Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

612 views

566 views

566 views

Published on

Published in:
Education

No Downloads

Total views

612

On SlideShare

0

From Embeds

0

Number of Embeds

2

Shares

0

Downloads

27

Comments

0

Likes

2

No embeds

No notes for slide

- 1. Republic of the PhilippinesMINDANAO STATE UNIVERSITYGeneral Santos City<br />GRADUATE PROGRAM<br />FACTORIAL ANALYSIS OF VARIANCE<br />A class report to the class of Dr. Ava Clare Marie O. Robles<br />Presented by:<br />Chellyn Mae P. Dalut<br /> MST Elementary Math<br />
- 2. LearningObjectives: At the end of this session, students are expected to:<br />
- 3. What is Factorial Analysis of Variance?<br />
- 4. What is Factorial Analysis of Variance?<br />
- 5. Two-way ANOVA/F-Test Two Factor/ANOVA Two-Factor<br />
- 6. Examples:<br />A study on of Effects of Method and class size on Achievement <br />Accebility of luncheon Meat from Commercial, Milkfish Bone Meal, and Goatfish Bone Meal<br />20 x 3=60 Luncheon Meat<br />2x2=4 Method<br />
- 7. Assumptions<br /> (www.statford.com)<br />
- 8. Steps in using Two-Way ANOVA<br />Consider the following when answering A RESEARCH PROBLEM:<br />
- 9. Steps in using Two-Way ANOVA<br />
- 10. Steps in using Two-Way ANOVA<br />
- 11. Illustration/Application:<br />Statement of the problem:<br />The researcher wishes to conduct a study on the flavor acceptability of luncheon meat from commercial, milk fish bone meal and goat fish bone meal (Hence: experimental groups)<br />Specific Research Problem: “ Is there a significant difference on the flavor acceptability of luncheon meat from commercial, milkfish bone meal, and goat fishbone meal?”<br />Null Hypothesis:<br />There is no significant difference on the flavor acceptability of luncheon meat from commercial, milkfish bone meal, and goatfish bone meal.<br />Ho: X = X2 = X3 =0 <br />Statistical tool: Two-way ANOVA<br />Significance Level: Alpha= 0.01<br />Sampling Distribution : N=20<br />
- 12. Rejection Region:<br />The null hypothesis is rejected if the computed F-value is equal to or greater that the tabular F-value.<br />Fcomputed>Ftabular<br />Computation:<br />Please refer to your excel exercises. (Slide 9 & 10)<br /> Lets do step 1 & 2<br />Illustration/Application:<br />
- 13.
- 14. Step No. 3<br />Illustration/Application:<br />Given: CF= (∑x)2 = (460)2<br />∑x2 = 71082 3N 60<br />P = 20 CF=3526.66667<br />Compute the Sum of Squares for Samples (SSs)<br />SSs=∑x2-CF<br /> P<br />Where:<br />SSS- Sum of Squares for Samples<br />∑x2 - Summation of X<br />P or N- Panelist or (N) (Subject)<br />CF - Correction Factor CF= ∑x<br /> N<br />SSs=∑x2-CF<br /> P<br />SSs=71082- 3526.66667 <br /> 20<br />SSs= 3554.1-3526.66667<br />SSs= 27.43333<br />
- 15. Given: CF= (∑x)2 = (460)2<br />∑y2 = 10624 3N 60<br />S = 3 CF=3526.66667<br />Step No. 4<br />Illustration/Application:<br />Compute the Sum of Squares for Panelist (SSp)<br />SSp=∑y2-CF<br /> S<br />Where:<br />SSp== Sum of squares for panelist<br /> ∑y2 = Sum of squared total for treatment<br /> CF = Correction Factor<br /> S = Sample (number of experimental group<br />SSP=∑y2-CF<br /> s<br />SSP =10624- 3526.66667 <br /> 3<br />SSP = 3541.33333-3526.66667<br />SSp= 14.66667<br />
- 16. Illustration/Application:<br />Given: CF= (∑x)2 = (460)2<br />∑∑ij2= 3574 3N 60<br />CF = 3526.66667<br /> Step No. 5<br />Compute the Sum of Squares for Total (SST)<br />SST= ∑∑ij2- CF<br />Where:<br />SST = Sum of squares for total<br /> ∑∑ij2= Grand sum of each observation per treatment<br /> CF = Correction factor<br />SST= ∑∑ij2- CF<br />SST = 3574 - 3526.66667<br />SST = 47.3333<br />
- 17. Illustration/Application:<br />Given: <br />SST = 47.3333 SSp= 14.66667<br />SSs= 27.43333<br /> Step No. 6<br />Compute the Sum of Square for Errors (SSE)<br />SSE=SST-(SSs+SSp)<br />Where:<br />SSE = Sum of squares for Errors<br /> SST = Sum of squares for total<br />SSp= Sum of squares for panelist<br />SSE=SST-(SSs+SSp)<br />SSE = 47.3333 – (27.43333 + 14.66667)<br />SSE = 47.3333 – 42.1<br />SSE = 5.23333<br />
