Post on 17-Jun-2015
Inferentia
l
Statistics
Inferential Statistics
Hypothesis Testing
Estimation (Confidence
Interval)
Understanding the Logic of Hypothesis Testing
:Claim: Our medicine reduces weight
tremendously
:Test: Initial average weight of 50 people is 85 kgAfter using medicine the average weight is 84 kg
:Conclusion: I don’t think so
Understanding the Logic of Hypothesis Testing
:Claim: Our medicine reduces weight tremendously
:Test: Initial average weight of 50 people is 85 kgAfter using medicine the average weight is 70 kg
Fantastic
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
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 Test Value
Decision: Reject H0 or Not
Conclusion: Test is Significant or Not
Reality
Innocent Guilty
Decision
Acquit
Punish
Correct Decision
Wrong Decision
Wrong Decision
Correct Decision
H1: The Accused is Guilty
Type I Error
Type II ErrorH0: The Accused is not GuiltyH0: The Accused is innocent
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
Differentiate Between CVM and PVM
CVM PVM
Reject H0
Don not Reject H0
TV ≥ CV
TV < CV
P ≤ Significance Level
P > Significance Level
CV
Alpha
NRR RR Reject Ho
Don’t Reject Ho
TV TV
Critical Value Method of Hypothesis
Testing
Alpha
NRR RR
Reject Ho as P ≤Alpha
Don’t Reject Ho as P > Alpha
TVProbability
Value Method of Hypothesis
Testing
P
P
TV
Inferential Statistics for One Population
QuantitativeQualitative
(Nominal, Ordinal)
Sigma Known
Sigma Unknown
Norm
al
Non
Pa
ram
etr
ic
Z test
t test
Z test
t test
Wilcoxon test
Binomial Test Chi Square Test
Kolmogorov-Smirnov Test
Runs Test
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?
t test for Qualitative Data
Assumptions
Normal Population or Large Sample
Formula T = Difference / SE
SPSS Procedure
Analyze > Compare Means > One Population t test
ExampleTest whether the majority of students are
satisfied or not.
Data Coding
zero & one
Wilcoxon Test
Assumptions
Symmetric
Formula W = Sum of Positive Ranks
SPSS Procedure
Analyze > NonParametric Test> 2 Related Samples> Wilcoxon Test
ExampleTest whether marks1 is more than 70 or
not
Binomial Test
Assumptions
Symmetric
Description Used for small sample qualitative test
SPSS Procedure
Analyze > NonParametric Test> legacy dialogue > Binomial
Example Test whether the majority is satisfied
Inferential Statistics for two Population
Qualitative (Nominal, Ordinal)
Quantitative
Independent
Samples
Paired Samples
Norm
al
Para
metr
ic
Pooled or Nonpooled t tests
Paired t-test
Mann Whitney Test
Independent
Samples
Paired Samples
Paired Wilcoxon Test
Fisher Exact, Chi Sq
Median T, MWT, KS, WWMcNemar,
Sign Test, WilcoxonPaired
Test
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
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
Same Results obtained taking differences of
Marks1 and Marks2 and then applying t-test for 1 sample
Mann Whitney Test
Assumptions
Independent Samples
SPSS Procedure
Analyze > NonParametric Test> 2 independent Samples
Example Marks1 is different from marks2
Same Shape Distribution