SlideShare uma empresa Scribd logo
1 de 31
Baixar para ler offline
PARAMETRIC TESTS
STATISTICAL TEST
• Statistical tests are intended
to decide whether a
hypothesis about distribution
of one or more populations or
samples should be rejected or
accepted.
Statistical
Tests
Parametric tests
Non –
Parametric tests
PARAMETRIC TESTS
Parametric test is a statistical test that makes assumptions
about the parameters of the population distribution(s) from
which one’s data is drawn.
APPLICATIONS
• Used for Quantitative data.
• Used for continuous variables.
• Used when data are measured on approximate interval or
ratio scales of measurement.
• Data should follow normal distribution.
PARAMETRIC TESTS
1. t-test
t-test
t-test for one
sample
t-test for two
samples
Unpaired two
sample t-test
Paired two
sample t-test
Contd..
2. ANOVA
3. Pearson’s r correlation
4. Z test
ANOVA
One way ANOVA
Two way ANOVA
STUDENT’S T-TEST
• Developed by Prof.W.S.Gossett
• A t-test compares the difference between two means of
different groups to determine whether the difference is
statistically significant.
One Sample t-test
Assumptions:
• Population is normally distributed
• Sample is drawn from the population and it should be
random
• We should know the population mean
Conditions:
• Population standard deviation is not known
• Size of the sample is small (<30)
Contd..
• In one sample t-test , we know the population mean.
• We draw a random sample from the population and then
compare the sample mean with the population mean and
make a statistical decision as to whether or not the sample
mean is different from the population.
Let x1, x2, …….,xn be a random sample of size “n” has drawn from a
normal population with mean (µ) and variance 𝜎2.
Null hypothesis (H0):
Population mean (μ) is equal to a specified value µ0.
Under H0, the test statistic is 𝒕 =
𝒙−µ
𝒔
𝒏
Two sample t-test
• Used when the two independent random samples come from the
normal populations having unknown or same variance.
• We test the null hypothesis that the two population means are same
i.e., µ1 = µ2
Contd…
Assumptions:
1. Populations are distributed normally
2. Samples are drawn independently and at random
Conditions:
1. Standard deviations in the populations are same and not known
2. Size of the sample is small
If two independent samples xi ( i = 1,2,….,n1) and yj ( j = 1,2, …..,n2) of
sizes n1and n2 have been drawn from two normal populations with
means µ1 and µ2 respectively.
Null hypothesis
H0 : µ1 = µ2
Under H0, the test statistic is
𝒕 =
ǀ 𝒙 − 𝒚ǀ
𝑺
𝟏
𝒏 𝟏
+
𝟏
𝒏 𝟐
Paired t-test
Used when measurements are taken from the same subject
before and after some manipulation or treatment.
Ex: To determine the significance of a difference in blood
pressure before and after administration of an experimental
pressure substance.
Assumptions:
1. Populations are distributed normally
2. Samples are drawn independently and at random
Conditions:
1. Samples are related with each other
2. Sizes of the samples are small and equal
3. Standard deviations in the populations are equal and not known
Null Hypothesis:
H0: µd = 0
Under H0, the test statistic
𝒕 =
ǀ𝒅̅ǀ
𝒔
𝒏
Where, d = difference between x1 and x2
d̅ = Average of d
s = Standard deviation
n = Sample size
Z-Test
• Z-test is a statistical test where normal distribution is applied
and is basically used for dealing with problems relating to
large samples when the frequency is greater than or equal to
30.
• It is used when population standard deviation is known.
Contd…
Assumptions:
• Population is normally distributed
• The sample is drawn at random
Conditions:
• Population standard deviation σ is known
