SlideShare uma empresa Scribd logo
1 de 56
Baixar para ler offline
Hazilah Mohd Amin Analysis of Variance (ANOVA)
Goals ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
Key Fact  F distribuition curve:
Find Critical Value: Example  ,[object Object],Critical value:  F  , df numerator,df denominator   =  F  , 8,14  =  ?
Table 12.1  (p. 534) Critical value:  F  , 8,14   = 2.70
Hypotheses of One-Way ANOVA ,[object Object],[object Object],[object Object],[object Object],[object Object],The analysis of variance is a procedure that tests to determine whether differences exits between two or more population means .
One-Factor ANOVA  All Means are the same: The Null Hypothesis is True  (No Treatment Effect)
One-Factor ANOVA  At least one mean is different: The Null Hypothesis is NOT true  (Treatment Effect is present) or
One-Way Analysis of Variance
 
 
One-Factor ANOVA  F Test: Example 1 ,[object Object],[object Object],[object Object],Club 1   Club 2   Club 3 254   234   200 263   218   222 241   235   197 237   227   206 251   216   204
[object Object],[object Object],[object Object],[object Object],One   Way   A n a l y s i s   o f   V a r i a n c e
Defining the Hypotheses ,[object Object],[object Object],[object Object]
N o t a t i o n Independent samples are drawn from k populations (treatments). X 11 x 21 . . . X n1,1 X 12 x 22 . . . X n2,2 X 1k x 2k . . . X nk,k Sample size Sample mean X is the “response variable”. The variables’ value are called “responses”.
T e r m i n o l o g y ,[object Object],[object Object],[object Object]
The rationale of the name of   A n a l y s i s   o f   V a r i a n c e  ( A N O V A )  ,[object Object],[object Object]
One   Way   A n a l y s i s   o f   V a r i a n c e Graphical demonstration : Employing two types of variability:  Within Samples  and  Between Samples
Treatment 1 Treatment 2 Treatment 3 20 16 15 14 11 10 9 The sample means are the same as before, but the larger within-sample variability  makes it harder to draw a conclusion about the population means. A small variability within the samples makes it easier to draw a conclusion about the  population means.  20 25 30 1 7 Treatment 1 Treatment 2 Treatment 3 10 12 19 9
One-Factor ANOVA Example: Scatter Diagram • • • • • 270 260 250 240 230 220 210 200 190 • • • • • • • • • • Distance Club 1   Club 2   Club 3 254   234   200 263   218   222 241   235   197 237   227   206 251   216   204 Club 1  2  3 From scatter diagram, we can clearly see sample means difference because of small within-sample variability
Test Statistics (F), Critical Value & Rejection Criterion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],H 0 :  μ 1 =  μ 2  = …   =  μ   k H A : At least two population means are different The hypothesis test:
One-Factor ANOVA Example Computations Club 1   Club 2   Club 3 254   234   200 263   218   222 241   235   197 237   227   206 251   216   204 x 1  = 249.2 x 2  = 226.0 x 3  = 205.8 x = 227.0 n 1  = 5 n 2  = 5 n 3  = 5 n = 15 k = 3 MSB = 4716.4 / (3-1) = 2358.2 MSW = 1119.6 / (15-3) = 93.3 SSB =  4716.4 SSW =  1119.6
One-Factor ANOVA Example Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],F   = 25.275 Test Statistic:  Decision:  Test statistic F is greater than critical value Conclusion: Reject H 0  at    = 0.05 There is evidence that at least one  μ i   differs from the rest 0      = .05 F .05  = 3.885 Reject H 0 Do not  reject H 0 Critical Value:  F  , k-1,n-k   =  F  , 2,12  = 3.885
ANOVA Single Factor: Excel Output EXCEL:  tools | data analysis | ANOVA: single factor F  , k-1,n-k   =  F  , 2,12  = 3.885 SUMMARY Groups Count Sum Average Variance Club 1 5 1246 249.2 108.2 Club 2 5 1130 226 77.5 Club 3 5 1029 205.8 94.2 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 4716.4 2 2358.2 25.275 4.99E-05 3.885 Within  Groups 1119.6 12 93.3 Total 5836.0 14        
Rationale 1: Variability Between Sample   ,[object Object],[object Object],[object Object]
[object Object],[object Object],Rationale II: Variability Within
Interpreting One-Factor ANOVA  F Statistic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 2 ,[object Object],[object Object],[object Object],[object Object]
Notation Used in ANOVA Factor Levels Sample from Sample from Sample from Sample from Replication Level 1 Level 2 Level 3 Level  k n = 1 x 1,1 x 2,1 x 3,1 x k ,1 n = 2 x 1,2 x 2,2 x 3,2 x k ,2 n = 3 x 1,3 x 2,3 x 3,3 x k ,3 Column T 1 T 2 T 3 T k T Totals T = grand total = sum of all  x 's =   x =   T i . . . . . . . . .
Sample Results  1 x  2 x  3 x
Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Partition of Total Variation ,[object Object],[object Object],[object Object],[object Object],[object Object],Variation Due to Factor/Treatment (SSB) Variation Due to Random Sampling (SSW) Sum of Squares Total (SST) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],= + Total variation SST can be split into two parts: SST = SSB + SSW
 
