Inferential Statistics
HypothesisTestingEstimation
(Confidence Interval)
Understanding the Logic of Hypothesis
Testing
:Claim:
Our medicine reduces weight tremendously
:Test:
Initial average weig...
Understanding the Logic of Hypothesis
Testing
:Claim:
Our medicine reduces weight tremendously
:Test:
Initial average weig...
Understanding the Logic of Hypothesis
Testing
Is there any Change?
Sample Statistic is very much
different from Population...
Hypothesis Testing Process in
General
State the Null &
Alternate Hypothesis
Select the Level of
Significance
Determine the...
Reality
Innocent Guilty
Decision
Acquit
Punish
Correct
Decision
Wrong
Decision
Wrong
Decision
Correct
Decision
H1: The Acc...
Reality
OK Not OK
Decision
Accept
Reject
Correct
Decision
Wrong
Decision
Wrong
Decision
Correct
Decision
H0:The lot is ok
...
Differentiate Between CVM and PVM
CVM PVM
Reject H0
Don not
Reject H0
TV ≥ CV
TV < CV
P ≤ Significance Level
P > Significa...
CV
Alpha
NRR RR Reject Ho
Don’t Reject Ho
TV TV
CriticalValue
Method of
HypothesisTesting
Alpha
NRR RR
Reject Ho as P ≤Alpha
Don’t Reject Ho as
P > Alpha
TV ProbabilityValue
Method of
HypothesisTesting
P
P
TV
Inferential Statistics for One
Population
Quantitative
Qualitative (Nominal,
Ordinal)
Sigma Known
Sigma
Unknown
Normal
Non...
t test for Quantitative Data
Assumptions Normal Population or Large Sample
Formula T = Difference / SE
SPSS
Procedure
Anal...
t test for Qualitative Data
Assumptions Normal Population or Large Sample
Formula T = Difference / SE
SPSS
Procedure
Analy...
WilcoxonTest
Assumptions Symmetric
Formula W = Sum of Positive Ranks
SPSS
Procedure
Analyze > NonParametric Test> 2 Relate...
BinomialTest
Assumptions Symmetric
Description Used for small sample qualitative test
SPSS
Procedure
Analyze > NonParametr...
Inferential Statistics for two
Population
Qualitative (Nominal,
Ordinal)
Quantitative
Independent
Samples
Paired
Samples
N...
Pooled t-test
Assumptions
Independent Samples
SPSS
Procedure
Analyze > Compare means> Independent Samples
Test
Example Mar...
Paired t-test
Assumptions
Dependent Samples
SPSS
Procedure
Analyze > Compare means> Paired t-test
Example Marks1 is differ...
Same Results obtained
taking differences of
Marks1 and Marks2 and
then applying t-test for
1 sample
MannWhitneyTest
Assumptions
Independent Samples
SPSS
Procedure
Analyze > NonParametric Test> 2 independent
Samples
Example...
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Variable inferential statistics
Upcoming SlideShare
Loading in …5
×

Variable inferential statistics

613 views

Published on

Published in: Education, Technology, Business
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
613
On SlideShare
0
From Embeds
0
Number of Embeds
15
Actions
Shares
0
Downloads
52
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

Variable inferential statistics

  1. 1. Inferential Statistics HypothesisTestingEstimation (Confidence Interval)
  2. 2. 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
  3. 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 70 kg Fantastic
  4. 4. 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
  5. 5. 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
  6. 6. 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
  7. 7. 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
  8. 8. Differentiate Between CVM and PVM CVM PVM Reject H0 Don not Reject H0 TV ≥ CV TV < CV P ≤ Significance Level P > Significance Level
  9. 9. CV Alpha NRR RR Reject Ho Don’t Reject Ho TV TV CriticalValue Method of HypothesisTesting
  10. 10. Alpha NRR RR Reject Ho as P ≤Alpha Don’t Reject Ho as P > Alpha TV ProbabilityValue Method of HypothesisTesting P P TV
  11. 11. 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
  12. 12. 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?
  13. 13. 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
  14. 14. 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
  15. 15. 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
  16. 16. 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
  17. 17. 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
  18. 18. 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
  19. 19. Same Results obtained taking differences of Marks1 and Marks2 and then applying t-test for 1 sample
  20. 20. MannWhitneyTest Assumptions Independent Samples SPSS Procedure Analyze > NonParametric Test> 2 independent Samples Example Marks1 is different from marks2 Same Shape Distribution

×