• Size of the sample is large (say n > 30)
Let x1, x2, ………x,n be a random sample size of n from a normal
population with mean µ and variance σ2 .
Let x̅ be the sample mean of sample of size “n”
Null Hypothesis:
Population mean (µ) is equal to a specified value µο
H0: µ = µο
Under Hο, the test statistic is
𝒁 =
ǀ 𝒙 − µ 𝝄ǀ
𝒔
𝒏
If the calculated value of Z < table value of Z at 5% level of
significance, H0 is accepted and hence we conclude that there is no
significant difference between the population mean and the one
specified in H0 as µο.
Pearson’s ‘r’ Correlation
• Correlation is a technique for investigating the relationship
between two quantitative, continuous variables.
• Pearson’s Correlation Coefficient (r) is a measure of the
strength of the association between the two variables
Types of correlation
Type of correlation Correlation coefficient
Perfect positive correlation r = +1
Partial positive correlation 0 < r < +1
No correlation r = 0
Partial negative correlation 0 > r > -1
Perfect negative correlation r = -1
ANOVA (Analysis of Variance)
• Analysis of Variance (ANOVA) is a collection of statistical
models used to analyse the differences between group means
or variances.
• Compares multiple groups at one time
• Developed by R.A.Fischer
ANOVA
One way ANOVA
Two way ANOVA
One way ANOVA
Compares two or more unmatched groups when data are categorized in
one factor
Ex:
1. Comparing a control group with three different doses of aspirin
2. Comparing the productivity of three or more employees based on
working hours in a company
Two way ANOVA
• Used to determine the effect of two nominal predictor variables on a
continuous outcome variable.
• It analyses the effect of the independent variables on the expected
outcome along with their relationship to the outcome itself.
Ex: Comparing the employee productivity based on the working hours
and working conditions.
Assumptions of ANOVA:
• The samples are independent and selected randomly.
• Parent population from which samples are taken is of normal
distribution.
• Various treatment and environmental effects are additive in
nature.
• The experimental errors are distributed normally with mean
zero and variance σ2.
• ANOVA compares variance by means of F-ratio
F =
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑎𝑚𝑝𝑙𝑒𝑠
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑤𝑖𝑡ℎ𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒𝑠
• It again depends on experimental designs
Null hypothesis:
Hο = All population means are same
• If the computed Fc is greater than F critical value, we are likely to reject the null
hypothesis.
• If the computed Fc is lesser than the F critical value , then the null hypothesis is
accepted.
ANOVA Table
Sources of
Variation
Sum of squares
(SS)
Degrees of
freedom (d.f)
Mean squares
(MS)
𝒔𝒖𝒎 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆𝒔
𝒅̅𝒆𝒈𝒓𝒆𝒆𝒔 𝒐𝒇 𝒇𝒓𝒆𝒆𝒅̅𝒐𝒎
F - Ratio
Between samples
or groups
(Treatments)
Treatment sum of
squares ( TrSS)
(k-1) 𝑇𝑟𝑆𝑆
(𝑘 − 1)
𝑇𝑟𝑀𝑆
𝐸𝑀𝑆
Within samples or
groups ( Errors )
Error sum of
squares (ESS)
(n-k) 𝐸𝑆𝑆
(𝑛 − 𝑘)
Total Total sum of
squares (TSS)
(n-1)
S.No Type of group Parametric test
1. Comparison of two paired groups Paired t-test
2. Comparison of two unpaired groups Unpaired two sample t-test
3. Comparison of population and sample
drawn from the same population
One sample t-test
4. Comparison of three or more matched
groups but varied in two factors
Two way ANOVA
5. Comparison of three or more matched
groups but varied in one factor
One way ANOVA
6. Correlation between two variables Pearson Correlation
Parametric tests