- 18. Illustration/Application:<br />Given: <br />Ns= 3<br /> NP=20<br /> NT = 60<br /> Step No. 7<br />Get the degrees of freedom of:<br />(dfs= N-1) and (dfP= N-1) and<br />(dfT= N-1) and dfE= dfT- (dfS + dfP)<br />Where:<br />dfE=degrees of freedom of error <br />dfs= degrees of freedom of samples<br />dfP= degrees of freedom of panelist<br />dfT= degrees of freedom of total<br />Ns = Number of samples<br /> NP = Number of panelist<br /> NT= Number of Total (P x N) <br />dfs= Ns-1 dfT = NT -1<br /> = 3-1 = 60-1<br />= 2= 59<br />dfP= NP-1 dfE=dfT- (dfS + dfP)<br /> = 20-1 =59-(2+19)<br />= 19 dfE=38<br />
- 19. Illustration/Application:<br />Given: <br />SSS= 27.43333 SSE= 5.23333<br />SSp =14.66667<br />dfs = 2 ; dfP=19; dfE= 38 <br /> Step No. 8 & 9<br />MSS = SSS (MSE)= SSE<br />dfsdfE<br />= 27.43333 = 5.23333<br /> 2 38 <br />=13.71667 = 0.137719<br /> (MSp)=SSp<br />dfp<br />=14.66667<br /> 19<br />=0.77193<br />Compute the Mean Square (MS) Computation and the Mean square of error <br />(MSS)= SSS and (MSp)=SSp and (MSE)= SSE<br />dfsdfpdfE<br />Where:<br /> MSS = Mean of Square for sample<br />MSp =Mean of Square for panelist<br /> SSS = Sum of square for samples<br />SSp = Sum of square for panelist<br />dfs= degrees of freedom of samples<br />dfP= degrees of freedom of panelist<br /> SSE = Sum of squares for error<br />dfE = Degrees of freedom of error<br />
- 20. Illustration/Application:<br />Given: <br />MSS= 13.71667 MSE=0.137719<br />MSp =0.77193<br /> Step No. 10<br />Observe F Computation<br />Fs = MSS and Fp = MSP<br />MSEMSE<br />Where<br />Fp= F-computation for panelist<br /> Fs = F-computation for samples<br /> MSS = Mean of Square for sample<br />MSp =Mean of Square for panelist<br /> MSE = Sum of squares for error<br />dfE = Degrees of freedom of error<br />FS = MSS Fp = MSP<br />MSE MSE<br />= 13.71667= 0.77193<br />0.1377190.137719<br />=99.59873 =5.605096<br />(Significant @ level 0.01) (Significant @ level 0.01)<br />
- 21. Illustration/Application:<br />Remember of our Rejection Region-<br />Fcomputed>Ftabular<br /> Interpretation:<br />The computed F-value obtained for samples is 99.59873 which is greater than the tabular F-value for samples of 5.21 which is significant at 0.01 level of significance with df=2,38.<br />For panelist, the computed F-value obtained is 5.605096<br />also greater than the tabular F-value of 2.42 and is also significant at .01 level of confidence with df = 19,38.<br />This means that the samples and evaluation of the panelist really differ with each other because milkfish bone meal luncheon meat is most acceptable. Hence, the null hypothesis is rejected.<br />There is significant difference on the flavor acceptability of luncheon meat, and goatfish bone meal.<br />FS = MSS Fp = MSP<br />MSE MSE<br />= 13.71667= 0.77193<br />0.1377190.137719<br />=99.59873 =5.605096<br />(Significant @ level 0.01) (Significant @ level 0.01)<br /> Tabular FS = Tabular Fp =<br />df2,38 (0.01) = 5.21 df19,38 (0.01) = 5.605096<br /> (Hence: Please see tabular value of F on your copy)<br />
- 22. Illustration/Application:<br />Remember of our Rejection Region-<br />Fcomputed>Ftabular<br /> Interpretation:<br />The computed F-value obtained for samples is 99.59873 which is greater than the tabular F-value for samples of 5.21 which is significant at 0.01 level of significance with df=2,38.<br />For panelist, the computed F-value obtained is 5.605096<br />also greater than the tabular F-value of 2.42 and is also significant at .01 level of confidence with df = 19,38.<br />This means that the samples and evaluation of the panelist really differ with each other because milkfish bone meal luncheon meat is most acceptable. Hence, the null hypothesis is rejected.<br />There is significant difference on the flavor acceptability of luncheon meat, and goatfish bone meal.<br />
