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