Mais conteúdo relacionado

Mais procurados (20)

Student t test
Student t testStudent t test
Student t test
 
PPT on Sample Size, Importance of Sample Size,
PPT on Sample Size, Importance of Sample Size,PPT on Sample Size, Importance of Sample Size,
PPT on Sample Size, Importance of Sample Size,
 
Wilcoxon signed rank test
Wilcoxon signed rank testWilcoxon signed rank test
Wilcoxon signed rank test
 
The mann whitney u test
The mann whitney u testThe mann whitney u test
The mann whitney u test
 
T test
T testT test
T test
 
01 parametric and non parametric statistics
01 parametric and non parametric statistics01 parametric and non parametric statistics
01 parametric and non parametric statistics
 
Non-Parametric Tests
Non-Parametric TestsNon-Parametric Tests
Non-Parametric Tests
 
Type i and type ii errors
Type i and type ii errorsType i and type ii errors
Type i and type ii errors
 
Chi square test
Chi square testChi square test
Chi square test
 
Test of significance in Statistics
Test of significance in StatisticsTest of significance in Statistics
Test of significance in Statistics
 
Null hypothesis
Null hypothesisNull hypothesis
Null hypothesis
 
Analysis of variance (anova)
Analysis of variance (anova)Analysis of variance (anova)
Analysis of variance (anova)
 
Anova ppt
Anova pptAnova ppt
Anova ppt
 
Student's t test
Student's t testStudent's t test
Student's t test
 
Kruskal Wall Test
Kruskal Wall TestKruskal Wall Test
Kruskal Wall Test
 
Analysis of variance anova
Analysis of variance anovaAnalysis of variance anova
Analysis of variance anova
 
Measures of Dispersion
Measures of DispersionMeasures of Dispersion
Measures of Dispersion
 
Chi squared test
Chi squared testChi squared test
Chi squared test
 
Mann Whitney U test
Mann Whitney U testMann Whitney U test
Mann Whitney U test
 
Standard error
Standard error Standard error
Standard error
 

Destaque

Z test
Z testZ test
Z testkagil
 
What is a Single Sample Z Test?
What is a Single Sample Z Test?What is a Single Sample Z Test?
What is a Single Sample Z Test?Ken Plummer
 
Single sample z test - explain (final)
Single sample z test - explain (final)Single sample z test - explain (final)
Single sample z test - explain (final)CTLTLA
 
Hypothesis Testing-Z-Test
Hypothesis Testing-Z-TestHypothesis Testing-Z-Test
Hypothesis Testing-Z-TestRoger Binschus
 
Hypothesis testing; z test, t-test. f-test
Hypothesis testing; z test, t-test. f-testHypothesis testing; z test, t-test. f-test
Hypothesis testing; z test, t-test. f-testShakehand with Life
 

Destaque (7)

Z-Test with Examples
Z-Test with ExamplesZ-Test with Examples
Z-Test with Examples
 
Z test
Z testZ test
Z test
 
What is a Single Sample Z Test?
What is a Single Sample Z Test?What is a Single Sample Z Test?
What is a Single Sample Z Test?
 
Single sample z test - explain (final)
Single sample z test - explain (final)Single sample z test - explain (final)
Single sample z test - explain (final)
 
Hypothesis Testing-Z-Test
Hypothesis Testing-Z-TestHypothesis Testing-Z-Test
Hypothesis Testing-Z-Test
 
Z test
Z testZ test
Z test
 
Hypothesis testing; z test, t-test. f-test
Hypothesis testing; z test, t-test. f-testHypothesis testing; z test, t-test. f-test
Hypothesis testing; z test, t-test. f-test
 

Semelhante a Parametric tests

Parametric test - t Test, ANOVA, ANCOVA, MANOVA
Parametric test  - t Test, ANOVA, ANCOVA, MANOVAParametric test  - t Test, ANOVA, ANCOVA, MANOVA
Parametric test - t Test, ANOVA, ANCOVA, MANOVAPrincy Francis M
 
Statistical analysis.pptx
Statistical analysis.pptxStatistical analysis.pptx
Statistical analysis.pptxChinna Chadayan
 
parameter Estimation and effect size
parameter Estimation and effect size parameter Estimation and effect size
parameter Estimation and effect size hannantahir30
 
T test^jsample size^j ethics
T test^jsample size^j ethicsT test^jsample size^j ethics
T test^jsample size^j ethicsAbhishek Thakur
 
tests of significance
tests of significancetests of significance
tests of significancebenita regi
 
Chi square test social research refer.ppt
Chi square test social research refer.pptChi square test social research refer.ppt
Chi square test social research refer.pptSnehamurali18
 
inferentialstatistics-210411214248.pdf
inferentialstatistics-210411214248.pdfinferentialstatistics-210411214248.pdf
inferentialstatistics-210411214248.pdfChenPalaruan
 
t Test- Thiyagu
t Test- Thiyagut Test- Thiyagu
t Test- ThiyaguThiyagu K
 
Parametric tests seminar
Parametric tests seminarParametric tests seminar
Parametric tests seminardrdeepika87
 
Assessment 3 ContextYou will review the theory, logic, and a.docx
Assessment 3 ContextYou will review the theory, logic, and a.docxAssessment 3 ContextYou will review the theory, logic, and a.docx
Assessment 3 ContextYou will review the theory, logic, and a.docxgalerussel59292
 
Test of hypothesis test of significance
Test of hypothesis test of significanceTest of hypothesis test of significance
Test of hypothesis test of significanceDr. Jayesh Vyas
 

