This document discusses hypothesis testing and inferential statistics. It covers topics like hypothesis testing process, types of errors, differentiating between critical value method and probability value method, tests for one and two populations including z-test, t-test, Wilcoxon test and binomial test. It also discusses assumptions and procedures for tests like pooled t-test, paired t-test, Mann-Whitney test and paired Wilcoxon test. Examples of applying these tests on quantitative and qualitative data are provided.

2. Inferential Statistics
HypothesisTestingEstimation
(Confidence Interval)

3. Understanding the Logic of Hypothesis
Testing
:Claim:
Our medicine reduces weight tremendously
:Test:
Initial average weight of 50 people is 85 kg
After using medicine the average weight is 84 kg
:Conclusion:
I don’t think so

4. Understanding the Logic of Hypothesis
Testing
:Claim:
Our medicine reduces weight tremendously
:Test:
Initial average weight of 50 people is 85 kg
After using medicine the average weight is 70 kg
Fantastic

5. Understanding the Logic of Hypothesis
Testing
Is there any Change?
Sample Statistic is very much
different from Population
Parameter
Sample Statistic is not very
much different from Population
Parameter
No Change:
Change is because of Sampling
Error/Randomness
Yes there is Change:
Change is because of Systematic
Change

6. Hypothesis Testing Process in
General
State the Null &
Alternate Hypothesis
Select the Level of
Significance
Determine the Test
Distribution to Use
Define the Critical
Region
Calculate the TestValue
Decision: Reject H0 or
Not
Conclusion:Test is
Significant or Not

8. Reality
Innocent Guilty
Decision
Acquit
Punish
Correct
Decision
Wrong
Decision
Wrong
Decision
Correct
Decision
H1: The Accused is Guilty
Type I Error
Type II Error
H0: The Accused is not Guilty
H0:The Accused is innocent

9. Reality
OK Not OK
Decision
Accept
Reject
Correct
Decision
Wrong
Decision
Wrong
Decision
Correct
Decision
H0:The lot is ok
H1:The lot is not ok
Type I Error
Type II Error

10. Differentiate Between CVM and PVM
CVM PVM
Reject H0
Don not
Reject H0
TV ≥ CV
TV < CV
P ≤ Significance Level
P > Significance Level

11. CV
Alpha
NRR RR Reject Ho
Don’t Reject Ho
TV TV
CriticalValue
Method of
HypothesisTesting

12. Alpha
NRR RR
Reject Ho as P ≤Alpha
Don’t Reject Ho as
P > Alpha
TV ProbabilityValue
Method of
HypothesisTesting
P
P
TV

13. Inferential Statistics for One
Population
Quantitative
Qualitative (Nominal,
Ordinal)
Sigma Known
Sigma
Unknown
Normal
Non
Parametric
Z test
t test
Z test
t test
Wilcoxon test
Binomial Test
Chi SquareTest
Kolmogorov-Smirnov
Test
Runs Test

14. t test for Quantitative Data
Assumptions Normal Population or Large Sample
Formula T = Difference / SE
SPSS
Procedure
Analyze > Compare Means > One Population t test
Example
The average marks of the students was 75 last year.
The data was collected from 25 students and the
mean was calculated. Can we conclude that mean is
more than 75?

17. t test for Qualitative Data
Assumptions Normal Population or Large Sample
Formula T = Difference / SE
SPSS
Procedure
Analyze > Compare Means > One Population t test
Example
Test whether the majority of students are satisfied
or not.
Data Coding zero & one

20. WilcoxonTest
Assumptions Symmetric
Formula W = Sum of Positive Ranks
SPSS
Procedure
Analyze > NonParametric Test> 2 Related Samples>
WilcoxonTest
Example Test whether marks1 is more than 70 or not

24. BinomialTest
Assumptions Symmetric
Description Used for small sample qualitative test
SPSS
Procedure
Analyze > NonParametric Test> legacy dialogue >
Binomial
Example Test whether the majority is satisfied

27. Inferential Statistics for two
Population
Qualitative (Nominal,
Ordinal)
Quantitative
Independent
Samples
Paired
Samples
NormalParametric
Pooled or Nonpooled
t tests
Paired t-test
Mann WhitneyTestIndependent
Samples
Paired
Samples
Paired WilcoxonTest
Fisher Exact, Chi Sq
Median T, MWT, KS,
WW
McNemar,
SignTest,
WilcoxonPaired Test

28. Pooled t-test
Assumptions
Independent Samples
SPSS
Procedure
Analyze > Compare means> Independent Samples
Test
Example Marks1 for boys and girls differ
Nonpooled t-test
Normal Populations or Large Sample
Equal Sigmas

32. Paired t-test
Assumptions
Dependent Samples
SPSS
Procedure
Analyze > Compare means> Paired t-test
Example Marks1 is different from marks2
Normal Differences or Large Sample
Sigma not known

35. Same Results obtained
taking differences of
Marks1 and Marks2 and
then applying t-test for
1 sample

36. MannWhitneyTest
Assumptions
Independent Samples
SPSS
Procedure
Analyze > NonParametric Test> 2 independent
Samples
Example Marks1 is different from marks2
Same Shape Distribution