 x and   x 2  Calculator:  Enter  x i  data, retrieve   x and   x 2 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Variation Sums of Squares
Mean Square The mean square for the factor being tested and for the error is obtained by dividing the sum-of-square value by the corresponding number of degrees of freedom Numerator degrees of freedom = df(factor) = k    1 = 3    1 = 2 df(total) =  n     1 = 19    1 = 18 Denominator degrees of freedom = df(error) =  n     k = 19    3 = 16 Calculations:
One-Way ANOVA Table Source of Variation df SS MS Between Samples SSB MSB = Within Samples n - k SSW MSW = Total n - 1 SST = SSB+SSW k - 1 MSB MSW F ratio SSB k - 1 SSW n - k F = ,[object Object],An  ANOVA table   is often used to record the sums of squares and to organize the rest of the calculations.  Format for the ANOVA Table:
The Completed ANOVA Table The Complete ANOVA Table: The Test Statistic:
Solution Continued The Results a. Decision:  Reject  H o   at    = 0.05 b. Conclusion : There is evidence to suggest the three population  means are not all the same.  The type of applicator has a significant effect on  the paint drying time at the 0.05 level of significance. Critical Value:  F  , k-1,n-k   =  F  , 2,16  = 3.63 The Test Statistic F = 4.27 is in the rejection region. Reject H 0 F .05  = 3.63 Do not  reject H 0    = .05
One-Way ANOVA F-Test: Exercise 1 ,[object Object],[object Object],[object Object],© 1984-1994 T/Maker Co. Answer: Critical Value = 4.07. Test statistic = 11.6
Hey!  Lets   get   our   hand  dirty …   Using   S P S S ….
One   Way   A n a l y s i s   o f   V a r i a n c e  U s i n g  S P S S ,[object Object],[object Object],[object Object]
One   Way   A n a l y s i s   o f   V a r i a n c e  U s i n g  S P S S ,[object Object],[object Object],[object Object]
After Clicking  Options …,  click off   Display  groups   defined by missing value , and click   Continue   then   OK . ,[object Object]
What is the Box-plot telling us? ,[object Object],[object Object],[object Object],[object Object]
One   Way   A n a l y s i s   o f   V a r i a n c e  U s i n g  S P S S ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Analyze>Descriptive Statistics>Explore ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Output has several parts, let focus on the tests of normality ,[object Object],[object Object]
One   Way   A n a l y s i s   o f   V a r i a n c e  U s i n g  S P S S ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
One   Way   A n a l y s i s   o f   V a r i a n c e  U s i n g  S P S S ,[object Object],[object Object],[object Object],[object Object]
Normality & Homogeneity of variances assumptions met … hence ,[object Object],[object Object],[object Object]
End of ANOVA See U Later…
One-Way ANOVA F-Test:  Exercise 1 Solution ,[object Object],[object Object],[object Object],© 1984-1994 T/Maker Co.
Summary Table  Solution* Source of Variation Degrees   of Freedom Sum of Squares Mean Square (Variance) F Treatment ( Methods ) 4 - 1 = 3 348 116 11.6 Error 12 - 4 = 8 80 10 Total 12 - 1 = 11 428
One-Way ANOVA F-Test  Solution* ,[object Object],[object Object],[object Object],[object Object],[object Object],F 0 4.07 Test Statistic:  Decision: Conclusion: Reject at    = .05 There Is Evidence Pop. Means Are Different    = .05 F MSB MSE    116 10 11 6 .