Semelhante a Parametric tests (20)

Parametric test - t Test, ANOVA, ANCOVA, MANOVA
Parametric test  - t Test, ANOVA, ANCOVA, MANOVAParametric test  - t Test, ANOVA, ANCOVA, MANOVA
Parametric test - t Test, ANOVA, ANCOVA, MANOVA
 
Statistical analysis.pptx
Statistical analysis.pptxStatistical analysis.pptx
Statistical analysis.pptx
 
Statistical analysis
Statistical  analysisStatistical  analysis
Statistical analysis
 
Anova, ancova
Anova, ancovaAnova, ancova
Anova, ancova
 
FandTtests.ppt
FandTtests.pptFandTtests.ppt
FandTtests.ppt
 
parameter Estimation and effect size
parameter Estimation and effect size parameter Estimation and effect size
parameter Estimation and effect size
 
Amrita kumari
Amrita kumariAmrita kumari
Amrita kumari
 
T test^jsample size^j ethics
T test^jsample size^j ethicsT test^jsample size^j ethics
T test^jsample size^j ethics
 
Comparing means
Comparing meansComparing means
Comparing means
 
Analysis of Variance
Analysis of VarianceAnalysis of Variance
Analysis of Variance
 
tests of significance
tests of significancetests of significance
tests of significance
 
Chi square test social research refer.ppt
Chi square test social research refer.pptChi square test social research refer.ppt
Chi square test social research refer.ppt
 
Inferential statistics
Inferential statisticsInferential statistics
Inferential statistics
 
inferentialstatistics-210411214248.pdf
inferentialstatistics-210411214248.pdfinferentialstatistics-210411214248.pdf
inferentialstatistics-210411214248.pdf
 
Hypothesis Testing.pptx
Hypothesis Testing.pptxHypothesis Testing.pptx
Hypothesis Testing.pptx
 
t Test- Thiyagu
t Test- Thiyagut Test- Thiyagu
t Test- Thiyagu
 
Parametric tests seminar
Parametric tests seminarParametric tests seminar
Parametric tests seminar
 
Shovan anova main
Shovan anova mainShovan anova main
Shovan anova main
 
Assessment 3 ContextYou will review the theory, logic, and a.docx
Assessment 3 ContextYou will review the theory, logic, and a.docxAssessment 3 ContextYou will review the theory, logic, and a.docx
Assessment 3 ContextYou will review the theory, logic, and a.docx
 
Test of hypothesis test of significance
Test of hypothesis test of significanceTest of hypothesis test of significance
Test of hypothesis test of significance
 

Mais de Ananya Sree Katta (10)

Experiments of satyagraha
Experiments of satyagrahaExperiments of satyagraha
Experiments of satyagraha
 
Hr practices of taj hotels
Hr practices of taj hotelsHr practices of taj hotels
Hr practices of taj hotels
 
Money laundering
Money laundering  Money laundering
Money laundering
 
Types of Contracts
Types of ContractsTypes of Contracts
Types of Contracts
 
Peter drucker
Peter druckerPeter drucker
Peter drucker
 
Controlling
ControllingControlling
Controlling
 
Sugar industry
Sugar industrySugar industry
Sugar industry
 
BREXIT
BREXITBREXIT
BREXIT
 
Budget 2017 18
Budget 2017 18Budget 2017 18
Budget 2017 18
 
Budget 2017 18
Budget 2017 18Budget 2017 18
Budget 2017 18
 

Último

Team B Mind Map for Organizational Chg..
Team B Mind Map for Organizational Chg..Team B Mind Map for Organizational Chg..
Team B Mind Map for Organizational Chg..dlewis191
 
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxChapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxesiyasmengesha
 
Entrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsEntrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsP&CO
 
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...Brian Solis
 
Harvard Business Review.pptx | Navigating Labor Unrest (March-April 2024)
Harvard Business Review.pptx | Navigating Labor Unrest (March-April 2024)Harvard Business Review.pptx | Navigating Labor Unrest (March-April 2024)
Harvard Business Review.pptx | Navigating Labor Unrest (March-April 2024)tazeenaila12
 
