# UW-Madison PSYCH 210 - Factorial ANOVA Calculations (3 pages)

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**View the full content.**## Factorial ANOVA Calculations

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## Factorial ANOVA Calculations

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- Lecture number:
- 24
- Pages:
- 3
- Type:
- Lecture Note
- School:
- University of Wisconsin, Madison
- Course:
- Psych 210 - Basic Statistics for Psychology
- Edition:
- 1

**Unformatted text preview:**

Psych 210 Lecture 24 Outline of Last Lecture I Final II Factorial ANOVA a Conceptual Example b New Concepts main effects and interactions Outline of Current Lecture I Factorial ANOVA a Calculational example with hypothesis testing steps b Post hoc tests c Assumptions Current Lecture I Calculation of F observed Step 3 of hypothesis testing a We need three different Fs one for each effect ME A ME B Interaction A x B i SS df and MS 1 For each of 6 pieces of variance ii SS total 2538 2402 30 618 iii SS within Sum of SS within each cell 16 68 40 34 40 208 iv SS Between AB2 n G2 N 1 252 5 752 5 502 5 202 5 302 5 402 5 2402 30 410 2 SS btwn SS total SS within v SSA A2 bn G2 N 1 1502 3 5 902 15 2402 30 120 vi SSB B2 an G2 N 1 452 2 5 1052 10 902 10 2402 N 195 vii SSAxB SSbtwn SSB SSA 410 120 195 95 viii dftotal N 1 30 1 29 ix dfwithin N ab 30 2 3 24 1 Different notation ab k of treatments x dfbetween ab 1 6 1 5 xi dfA a 1 2 1 1 These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute II xii dfB b 1 3 1 2 xiii dfAxb dfbetween dfA dfB 5 1 2 2 b FA MSA MSwithin c FB MSB MSwithin d FAxB MSAxB MSwithin i MSA SSA dfA 120 1 120 ii MSB SSB dfB 195 2 97 5 iii MSAxB MSAxB dfAxB 95 2 47 5 iv MSwithin SSwithin dfwithin 208 24 e FA 120 8 67 f FB 97 5 8 67 g FAxB 47 5 8 67 Factorial ANOVA Return to hypothesis testing steps a ME A i Hypotheses 1 H0 A1 A2 2 H1 A1 A2 ii Critical Value of F new table 1 FA MSA MSwithin a MSA SSA dfA b MSwithin SSwithin dfwithin 2 Fcrit 1 24 4 26 iii Fobs 13 85 iv Decision About H0 1 Reject H0 b When do we need post hoc test i For main effects run post hoc if 1 Overall F is significant Reject H0 2 There are 2 levels of the IV a H1 Not H0 ii Conclusion 1 See handout c ME B i Hypothesis 1 H1 B1 B2 B3 2 H0 Not H0 a Do this any time there are more than 2 ii Fcrit 2 24 3 40 iii Fobs 11 25 iv Decision H0 1 Reject H0 v Conclusion 1 Must perform post hoc test a Test where the differences lie between 3 B means 2 See handout d MEAxB i Hypothesis 1 H1 No interaction 2 H0 There is an interaction a Too many possibilities to write out statistically ii Fcrit 2 24 3 40 iii Fobs 5 48 iv Decision H0 1 Reject H0 2 Significant Interaction nonparallel v Conclusion 1 Still do not know what interaction is Continue next class

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