- 23. Illustration/Application:<br />Use the data that I gave for solving this, refer to your excel file.<br /> Using computer:<br />
- 24. The computer displays as follows:<br />
- 25. What is Friedman Two-Way Analysis of Variance by ranks (xr2)?<br />
- 26. What is Factorial Analysis of Variance?<br />
- 27. To substitute formula, the steps are as follows:<br />
- 28. Illustration/Application:<br />Statementof the problem:<br />The researcher wishes to conduct a study on the adequacy of facilities at the Northern Ilo-Ilo Polytechnic<br /> State College as perceived by top managers, middle managers, lower managers, and professors. <br />Specific Research Problem: “ Is there a significant difference on the adequacy of facilities at the Northern Ilo-Ilo Polytechnic State College as perceived by top managers, middle managers, lower managers, and professors?”<br />Null Hypothesis:<br />There is no significant difference on the on the adequacy of facilities at the Northern Ilo-Ilo Polytechnic State College as perceived by top managers, middle managers, lower managers, and professors.<br />Ho : X = X2 = X3 =X4=0 <br />Statistical tool: Friedman Two-way ANOVA by ranks<br />Significance Level: Alpha= 0.01<br />Sampling Distribution : K= 4 N=20<br />
- 29. Rejection Region:<br />The null hypothesis is rejected if the computed Friedman (XR2) value is equal to or greater that the tabular F-value. (Refer to the chi-square (X2) <br />(XR2) compute>(X2) tabular<br />Computation:<br />Please refer to your excel exercises. (Slide 26)<br />Lets do step 1 & 2<br />Illustration/Application:<br />
- 30.
- 31. Illustration/Application:<br />Scale :<br />-very much adequate<br />-adequate<br />-fairly adequate<br />1 -Inadequate<br />Friedman (XR2) Test Computation<br />Xr2= 12 ∑(R) 2 – 3N (K +1) <br /> NK (K+1)<br />=12 (10272.5 ) - 3(20) (4+1)<br /> 20(40) (4+1)<br /> = 0.03 (10272.5) – 300<br /> =308.175-300<br />Xr2 = 8.75 (insignificant at 0.01 level)<br />Degrees of freedom tabular value<br />df = K-1 df3(0.01)= 11.34<br />Df = 4-1<br />Df = 3<br />Given:<br /> ∑(R) 2 =102722.5<br /> N =20<br /> K =4<br />Where:<br /> Xr2 = Friedman 2-way ANOVA by rank<br /> N =Number of rows<br /> K =Number of columns<br />
- 32. Illustration/Application:<br />Remember of our Rejection Region-<br /> (XR2) compute> (X2) tabular<br /> Interpretation:<br />The computed Friedman test XR2 value obtained of 8.175 is insignificant because it is lesser than the tabular value of 11.34 with df = 3 at 0.01 level of confidence. This means that the adequacy of facilities at the Northern Ilo-Ilo Polytechnic State College as perceived by top managers, middle managers, lower managers, and professors are almost the same.<br />ACCEPTANCE OF NULL HYPOTHESIS:<br />The null hypothesis is accepted because there is no significant difference on the adequacy of facilities at the Northern Ilo-Ilo Polytechnic State College as perceived<br /> by top managers, middle managers, lower managers and professor.<br />Xr2 = 8.75 (insignificant at 0.01 level)<br />Degrees of freedom Tabular value<br />df = K-1 df3(0.01)= 11.34<br />Df = 4-1<br />Df = 3<br /> (Hence: Please see critical values of Chi-square)<br />
- 33. References:<br />Online Resources:<br />Books :<br />www. statford.com<br />www.psych.nyu.edu<br />www.mathworks.com<br />www.statsoft.com<br />Calmorin, Laurentina Paler (2010). Reaserch and Statistics with computer. National BookStore, Mandaluyong City, Metro Manila<br />Fraenkel, J and Nancy Wallen (2007). How to Design and Evaluate Research in Education,3rd Edition, McGraw Hills Companies, Inc. New York<br />Robles, Ava Clare Marie (2011).Parametric Statistics Made Easy using MS Excel (2011). MECS Publishing House, Inc.,LeonLlido St., General Santos City<br />

No public clipboards found for this slide

Be the first to comment