Mais conteúdo relacionado

Mais procurados (20)

Analysis of variance ppt @ bec doms
Analysis of variance ppt @ bec domsAnalysis of variance ppt @ bec doms
Analysis of variance ppt @ bec doms
 
Non parametric test
Non parametric testNon parametric test
Non parametric test
 
Chi – square test
Chi – square testChi – square test
Chi – square test
 
In Anova
In  AnovaIn  Anova
In Anova
 
Analysis of variance (ANOVA)
Analysis of variance (ANOVA)Analysis of variance (ANOVA)
Analysis of variance (ANOVA)
 
Analysis of variance (ANOVA)
Analysis of variance (ANOVA)Analysis of variance (ANOVA)
Analysis of variance (ANOVA)
 
Mann Whitney U Test And Chi Squared
Mann Whitney U Test And Chi SquaredMann Whitney U Test And Chi Squared
Mann Whitney U Test And Chi Squared
 
Regression analysis
Regression analysisRegression analysis
Regression analysis
 
One way anova
One way anovaOne way anova
One way anova
 
Analysis of variance (ANOVA) everything you need to know
Analysis of variance (ANOVA) everything you need to knowAnalysis of variance (ANOVA) everything you need to know
Analysis of variance (ANOVA) everything you need to know
 
Sample Size Determination
Sample Size DeterminationSample Size Determination
Sample Size Determination
 
T test statistics
T test statisticsT test statistics
T test statistics
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 
Non parametric test
Non parametric testNon parametric test
Non parametric test
 
Repeated Measures ANOVA
Repeated Measures ANOVARepeated Measures ANOVA
Repeated Measures ANOVA
 
Analysis of variance anova
Analysis of variance anovaAnalysis of variance anova
Analysis of variance anova
 
Chi squared test
Chi squared testChi squared test
Chi squared test
 
Degrees of freedom
Degrees of freedomDegrees of freedom
Degrees of freedom
 
Statistical inference: Statistical Power, ANOVA, and Post Hoc tests
Statistical inference: Statistical Power, ANOVA, and Post Hoc testsStatistical inference: Statistical Power, ANOVA, and Post Hoc tests
Statistical inference: Statistical Power, ANOVA, and Post Hoc tests
 
Kruskal-Wallis H test
Kruskal-Wallis H testKruskal-Wallis H test
Kruskal-Wallis H test
 

Destaque

9. basic concepts_of_one_way_analysis_of_variance_(anova)
9. basic concepts_of_one_way_analysis_of_variance_(anova)9. basic concepts_of_one_way_analysis_of_variance_(anova)
9. basic concepts_of_one_way_analysis_of_variance_(anova)Irfan Hussain
 
One Way Anova
One Way AnovaOne Way Anova
One Way Anovashoffma5
 
Contingency Table Test, M. Asad Hayat, UET Taxila
Contingency Table Test, M. Asad Hayat, UET TaxilaContingency Table Test, M. Asad Hayat, UET Taxila
Contingency Table Test, M. Asad Hayat, UET TaxilaMuhammad Warraich
 
metodologi penelitian
metodologi penelitianmetodologi penelitian
metodologi penelitianEDIS BLOG
 
Analisis varian (anava)
Analisis varian (anava)Analisis varian (anava)
Analisis varian (anava)Irfan Sidiq
 
PPT ANALISIS DATA SURVEI
PPT ANALISIS DATA SURVEIPPT ANALISIS DATA SURVEI
PPT ANALISIS DATA SURVEIDarliana Darwis
 
Anova single factor
Anova single factorAnova single factor
Anova single factorDhruv Patel
 
Imad Feneir - One way anova
Imad Feneir - One way anovaImad Feneir - One way anova
Imad Feneir - One way anovaImad Feneir
 
Imad Feneir - Two-way ANOVA - replication
Imad Feneir - Two-way ANOVA - replicationImad Feneir - Two-way ANOVA - replication
Imad Feneir - Two-way ANOVA - replicationImad Feneir
 
Biogeochemical cycles C, H2O, N, and O
Biogeochemical cycles C, H2O, N, and O Biogeochemical cycles C, H2O, N, and O
Biogeochemical cycles C, H2O, N, and O Stephanie Beck
 
