Statistics

1. HYPOTHESIS TESTING
By Shirali, Elmir, Ragim (BBA-020)

2. Agenda:
• Hypothesis : Meaning, Types,
characteristics, sources
• Formulation of Hypothesis,
Errors in hypothesis testing
Parametric and Nonparametric
test
T-test, Z-test, F-test

3. What is a statistical hypothesis
test?
A statistical hypothesis test is a method of
making decisions using data, whether from
a controlled experiment or an observational
study

4. What is a statistical hypothesis
test?
It is an unproven statement or
proposition about a factor or
phenomenon that is of interest to the
researcher.
An important role of a hypothesis is to
suggest variables to be included in the
research design

5. Types:
Null Hypothesis (H0) –
This hypothesis states that there
is no difference between the
parameter and the statistic that is
being computed.

6. Types:
Analytical Hypothesis (H1) – Here
relationship of analytical variable
is found. These are used when
one would like to specify the
relationship between changes in
one property leading to change in
another.

7. Characteristics of a
Hypothesis:
• Clarity of concepts – Concepts should
not be abstract. If concepts are not
clear, precise problem formulation will
be difficult leading to difficulty in data
collection. Concepts are important
because, it means different to
different people.
• Ability to test – It should be possible
to verify the hypothesis. Therefore, a
good hypothesis is one in which there
is empirical evidence.

8. • Specific/Clear – What is to be tested
should be clear. The relationship
between the variables should be clear
or the statistic under verification
should be mentioned clearly.
• Statistical Tools – Hypothesis should
be such that, it is possible to use
statistical techniques. Such as Anova,
Chi square, t- test or other non
parametric tests.

9. • Logical – If there is two or more
Hypothesis derived from the same
basic theory, they should not
contradict each other.
• Subjectivity – Researchers subjectivity
or his biased Judgment should be
eliminated from the hypothesis.
• Theory – Hypothesis must be
supported or backed up by theoretical
relevance.

10. Steps involved in Hypothesis
Testing:
Formulate H0 and H1 Select an appropriate test
Choose the level of
• significance, α
Collect data and calculate
the test statistic.
Determine the probability Determine the critical value
associated with the test statistic. of the test statistic, TSCR
Compare probability with level Determine if TSCR falls into rejection
of significance, α or non-rejection region.
Reject or do not reject H0.
Draw a marketing research conclusion.

11. Parametric tests:
• These tests are based on some assumptions
about the parent population from which the
sample has been drawn. These assumptions
can be with respect to sample size, type of
distribution or on population parameters like
mean, standard deviation etc.
• Parametric tests are more powerful.
• In parametric tests, it is assumed that the
data follows normal distributions. Ex: Of
parametric tests are Z Test, T-Test and F-Test.

12. T test:
• T-Test is a univariate test.
• Uses t-distribution, which is a
symmetrical bell-shaped curve, for
testing sample mean and proportion.
• Assumes that the variable is normally
distributed and the mean is known and
the population variance is estimated
from the sample.
• It is used when the standard deviation
is unknown and the size of sample is
small (i.e. less than 30).

13. X − µ0
~ N (0,1)
Z test - σ/ n
• It is a popular test for judging the significance
of mean and proportions.
• It is used for t-distribution and binomial or
Poisson distribution also when the size of
sample is very large (more than 30) on the
presumption that such a distribution tends to
approximate normal distribution as sample
size becomes larger.
• Testing the hypothesis about difference
between two means: This can be used when
two population means are given and null
hypothesis is H0: P1 = P2.

14. F test:
• An F test of sample variance may be
performed if it is not known whether the two
populations have equal variance.
• It is used to test the equality of variance of
two normal populations i.e. to find whether
two samples can be regarded as drawn from
normal populations having the same
variance.
• This test is particularly useful when multiple
sample cases are involved and the data has
been measured on interval or ratio scale.
• If the probability of F is greater than the
significance level α, H0 is not rejected

15. Non Parametric Tests:
• Non Parametric tests are used to test the
hypothesis with nominal and ordinal data.
• We do not make assumptions about the
shape of population distribution.
• These are distribution-free tests.
• The hypothesis of non-parametric test is
concerned with something other than the
value of a population parameter.
• Easy to compute. There are certain situations
particularly in marketing research, where the
assumptions of parametric tests are not
valid.
• Examples are Chi-Square Test, Mann Whitney
U Test, Kruskal-Wallis Test, Rank Correlation

16. Basic test statistic for a mean:
point estimate of µ - target value of µ
test statistic =
σ point estimate of µ
•σ = standard deviation
•For 2-sided test: Reject H0 when
the test statistic is in the upper or
lower 100*α/2% of the reference
distribution

17. Non Parametric Tests:
• Non Parametric tests are used to test the
hypothesis with nominal and ordinal data.
• We do not make assumptions about the
shape of population distribution.
• These are distribution-free tests.
• The hypothesis of non-parametric test is
concerned with something other than the
value of a population parameter.
• Easy to compute. There are certain situations
particularly in marketing research, where the
assumptions of parametric tests are not
valid.
• Examples are Chi-Square Test, Mann Whitney
U Test, Kruskal-Wallis Test, Rank Correlation

18. P value
The P value is a probability, with
value ranging from zero to one.
The smaller the p-value, the more
statistical evidence exists to
support the alternative
hypothesis.

19. P value
• If the p-value is less than 1%, there is
overwhelming evidence that supports
the alternative hypothesis.
• If the p-value is between 1% and 5%,
there is a strong evidence that
supports the alternative hypothesis.
• If the p-value is between 5% and 10%
there is a weak evidence that supports
the alternative hypothesis.
• If the p-value exceeds 10%, there is no
evidence that supports the alternative
hypothesis.

20. BBA, any questions? ;)

21. Thanks for Attention!
References:
• Moore, David S. 2002. The Basic Practice of Statistics, 2nd
edition
• Schervish, M (1996) Theory of Statistics, p. 218. Springer
• Shirali Orujlu
• Ragim Abdullayev
• Elmir Huseynov