2. Basic Concepts in Hypotheses
Testing
Meaning of Hypothesis Testing
Null Hypotheses & Alternate Hypotheses
Type I & Type II Errors
One Tailed & Two Tailed Test
Steps in formulating Hypotheses Testing
3. What is Hypothesis testing
Hypothesis is the making an assumption about the
population parameter. OR
A set of logical and statistical guidelines used to make
decisions from sample statistics to population
characteristics.
For example:
The customer loyalty of brand A is better than brand B.
4. Null Hypothesis(Ho):
The null hypothesis (H0) refers to a hypothesized testing
numerical value or range of values of the population
parameter.
Specific statement about a population parameter made for
the purposes of argument.
States the assumption to be tested, is a status quo.
Is always about a population parameter, not about a sample
statistic.
5. Example of Ho:
In a clinical trial of a new drug, the null
hypothesis might be that the new drug is no
better, on average, than the current drug. We
would write
H0: there is no difference between the two drugs
on an average.
6. Alternate Hypothesis(HA)
An alternatives hypothesis (H1) is the logical opposite
of the null hypothesis.
Represents all other possible parameter values except
that stated in the null hypothesis.
Challenges the status quo.
Hypothesis that is believed (or needs to be supported)
by the researcher –a research hypothesis.
7. Example of HA
In the clinical trial of a new drug, the alternative
hypothesis might be that the 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’
8. Type I Error:
If the null hypothesis is true and we reject it is called
type I error.
Rejected H0 because the results occurred by chance
Conclude that there is a significant effect, even though
no true effect exists
Probabilities of Type 1 error called – alpha ( )
Determined in advance, typically 5%
9. Type II Error:
If the null hypothesis is false and we accept it is called
type II error.
Accept H0 even though it is not true
Conclude that there is no significant effect, even
though a true difference exists
Probabilities of Type II error called – beta ( )
10. Type I Error & Type II Error
Accept H0 Reject H0
Correct Decision Type I Error
Type II Error Correct Decision
Ho (True)
Ho (False)
11. One Tail Test:
Rejection of null hypothesis for significant deviation
from the specified value Ho in one direction (tail) of
the curve of sampling distribution is called one tailed
test.
For example:
Boll pen better then ink pen .
12. Two Tailed Test:
Rejection of null hypothesis for significant deviation
from the specified value Ho in both the direction (tail)
of the curve of sampling distribution is called two
tailed test.
Foe example:
A product is manufactured by a semi-automatic
machine. Now, assume that the same product is
manufactured by the fully automatic machine.
This will be two-sided test, because the null
hypothesis is that “the two methods used for
manufacturing the product do not differ
significantly.
13. Steps in Hypotheses Testing
1. Formulation of the null and alternate hypothesis
2. Definition of a test statistic
3. Determination of the distribution of the test
statistic
4. Definition of critical region of the test statistic
5. Testing whether the calculated value of the test
statistic falls within the acceptance region.
14. 1: Formulation of H0
The Null hypothesis assumes a certain specific value
for the unknown population parameter.
Defined as an inequality – greater than or less than.
For example, if the mean of a population is
considered, then
H0: μ ≤ μ0
H0: μ = μ0
H0: μ ≥ μ0
15. 2: Formulation of Ha
The alternate hypothesis assigns the values to the
population parameter that is not contained in the null
hypothesis.
For example,
Ha: μ > μ0
Ha: μ ≠ μ0
Ha: μ < μ0
The null hypothesis is accepted or rejected on the basis
of the information provided by the sample.
16. 3: Definition of a Test Statistic
A test statistic must be defined to test the validity of
the hypothesis.
The test statistic is computed from sample
information.
A number calculated to represent the match between a
set of data and the expectation under the null
hypothesis
17. 4: Determination of the
distribution of the test statistic
The probability distribution of the test statistic
depends on the null hypothesis assumed, the
parameter to be tested, and the sample size.
Commonly used ones are the Normal, “t”, Chi-square
and F-distributions.
18. 5: Definition of the critical region
for the test statistic
The set of values of the test statistic that leads to the
rejection of H0 in favour of Ha is called the rejection
region or critical region.
Depends upon whether the testing is one-sided or
two-sided.
19. 6: Decision rule
A decision rule is used to accept or reject the null hypothesis.
P- value
P < α
Reject the null hypothesis
Statistically significant
Test statistic
Test statistic (calculated value) < Table value of α
Accept H0
Statistically insignificant