One way anova final ppt.
One way anova final ppt.One way anova final ppt.
One way anova final ppt.Aadab Mushrib
 
Biogeochemical Cycles: Natural Cycles of Elements
Biogeochemical Cycles: Natural Cycles of ElementsBiogeochemical Cycles: Natural Cycles of Elements
Biogeochemical Cycles: Natural Cycles of ElementsMichael Payne
 
Extended case studies
Extended case studiesExtended case studies
Extended case studiesSapna2410
 
Falsification of data
Falsification of dataFalsification of data
Falsification of dataSapna2410
 

Destaque (19)

9. basic concepts_of_one_way_analysis_of_variance_(anova)
9. basic concepts_of_one_way_analysis_of_variance_(anova)9. basic concepts_of_one_way_analysis_of_variance_(anova)
9. basic concepts_of_one_way_analysis_of_variance_(anova)
 
One Way Anova
One Way AnovaOne Way Anova
One Way Anova
 
Contingency Table Test, M. Asad Hayat, UET Taxila
Contingency Table Test, M. Asad Hayat, UET TaxilaContingency Table Test, M. Asad Hayat, UET Taxila
Contingency Table Test, M. Asad Hayat, UET Taxila
 
Chapter 5 Anova2009
Chapter 5 Anova2009Chapter 5 Anova2009
Chapter 5 Anova2009
 
metodologi penelitian
metodologi penelitianmetodologi penelitian
metodologi penelitian
 
analisis varians
analisis varians analisis varians
analisis varians
 
Analisis varian (anava)
Analisis varian (anava)Analisis varian (anava)
Analisis varian (anava)
 
PPT ANALISIS DATA SURVEI
PPT ANALISIS DATA SURVEIPPT ANALISIS DATA SURVEI
PPT ANALISIS DATA SURVEI
 
T14 anova
T14 anovaT14 anova
T14 anova
 
Anova single factor
Anova single factorAnova single factor
Anova single factor
 
Imad Feneir - One way anova
Imad Feneir - One way anovaImad Feneir - One way anova
Imad Feneir - One way anova
 
Imad Feneir - Two-way ANOVA - replication
Imad Feneir - Two-way ANOVA - replicationImad Feneir - Two-way ANOVA - replication
Imad Feneir - Two-way ANOVA - replication
 
Anova (Statistics)
Anova (Statistics)Anova (Statistics)
Anova (Statistics)
 
Biogeochemical cycles C, H2O, N, and O
Biogeochemical cycles C, H2O, N, and O Biogeochemical cycles C, H2O, N, and O
Biogeochemical cycles C, H2O, N, and O
 
One way anova final ppt.
One way anova final ppt.One way anova final ppt.
One way anova final ppt.
 
Biogeochemical Cycles: Natural Cycles of Elements
Biogeochemical Cycles: Natural Cycles of ElementsBiogeochemical Cycles: Natural Cycles of Elements
Biogeochemical Cycles: Natural Cycles of Elements
 
Marsyas
MarsyasMarsyas
Marsyas
 
Extended case studies
Extended case studiesExtended case studies
Extended case studies
 
Falsification of data
Falsification of dataFalsification of data
Falsification of data
 

Semelhante a Anova by Hazilah Mohd Amin

Semelhante a Anova by Hazilah Mohd Amin (20)

test_using_one-way_analysis_of_varianceANOVA_063847.pptx
test_using_one-way_analysis_of_varianceANOVA_063847.pptxtest_using_one-way_analysis_of_varianceANOVA_063847.pptx
test_using_one-way_analysis_of_varianceANOVA_063847.pptx
 
ANOVA.ppt
ANOVA.pptANOVA.ppt
ANOVA.ppt
 
Ch7 Analysis of Variance (ANOVA)
Ch7 Analysis of Variance (ANOVA)Ch7 Analysis of Variance (ANOVA)
Ch7 Analysis of Variance (ANOVA)
 
10.Analysis of Variance.ppt
10.Analysis of Variance.ppt10.Analysis of Variance.ppt
10.Analysis of Variance.ppt
 
Experimental design data analysis
Experimental design data analysisExperimental design data analysis
Experimental design data analysis
 