Building Your Personal Brand on LinkedIn - Expert Planet- 2024
 Building Your Personal Brand on LinkedIn - Expert Planet-  2024 Building Your Personal Brand on LinkedIn - Expert Planet-  2024
Building Your Personal Brand on LinkedIn - Expert Planet- 2024Stephan Koning
 
Live-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarLive-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarNathanielSchmuck
 
Borderless Access - Global B2B Panel book-unlock 2024
Borderless Access - Global B2B Panel book-unlock 2024Borderless Access - Global B2B Panel book-unlock 2024
Borderless Access - Global B2B Panel book-unlock 2024Borderless Access
 
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John MeulemansBCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John MeulemansBBPMedia1
 
NewBase 25 March 2024 Energy News issue - 1710 by Khaled Al Awadi_compress...
NewBase  25 March  2024  Energy News issue - 1710 by Khaled Al Awadi_compress...NewBase  25 March  2024  Energy News issue - 1710 by Khaled Al Awadi_compress...
NewBase 25 March 2024 Energy News issue - 1710 by Khaled Al Awadi_compress...Khaled Al Awadi
 
Developing Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursDeveloping Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursKaiNexus
 
7movierulz.uk
7movierulz.uk7movierulz.uk
7movierulz.ukaroemirsr
 
PDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfPDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfHajeJanKamps
 
Michael Vidyakin: Introduction to PMO (UA)
Michael Vidyakin: Introduction to PMO (UA)Michael Vidyakin: Introduction to PMO (UA)
Michael Vidyakin: Introduction to PMO (UA)Lviv Startup Club
 
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003believeminhh
 
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHelene Heckrotte
 
Cracking the ‘Business Process Outsourcing’ Code Main.pptx
Cracking the ‘Business Process Outsourcing’ Code Main.pptxCracking the ‘Business Process Outsourcing’ Code Main.pptx
Cracking the ‘Business Process Outsourcing’ Code Main.pptxWorkforce Group
 
MoneyBridge Pitch Deck - Investor Presentation
MoneyBridge Pitch Deck - Investor PresentationMoneyBridge Pitch Deck - Investor Presentation
MoneyBridge Pitch Deck - Investor Presentationbaron83
 
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfGraham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfAnhNguyen97152
 

Último (20)

Team B Mind Map for Organizational Chg..
Team B Mind Map for Organizational Chg..Team B Mind Map for Organizational Chg..
Team B Mind Map for Organizational Chg..
 
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxChapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
 
Entrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizationsEntrepreneurship & organisations: influences and organizations
Entrepreneurship & organisations: influences and organizations
 
Investment Opportunity for Thailand's Automotive & EV Industries
Investment Opportunity for Thailand's Automotive & EV IndustriesInvestment Opportunity for Thailand's Automotive & EV Industries
Investment Opportunity for Thailand's Automotive & EV Industries
 
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
 
Harvard Business Review.pptx | Navigating Labor Unrest (March-April 2024)
Harvard Business Review.pptx | Navigating Labor Unrest (March-April 2024)Harvard Business Review.pptx | Navigating Labor Unrest (March-April 2024)
Harvard Business Review.pptx | Navigating Labor Unrest (March-April 2024)
 
Building Your Personal Brand on LinkedIn - Expert Planet- 2024
 Building Your Personal Brand on LinkedIn - Expert Planet-  2024 Building Your Personal Brand on LinkedIn - Expert Planet-  2024
Building Your Personal Brand on LinkedIn - Expert Planet- 2024
 
Live-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarLive-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry Webinar
 
Borderless Access - Global B2B Panel book-unlock 2024
Borderless Access - Global B2B Panel book-unlock 2024Borderless Access - Global B2B Panel book-unlock 2024
Borderless Access - Global B2B Panel book-unlock 2024
 
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John MeulemansBCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
BCE24 | Virtual Brand Ambassadors: Making Brands Personal - John Meulemans
 
NewBase 25 March 2024 Energy News issue - 1710 by Khaled Al Awadi_compress...
NewBase  25 March  2024  Energy News issue - 1710 by Khaled Al Awadi_compress...NewBase  25 March  2024  Energy News issue - 1710 by Khaled Al Awadi_compress...
NewBase 25 March 2024 Energy News issue - 1710 by Khaled Al Awadi_compress...
 
