Specific Comparisons This is the same basic formula The only difference is that you are now performing comps on different IVs so it is important to keep.

Slides:



Advertisements
Similar presentations
Multiple-choice question
Advertisements

Mixed Designs: Between and Within Psy 420 Ainsworth.
Analysis of Variance (ANOVA)
FACTORIAL ANOVA Overview of Factorial ANOVA Factorial Designs Types of Effects Assumptions Analyzing the Variance Regression Equation Fixed and Random.
FACTORIAL ANOVA. Overview of Factorial ANOVA Factorial Designs Types of Effects Assumptions Analyzing the Variance Regression Equation Fixed and Random.
Sample Size Power and other methods. Non-central Chisquare.
PSY 307 – Statistics for the Behavioral Sciences
One-Way ANOVA Multiple Comparisons.
1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour.
Two Factor ANOVA.
FACTORIAL ANOVA.
2 n Factorial Experiment 4 Factor used to Remove Chemical Oxygen demand from Distillery Spent Wash R.K. Prasad and S.N. Srivastava (2009). “Electrochemical.
Analysis – Regression The ANOVA through regression approach is still the same, but expanded to include all IVs and the interaction The number of orthogonal.
PSY 307 – Statistics for the Behavioral Sciences
Fractional factorial Chapter 8 Hand outs. Initial Problem analysis Eyeball, statistics, few graphs Note what problems are and what direction would be.
One-way Between Groups Analysis of Variance
Intro to Statistics for the Behavioral Sciences PSYC 1900
Factorial Designs More than one Independent Variable: Each IV is referred to as a Factor All Levels of Each IV represented in the Other IV.
Intro to Statistics for the Behavioral Sciences PSYC 1900 Lecture 14: Factorial ANOVA.
Introduction to Analysis of Variance (ANOVA)
Analysis of Variance Introduction The Analysis of Variance is abbreviated as ANOVA The Analysis of Variance is abbreviated as ANOVA Used for hypothesis.
Factorial Within Subjects Psy 420 Ainsworth. Factorial WS Designs Analysis Factorial – deviation and computational Power, relative efficiency and sample.
1 Two Factor ANOVA Greg C Elvers. 2 Factorial Designs Often researchers want to study the effects of two or more independent variables at the same time.
If = 10 and = 0.05 per experiment = 0.5 Type I Error Rates I.Per Comparison II.Per Experiment (frequency) = error rate of any comparison = # of comparisons.
Statistics for the Social Sciences Psychology 340 Fall 2013 Thursday, November 21 Review for Exam #4.
ANOVA Chapter 12.
Factorial Experiments
Statistical Techniques I EXST7005 Factorial Treatments & Interactions.
ANOVA Greg C Elvers.
Dr. Gary Blau, Sean HanMonday, Aug 13, 2007 Statistical Design of Experiments SECTION V SCREENING.
Analysis of Variance (Two Factors). Two Factor Analysis of Variance Main effect The effect of a single factor when any other factor is ignored. Example.
© Copyright McGraw-Hill CHAPTER 12 Analysis of Variance (ANOVA)
PSY 307 – Statistics for the Behavioral Sciences Chapter 16 – One-Factor Analysis of Variance (ANOVA)
Chapter 11 Multifactor Analysis of Variance.
Orthogonal Linear Contrasts This is a technique for partitioning ANOVA sum of squares into individual degrees of freedom.
Between-Groups ANOVA Chapter 12. >When to use an F distribution Working with more than two samples >ANOVA Used with two or more nominal independent variables.
Orthogonal Linear Contrasts
Running Scheffe’s Multiple Comparison Test in Excel
Multivariate Analysis. One-way ANOVA Tests the difference in the means of 2 or more nominal groups Tests the difference in the means of 2 or more nominal.
Two-Way Balanced Independent Samples ANOVA Computations.
Chapter 10: Analyzing Experimental Data Inferential statistics are used to determine whether the independent variable had an effect on the dependent variance.
Chapter 19 Analysis of Variance (ANOVA). ANOVA How to test a null hypothesis that the means of more than two populations are equal. H 0 :  1 =  2 =
Psych 5500/6500 Other ANOVA’s Fall, Factorial Designs Factorial Designs have one dependent variable and more than one independent variable (i.e.
IE341 Midterm. 1. The effects of a 2 x 2 fixed effects factorial design are: A effect = 20 B effect = 10 AB effect = 16 = 35 (a) Write the fitted regression.
1 Blocking & Confounding in the 2 k Factorial Design Text reference, Chapter 7 Blocking is a technique for dealing with controllable nuisance variables.
Orthogonal Linear Contrasts This is a technique for partitioning ANOVA sum of squares into individual degrees of freedom.
1 Orthogonality One way to delve further into the impact a factor has on the yield is to break the Sum of Squares (SSQ) into “orthogonal” components. If.
Psy 230 Jeopardy Related Samples t-test ANOVA shorthand ANOVA concepts Post hoc testsSurprise $100 $200$200 $300 $500 $400 $300 $400 $300 $400 $500 $400.
Research Methods and Data Analysis in Psychology Spring 2015 Kyle Stephenson.
Chapter 4 Analysis of Variance
Smith/Davis (c) 2005 Prentice Hall Chapter Fifteen Inferential Tests of Significance III: Analyzing and Interpreting Experiments with Multiple Independent.
Statistics for Political Science Levin and Fox Chapter Seven
1 Example: Groupings on 3-Variable K-Maps BC F(A,B,C) = A ’ B ’ A BC F(A,B,C) = B ’ A
Introduction to ANOVA Research Designs for ANOVAs Type I Error and Multiple Hypothesis Tests The Logic of ANOVA ANOVA vocabulary, notation, and formulas.
Topic 22: Inference. Outline Review One-way ANOVA Inference for means Differences in cell means Contrasts.
1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay Blocking a Replicated Design Consider the example from Section 6-2; k = 2 factors, n = 3 replicates.
Designs for Experiments with More Than One Factor When the experimenter is interested in the effect of multiple factors on a response a factorial design.
Stats/Methods II JEOPARDY. Jeopardy Estimation ANOVA shorthand ANOVA concepts Post hoc testsSurprise $100 $200$200 $300 $500 $400 $300 $400 $300 $400.
Factorial BG ANOVA Psy 420 Ainsworth. Topics in Factorial Designs Factorial? Crossing and Nesting Assumptions Analysis Traditional and Regression Approaches.
Between-Groups ANOVA Chapter 12. Quick Test Reminder >One person = Z score >One sample with population standard deviation = Z test >One sample no population.
Test the Main effect of A Not sign Sign. Conduct Planned comparisons One-way between-subjects designs Report that the main effect of A was not significant.
Factorial ANOVA 11/15. Multiple Independent Variables Simple ANOVA tells whether groups differ – Compares levels of a single independent variable Sometimes.
ANOVA: Analysis of Variation
ANOVA: Analysis of Variation
Statistics for the Social Sciences
تصنيف التفاعلات الكيميائية
Design and Analysis of Multi-Factored Experiments
Fractional Factorial Design
Design matrix Run A B C D E
Graziano and Raulin Research Methods: Chapter 12
Presentation transcript:

