rock climbing equipment may not be safe when, in
fact, it really is safe.
Type II error: Frank thinks that his rock climbing equipment may be safe when, in
fact, it is not safe.
α= probability that Frank thinks his rock climbing equipment may not be safe when,
in fact, it really is safe.
β=probability that Frank thinks his rock climbing equipment may be safe when, in
fact, it is not safe.
Notice that, in this case, the error with the greater consequence is the Type II error.
(If Frank thinks his rock climbing equipment is safe, he will go ahead and use it.)
EXAMPLE 2

13. Suppose the null hypothesis, H0, is: The victim of an
automobile accident is alive when he arrives at the emergency
room of a hospital.
Type I error: The emergency crew thinks that the victim is
dead when, in fact, the victim is alive.
Type II error: The emergency crew does not know if the victim
is alive when, in fact, the victim is dead.
α=probability that the emergency crew thinks the victim is
dead when, in fact, he is really alive =P(Type I error)
β= probability that the emergency crew does not know if the
victim is alive when, in fact, the victim is dead =P(Type II
error)
The error with the greater consequence is the Type I error. (If
the emergency crew thinks the victim is dead, they will not
treat him.)
EXAMPLE 3

14. EXAMPLE 4
It’s a Boy Genetic Labs claim to be able to increase the
likelihood that a pregnancy will result in a boy being born.
Statisticians want to test the claim. Suppose that the null
hypothesis, H0 , is: It’s a Boy Genetic Labs has no effect on
gender outcome.
Type I error: This results when a true null hypothesis is
rejected. In the context of this scenario, we would state that
we believe that It’s a Boy Genetic Labs influences the gender
outcome, when in fact it has no effect. The probability of this
error occurring is denoted by the Greek letter alpha, α
Type II error: This results when we fail to reject a false null
hypothesis. In context, we would state that It’s a Boy
Genetic Labs does not influence the gender outcome of a
pregnancy when, in fact, it does. The probability of this
error occurring is denoted by the Greek letter beta, β
The error of greater consequence would be the Type I error
since couples would use the It’s a Boy Genetic Labs product
in hopes of increasing the chances of having a boy.

15. REDUCING TYPE I ERRORS
Prescriptive testing is used to increase the level of confidence, which
in turn reduces Type I errors. The chances of making a Type I error are
reduced by increasing the level of confidence.

16. REDUCING TYPE II ERRORS
Descriptive testing is used to better describe the test condition and
acceptance criteria, which in turn reduces Type II errors. This increases
the number of times we reject the Null hypothesis – with a resulting
increase in the number of Type I errors (rejecting H0 when it was
really true and should not have been rejected).
Therefore, reducing one type of error comes at the expense of increasing the other type
of error! THE SAME MEANS CANNOT REDUCE BOTH TYPES OF ERRORS
SIMULTANEOUSLY!

17. Therefore, reducing one type of error comes at the expense of
increasing the other type of error! THE SAME MEANS
CANNOT REDUCE BOTH TYPES OF ERRORS
SIMULTANEOUSLY!

18. THANK YOU