Developing Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursDeveloping Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, Ours
 
7movierulz.uk
7movierulz.uk7movierulz.uk
7movierulz.uk
 
PDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdfPDT 88 - 4 million seed - Seed - Protecto.pdf
PDT 88 - 4 million seed - Seed - Protecto.pdf
 
Michael Vidyakin: Introduction to PMO (UA)
Michael Vidyakin: Introduction to PMO (UA)Michael Vidyakin: Introduction to PMO (UA)
Michael Vidyakin: Introduction to PMO (UA)
 
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
 
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
 
Cracking the ‘Business Process Outsourcing’ Code Main.pptx
Cracking the ‘Business Process Outsourcing’ Code Main.pptxCracking the ‘Business Process Outsourcing’ Code Main.pptx
Cracking the ‘Business Process Outsourcing’ Code Main.pptx
 
MoneyBridge Pitch Deck - Investor Presentation
MoneyBridge Pitch Deck - Investor PresentationMoneyBridge Pitch Deck - Investor Presentation
MoneyBridge Pitch Deck - Investor Presentation
 
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfGraham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
 

Parametric tests

  • 2. STATISTICAL TEST • Statistical tests are intended to decide whether a hypothesis about distribution of one or more populations or samples should be rejected or accepted. Statistical Tests Parametric tests Non – Parametric tests
  • 3. PARAMETRIC TESTS Parametric test is a statistical test that makes assumptions about the parameters of the population distribution(s) from which one’s data is drawn.
  • 4. APPLICATIONS • Used for Quantitative data. • Used for continuous variables. • Used when data are measured on approximate interval or ratio scales of measurement. • Data should follow normal distribution.
  • 5. PARAMETRIC TESTS 1. t-test t-test t-test for one sample t-test for two samples Unpaired two sample t-test Paired two sample t-test
  • 6. Contd.. 2. ANOVA 3. Pearson’s r correlation 4. Z test ANOVA One way ANOVA Two way ANOVA
  • 7. STUDENT’S T-TEST • Developed by Prof.W.S.Gossett • A t-test compares the difference between two means of different groups to determine whether the difference is statistically significant.
  • 8. One Sample t-test Assumptions: • Population is normally distributed • Sample is drawn from the population and it should be random • We should know the population mean Conditions: • Population standard deviation is not known • Size of the sample is small (<30)
  • 9. Contd.. • In one sample t-test , we know the population mean. • We draw a random sample from the population and then compare the sample mean with the population mean and make a statistical decision as to whether or not the sample mean is different from the population.
  • 10. Let x1, x2, …….,xn be a random sample of size “n” has drawn from a normal population with mean (µ) and variance 𝜎2. Null hypothesis (H0): Population mean (μ) is equal to a specified value µ0. Under H0, the test statistic is 𝒕 = 𝒙−µ 𝒔 𝒏
  • 11. Two sample t-test • Used when the two independent random samples come from the normal populations having unknown or same variance. • We test the null hypothesis that the two population means are same i.e., µ1 = µ2
  • 12. Contd… Assumptions: 1. Populations are distributed normally 2. Samples are drawn independently and at random Conditions: 1. Standard deviations in the populations are same and not known 2. Size of the sample is small
  • 13. If two independent samples xi ( i = 1,2,….,n1) and yj ( j = 1,2, …..,n2) of sizes n1and n2 have been drawn from two normal populations with means µ1 and µ2 respectively. Null hypothesis H0 : µ1 = µ2 Under H0, the test statistic is 𝒕 = ǀ 𝒙 − 𝒚ǀ 𝑺 𝟏 𝒏 𝟏 + 𝟏 𝒏 𝟐
  • 14. Paired t-test Used when measurements are taken from the same subject before and after some manipulation or treatment. Ex: To determine the significance of a difference in blood pressure before and after administration of an experimental pressure substance.
  • 15. Assumptions: 1. Populations are distributed normally 2. Samples are drawn independently and at random Conditions: 1. Samples are related with each other 2. Sizes of the samples are small and equal 3. Standard deviations in the populations are equal and not known
  • 16. Null Hypothesis: H0: µd = 0 Under H0, the test statistic 𝒕 = ǀ𝒅̅ǀ 𝒔 𝒏 Where, d = difference between x1 and x2 d̅ = Average of d s = Standard deviation n = Sample size
  • 17. Z-Test • Z-test is a statistical test where normal distribution is applied and is basically used for dealing with problems relating to large samples when the frequency is greater than or equal to 30. • It is used when population standard deviation is known.