Specific Comparisons This is the same basic formula The only difference is that you are now performing comps on different IVs so it is important to keep track of the number of subjects in each group of the comp

Specific Comparisons If a main effect is significant than you need to do marginal comparisons If you performed ANOVA through regression than just use the codes for each sub test of each IV

Specific Comparisons If one IV is significant (A), the others are not (B), but the interaction is significant You should break the interaction down by performing a simple effect analysis of A at each level of B (The effect of A at B1, A at B2, A at B3, etc.) If any of them are significant and if A has more than 2 levels, follow up with simple contrasts

Specific Comparisons If everything is significant: If the interaction is significant than you need to perform interaction contrasts If you performed ANOVA through regression than just use the codes for each sub test for the interactions

Specific Comparisons

If the comparisons were planned than analyze them without any adjustment to the critical value If they were post-hoc than the F-critical value needs to be adjusted (e.g. Scheffe, Tukey, etc.) This is the same as previously covered

Higher-Order Designs Higher-order – meaning more than 2 IVs With 3 IVs; each with 2 levels you have a 2 x 2 x 2 design If we have even 5 subjects per cell we are talking about a minimum of 40 subjects We are also talking about: SS T = SS A + SS B + SS C + SS AB + SS AC + SS BC + SS ABC + SS S/ABC

Higher-Order Designs Higher-order – meaning more than 2 IVs With 4 IVs; each with 2 levels you have a 2 x 2 x 2 x 2 design If we have even 5 subjects per cell we are talking about a minimum of 80 subjects We are also talking about: SS T = SS A + SS B + SS C + SS D + SS ABC + SS ABD + SS ACD + SS BCD + SS AB + SS AC + SS AD + SS BC + SS BD + SS CD + SS ABCD + SS S/ABCD

Higher-Order Designs Rules for creating the equations 1.List all IVs. There is a main effect for each IV, with degrees of freedom equal to the number of levels of that IV minus 1. 2.Form all combinations of two-way interactions among IVs. Degrees of freedom for each interaction are the products of the degrees of freedom for each of the IVs forming the interaction.

Higher-Order Designs Rules for creating the equations 3.Form all combinations of three-way interactions among IVs… 4.Continue forming interactions until you reach the highest level of interaction. 5.The error term: S before the slash, the highest level interaction after the slash

Higher-Order Designs Rules for creating the equations 6.Expand the degrees of freedom equations to develop the pieces of the equations. 7.Each piece gets placed in the numerator with everything else in the denominator (e.g. in an A x B x C design; if A is on top, bcn is on the bottom) 8.Replace every 1 with (ΣY) 2 /abcn 9.Replace every N (or abcn at the beginning of equation) with ΣY 2

Dangling Group Design Often a research design will have two or more factorial IVs but only a single control.

Dangling Group Design In this particular design the first step would be to treat it as a 1-way design with 5 levels in order to calculate the error term You calculate the SS the same but the DF are #groups(n – 1) Use this DF to calculate the MS S/AB Then test comparisons (e.g. control vs. the other four averaged {1, 1, 1, 1, -4})

Power and Sample Size The best advice is to calculate the number of subjects based on the each main effect and the interaction and use the largest estimate.

Power and Sample Size When calculating based on main effects divide the estimate by the number of levels of the other IV When calculating based on the interaction you may need to multiply by the number of cells that were averaged together to create the interaction difference. Recommend using PC-Size or other program