Chapter15
Chapter15Chapter15
Chapter15
 
Descriptive Statistics Formula Sheet Sample Populatio.docx
Descriptive Statistics Formula Sheet    Sample Populatio.docxDescriptive Statistics Formula Sheet    Sample Populatio.docx
Descriptive Statistics Formula Sheet Sample Populatio.docx
 
Stat2013
Stat2013Stat2013
Stat2013
 
One-Way ANOVA
One-Way ANOVAOne-Way ANOVA
One-Way ANOVA
 
Notes7
Notes7Notes7
Notes7
 
ANOVA BIOstat short explaination .pptx
ANOVA BIOstat short explaination   .pptxANOVA BIOstat short explaination   .pptx
ANOVA BIOstat short explaination .pptx
 
Anova.ppt
Anova.pptAnova.ppt
Anova.ppt
 
Anova test
Anova testAnova test
Anova test
 
One-way ANOVA research paper
One-way ANOVA research paperOne-way ANOVA research paper
One-way ANOVA research paper
 
Anova (1)
Anova (1)Anova (1)
Anova (1)
 
Anova (1)
Anova (1)Anova (1)
Anova (1)
 
Anova; analysis of variance
Anova; analysis of varianceAnova; analysis of variance
Anova; analysis of variance
 
Anova n metaanalysis
Anova n metaanalysisAnova n metaanalysis
Anova n metaanalysis
 
Tugasan kumpulan anova
Tugasan kumpulan anovaTugasan kumpulan anova
Tugasan kumpulan anova
 
Quality Engineering material
Quality Engineering materialQuality Engineering material
Quality Engineering material
 

Último

How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17Celine George
 
Ultra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxUltra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxDr. Asif Anas
 
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxiammrhaywood
 
UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfTechSoup
 
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...Nguyen Thanh Tu Collection
 
In - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxIn - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxAditiChauhan701637
 
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfP4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfYu Kanazawa / Osaka University
 
How to Solve Singleton Error in the Odoo 17
How to Solve Singleton Error in the  Odoo 17How to Solve Singleton Error in the  Odoo 17
How to Solve Singleton Error in the Odoo 17Celine George
 
How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17Celine George
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxDr. Santhosh Kumar. N
 
Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.raviapr7
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice documentXsasf Sfdfasd
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesCeline George
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsEugene Lysak
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxheathfieldcps1
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxKatherine Villaluna
 
How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17Celine George
 
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptxClinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptxraviapr7
 

Último (20)

How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17
 
Ultra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxUltra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptx
 
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
 
UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
 
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
 
In - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxIn - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptx
 
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfP4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
 
How to Solve Singleton Error in the Odoo 17
How to Solve Singleton Error in the  Odoo 17How to Solve Singleton Error in the  Odoo 17
How to Solve Singleton Error in the Odoo 17
 
How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptx
 
Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice document
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 Sales
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George Wells
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptx
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptx
 
How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17
 
Prelims of Kant get Marx 2.0: a general politics quiz
Prelims of Kant get Marx 2.0: a general politics quizPrelims of Kant get Marx 2.0: a general politics quiz
Prelims of Kant get Marx 2.0: a general politics quiz
 
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptxClinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
 