  • 18. Contd… Assumptions: • Population is normally distributed • The sample is drawn at random Conditions: • Population standard deviation σ is known • Size of the sample is large (say n > 30)
  • 19. Let x1, x2, ………x,n be a random sample size of n from a normal population with mean µ and variance σ2 . Let x̅ be the sample mean of sample of size “n” Null Hypothesis: Population mean (µ) is equal to a specified value µο H0: µ = µο
  • 20. Under Hο, the test statistic is 𝒁 = ǀ 𝒙 − µ 𝝄ǀ 𝒔 𝒏 If the calculated value of Z < table value of Z at 5% level of significance, H0 is accepted and hence we conclude that there is no significant difference between the population mean and the one specified in H0 as µο.
  • 21. Pearson’s ‘r’ Correlation • Correlation is a technique for investigating the relationship between two quantitative, continuous variables. • Pearson’s Correlation Coefficient (r) is a measure of the strength of the association between the two variables
  • 22. Types of correlation Type of correlation Correlation coefficient Perfect positive correlation r = +1 Partial positive correlation 0 < r < +1 No correlation r = 0 Partial negative correlation 0 > r > -1 Perfect negative correlation r = -1
  • 23. ANOVA (Analysis of Variance) • Analysis of Variance (ANOVA) is a collection of statistical models used to analyse the differences between group means or variances. • Compares multiple groups at one time • Developed by R.A.Fischer
  • 25. One way ANOVA Compares two or more unmatched groups when data are categorized in one factor Ex: 1. Comparing a control group with three different doses of aspirin 2. Comparing the productivity of three or more employees based on working hours in a company
  • 26. Two way ANOVA • Used to determine the effect of two nominal predictor variables on a continuous outcome variable. • It analyses the effect of the independent variables on the expected outcome along with their relationship to the outcome itself. Ex: Comparing the employee productivity based on the working hours and working conditions.
  • 27. Assumptions of ANOVA: • The samples are independent and selected randomly. • Parent population from which samples are taken is of normal distribution. • Various treatment and environmental effects are additive in nature. • The experimental errors are distributed normally with mean zero and variance σ2.
  • 28. • ANOVA compares variance by means of F-ratio F = 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑤𝑖𝑡ℎ𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 • It again depends on experimental designs Null hypothesis: Hο = All population means are same • If the computed Fc is greater than F critical value, we are likely to reject the null hypothesis. • If the computed Fc is lesser than the F critical value , then the null hypothesis is accepted.
  • 29. ANOVA Table Sources of Variation Sum of squares (SS) Degrees of freedom (d.f) Mean squares (MS) 𝒔𝒖𝒎 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆𝒔 𝒅̅𝒆𝒈𝒓𝒆𝒆𝒔 𝒐𝒇 𝒇𝒓𝒆𝒆𝒅̅𝒐𝒎 F - Ratio Between samples or groups (Treatments) Treatment sum of squares ( TrSS) (k-1) 𝑇𝑟𝑆𝑆 (𝑘 − 1) 𝑇𝑟𝑀𝑆 𝐸𝑀𝑆 Within samples or groups ( Errors ) Error sum of squares (ESS) (n-k) 𝐸𝑆𝑆 (𝑛 − 𝑘) Total Total sum of squares (TSS) (n-1)
  • 30. S.No Type of group Parametric test 1. Comparison of two paired groups Paired t-test 2. Comparison of two unpaired groups Unpaired two sample t-test 3. Comparison of population and sample drawn from the same population One sample t-test 4. Comparison of three or more matched groups but varied in two factors Two way ANOVA 5. Comparison of three or more matched groups but varied in one factor One way ANOVA 6. Correlation between two variables Pearson Correlation

Notas do Editor

  1. One sample t-test is a statistical procedure that is used to know the population mean and the known value of the population mean. In one sample t-test, we know the population mean. We draw a random sample from the population and then compare the sample mean with population mean and make a statistical decision as to whether or not the sample mean is different from the population mean. In one sample t-test, sample size should be less than 30.
  2. Now we compare calculated value with table value at certain level of significance ( generally at 5% ). If absolute value of ‘t’ obtained is greater than table value then reject the null hypothesis and if it is less than table value , the null hypothesis may be accepted.