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Lecture

Split-Plot Part II.pdf

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Department
Psychology
Course
PSYC 2040
Professor
David Stanley
Semester
Winter

Description
Split-Plot Analysis of Variance Part II: Split-Plot Analysis of Variance Part II: Exploring the Interaction! Exploring the Interaction! 1)  Interaction Overview! " 1)  Interaction Overview! " 2)  Two types of situations with different error terms" 2)  Two types of situations with different error terms**" ! ! 3)  Situation 1: Comparing effect of the between-subjects factor at a particular level of 3)  Situation 1: Comparing effect of the between-subjects factor at a particular level of the within-subjects factor! the within-subjects factor! 4)  Situation 1: Denominator calculations! 4)  Situation 1: Denominator calculations! 5)  Situation 1: Numerator calculations! 5)  Situation 1: Numerator calculations! 6)  Situation 1: F-values and significance! 6)  Situation 1: F-values and significance! 7)  Situation 1: Effect size calculation! 7)  Situation 1: Effect size calculation! 8)  Situation 1: Sample Results Paragraph! 8)  Situation 1: Sample Results Paragraph! 9)  Situation 2: Comparing effect of the within-subjects factor at a particular level of the 9)  Situation 2: Comparing effect of the within-subjects factor at a particular level of the between-subjects factor! between-subjects factor! 10)  Situation 2: Understanding the SPSS syntax! 10)  Situation 2: Understanding the SPSS syntax! 11)  Situation 2: Understanding SPSS Output! 11)  Situation 2: Understanding SPSS Output! 12)  Situation 2: Effect size calculation! 1 12)  Situation 2: Effect size calculation! 2 Investigating a significant 2-way interaction To understand an interaction, need to conduct simple main effect Split-Plot design analyses 2-way interaction The effect of 1 factor on the DV varies depending on the level 1) check out the interaction cell means of the other factor 2) which set of simple main effects makes more sense theoretically? 3) do the math The simple main effects of 1 factor are different what we do in SPSS depends on which set of simple main effects at the various levels of the other we want Simple Main Effect The effect of a factor (e.g., audience) at a specific level of another factor (e.g., males) 3 4 Problem: The Error term for SME Gender by Audience Interaction depends upon the situation 2 Situations 10 Audience 1) Examining a Between-Subject aud0 aud1 aud2 aud3 independent variable at a 8 Men males 8.0 6.2 4.2 4.0 specific level of a Within- Women Subjects variable females 9.8 6.4 3.0 2.0 6 c o r 4 Audience m 2) Examining a Within-Subjects aud0 aud1 aud2 aud3 a variable at a specific level M 2 of a Between-Subjects males 8.0 6.2 4.2 4.0 independent variable females 9.8 6.4 3.0 2.0 0 0 1 2 3 Audience 5 6 Split-Plot Analysis of Variance Part II: Problem: The Error term for SME Exploring the Interaction! depends upon the situation 1)  Interaction Overview! " 2 Situations 2)  Two types of situations with different error terms" ! Audience 1) Examining a Between-Subject aud0 aud1 aud2 aud3 3)  Situation 1: Comparing effect of the between-subjects factor at a particular level of independent variable at a the within-subjects factor**! males 8.0 6.2 4.2 4.0 specific level of a Within- 4)  Situation 1: Denominator calculations! Subjects variable females 9.8 6.4 3.0 2.0 5)  Situation 1: Numerator calculations! 6)  Situation 1: F-values and significance! 7)  Situation 1: Effect size calculation! Audience 8)  Situation 1: Sample Results Paragraph! 2) Examining a Within-Subjects aud0 aud1 aud2 aud3 variable at a specific level of a Between-Subjects males 8.0 6.2 4.2 4.0 9)  Situation 2: Comparing effect of the within-subjects factor at a particular level of the independent variable between-subjects factor! females 9.8 6.4 3.0 2.0 10)  Situation 2: Understanding the SPSS syntax! 11)  Situation 2: Understanding SPSS Output! 12)  Situation 2: Effect size calculation! 7 8 Gender by Audience Interaction What about gender at the different levels of audience? 