Anova by Hazilah Mohd Amin

  • 1. Hazilah Mohd Amin Analysis of Variance (ANOVA)
  • 2.
  • 3.
  • 4. Key Fact F distribuition curve:
  • 5.
  • 6. Table 12.1 (p. 534) Critical value: F  , 8,14 = 2.70
  • 7.
  • 8. One-Factor ANOVA All Means are the same: The Null Hypothesis is True (No Treatment Effect)
  • 9. One-Factor ANOVA At least one mean is different: The Null Hypothesis is NOT true (Treatment Effect is present) or
  • 11.  
  • 12.  
  • 13.
  • 14.
  • 15.
  • 16. N o t a t i o n Independent samples are drawn from k populations (treatments). X 11 x 21 . . . X n1,1 X 12 x 22 . . . X n2,2 X 1k x 2k . . . X nk,k Sample size Sample mean X is the “response variable”. The variables’ value are called “responses”.
  • 17.
  • 18.
  • 19. One Way A n a l y s i s o f V a r i a n c e Graphical demonstration : Employing two types of variability: Within Samples and Between Samples
  • 20. Treatment 1 Treatment 2 Treatment 3 20 16 15 14 11 10 9 The sample means are the same as before, but the larger within-sample variability makes it harder to draw a conclusion about the population means. A small variability within the samples makes it easier to draw a conclusion about the population means. 20 25 30 1 7 Treatment 1 Treatment 2 Treatment 3 10 12 19 9
  • 21. One-Factor ANOVA Example: Scatter Diagram • • • • • 270 260 250 240 230 220 210 200 190 • • • • • • • • • • Distance Club 1 Club 2 Club 3 254 234 200 263 218 222 241 235 197 237 227 206 251 216 204 Club 1 2 3 From scatter diagram, we can clearly see sample means difference because of small within-sample variability
  • 22.
  • 23. One-Factor ANOVA Example Computations Club 1 Club 2 Club 3 254 234 200 263 218 222 241 235 197 237 227 206 251 216 204 x 1 = 249.2 x 2 = 226.0 x 3 = 205.8 x = 227.0 n 1 = 5 n 2 = 5 n 3 = 5 n = 15 k = 3 MSB = 4716.4 / (3-1) = 2358.2 MSW = 1119.6 / (15-3) = 93.3 SSB = 4716.4 SSW = 1119.6
  • 24.
  • 25. ANOVA Single Factor: Excel Output EXCEL: tools | data analysis | ANOVA: single factor F  , k-1,n-k = F  , 2,12 = 3.885 SUMMARY Groups Count Sum Average Variance Club 1 5 1246 249.2 108.2 Club 2 5 1130 226 77.5 Club 3 5 1029 205.8 94.2 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 4716.4 2 2358.2 25.275 4.99E-05 3.885 Within Groups 1119.6 12 93.3 Total 5836.0 14        
  • 26.
  • 27.
  • 28.
  • 29.
  • 30. Notation Used in ANOVA Factor Levels Sample from Sample from Sample from Sample from Replication Level 1 Level 2 Level 3 Level k n = 1 x 1,1 x 2,1 x 3,1 x k ,1 n = 2 x 1,2 x 2,2 x 3,2 x k ,2 n = 3 x 1,3 x 2,3 x 3,3 x k ,3 Column T 1 T 2 T 3 T k T Totals T = grand total = sum of all x 's =  x =  T i . . . . . . . . .
  • 31. Sample Results  1 x  2 x  3 x
  • 32.
  • 33.
  • 34.  
  • 35.
  • 36. Variation Sums of Squares
  • 37. Mean Square The mean square for the factor being tested and for the error is obtained by dividing the sum-of-square value by the corresponding number of degrees of freedom Numerator degrees of freedom = df(factor) = k  1 = 3  1 = 2 df(total) = n  1 = 19  1 = 18 Denominator degrees of freedom = df(error) = n  k = 19  3 = 16 Calculations:
  • 38.
  • 39. The Completed ANOVA Table The Complete ANOVA Table: The Test Statistic:
  • 40. Solution Continued The Results a. Decision: Reject H o at  = 0.05 b. Conclusion : There is evidence to suggest the three population means are not all the same. The type of applicator has a significant effect on the paint drying time at the 0.05 level of significance. Critical Value: F  , k-1,n-k = F  , 2,16 = 3.63 The Test Statistic F = 4.27 is in the rejection region. Reject H 0 F .05 = 3.63 Do not reject H 0  = .05
  • 41.
  • 42. Hey! Lets get our hand dirty … Using S P S S ….
  • 43.
  • 44.
  • 45.
  • 46.
  • 47.
  • 48.
  • 49.
  • 50.
  • 51.
  • 52.
  • 53. End of ANOVA See U Later…
  • 54.
  • 55. Summary Table Solution* Source of Variation Degrees of Freedom Sum of Squares Mean Square (Variance) F Treatment ( Methods ) 4 - 1 = 3 348 116 11.6 Error 12 - 4 = 8 80 10 Total 12 - 1 = 11 428
  • 56.

Notas do Editor

  1. Change to page 800
  2. Change to page 803
  3. Change to page 803
  4. Delete slide and insert procedure 16.1 (steps 1-4) from page 813
  5. Delete slide and insert procedure 16.1 (steps 5-7 critical value approach) from page 813
  6. Change to page 803
  7. You assign randomly 3 people to each method, making sure that they are similar in intelligence etc.
  8. You assign randomly 3 people to each method, making sure that they are similar in intelligence etc.