10 8 aud0 aud1 aud2 aud3 aud0 aud1 aud2 aud3 Men Women males 8.0 6.2 4.2 4.0 males 8.0 6.2 4.2 4.0 6 females 9.8 6.4 3.0 2.0 females 9.8 6.4 3.0 2.0 s e f b 4 aud0 aud1 aud2 aud3 aud0 aud1 aud2 aud3 n M males 8.0 6.2 4.2 4.0 males 8.0 6.2 4.2 4.0 2 females 9.8 6.4 3.0 2.0 females 9.8 6.4 3.0 2.0 0 0 1 2 3 Audience 9 10 Interested in: Effect of gender at the different levels of audience aud0 aud1 aud2 aud3 aud0 aud1 aud2 aud3 males 8.0 6.2 4.2 4.0 males 8.0 6.2 4.2 4.0 females 9.8 6.4 3.0 2.0 females 9.8 6.4 3.0 2.0 aud0: F(?, ?) = ?? / ?? aud0: F(?, ?) = ?? / ?? Calculate Calculate 4 F-ratios aud1: F(?, ?) = ?? / ?? 4 F-ratios aud1: F(?, ?) = ?? / ?? aud2: F(?, ?) = ?? / ?? aud2: F(?, ?) = ?? / ?? aud3: F(?, ?) = ?? / ?? aud3: F(?, ?) = ?? / ?? 11 12 aud0 aud1 aud2 aud3 aud0 aud1 aud2 aud3 males 8.0 6.2 4.2 4.0 males 8.0 6.2 4.2 4.0 females 9.8 6.4 3.0 2.0 females 9.8 6.4 3.0 2.0 aud0: F(?, ?) = ?? / ?? aud0: F(?, ?) = ?? / ?? Calculate Calculate 4 F-ratios aud1: F(?, ?) = ?? / ?? 4 F-ratios aud1: F(?, ?) = ?? / ?? aud2: F(?, ?) = ?? / ?? aud2: F(?, ?) = ?? / ?? aud3: F(?, ?) = ?? / ?? aud3: F(?, ?) = ?? / ?? 13 14 For each F-ratio For each F-ratio •  There is a Numerator •  There is a Numerator •  There is Denominator •  There is Denominator •  F = MSeffect Numerator •  F = MSeffect Numerator MSerror MSerror Denominator •  Must determine both, and then calculate F •  Must determine both, and then calculate F 15 16 Calculate the Denominator for the F-ratio First, we'll determine the proper denominator Calculate F-ratio By Hand 1)  Calculate a new pooled MS (denominator) to put into each error F-ratio. Next, we'll determine the numerators 2)  Calculate d.f. for new pooled MS errordenominator). 3)  Use ONEWAY command to get appropriate MS betweenand d.f. for them. Finally, we'll calculate the F-ratios 4)  Calculate F-ratios by hand 5)  Determine critical F-ratio using df MS and MS between error and compare to obtained F-values 17 18 Calculate the Numerator for the F-ratio Combine them, calculate F, and determine significance. Calculate F-ratio By Hand Calculate F-ratio By Hand 1)  Calculate a new pooled MS (denominator) to put into each 1)  Calculate a new pooled MS (denominator) to put into each error error F-ratio. F-ratio. 2)  Calculate d.f. for new pooled MS errordenominator). 2)  Calculate d.f. for new pooled MS errordenominator). 3)  Use ONEWAY command to get appropriate MS betweenand d.f. 3)  Use ONEWAY command to get appropriate MS betweenand d.f. for them. for them. 4)  Calculate F-ratios by hand 4)  Calculate F-ratios by hand 5)  Determine critical F-ratio using df MS and MS 5)  Determine critical F-ratio using df MS and MS between error between error and compare to obtained F-values and compare to obtained F-values 19 20 Split-Plot Analysis of Variance Part II: Exploring the Interaction! Calculating F-ratios by hand 1)  Interaction Overview! " 2)  Two types of situations with different error terms" ! 3)  Situation 1: Comparing effect of the between-subjects factor at a particular level of the within-subjects factor! 4)  Situation 1: Denominator calculations**! 1)  **Calculate a new pooled MS error(denominator) to put into 5)  Situation 1: Numerator calculations! each F-ratio. 6)  Situation 1: F-values and significance! 2)  Calculate d.f. for new pooled MS (denominator). error 7)  Situation 1: Effect size calculation! 3)  Use ONEWAY command to get appropriate MS and d.f. 8)  Situation 1: Sample Results Paragraph! between for them. 9)  Situation 2: Comparing effect of the within-subjects factor at a particular level of the 4)  Calculate F-ratios by hand between-subjects factor! 5)  Determine critical F-ratio using df MS between and MS error 10)  Situation 2: Understanding the SPSS syntax! and compare to obtained F-values 11)  Situation 2: Understanding SPSS Output! 12)  Situation 2: Effect size calculation! 21 22 Tests of Between-Subjects Effects Measure: MEASURE_1 Need to pool error terms when doing simple main effects of the Transformed Variable: Average independent groups variable at the different levels of the repeated Type III Sum Partial Eta measures variable Source of Squares df Mean Square F Sig. Squared Intercept 1188.100 1 1188.100 760.384 .000 .990 gender .900 1 .900 .576 .470 .067 effects of Gender at different levels of Audience: Error 12.500 8 1.563 Gender & interaction have different error terms, so pool them (use sphericity assumed line) Step 1: Calculate a new pooled MS error(denominator) Tests of Within-Subjects Effects new MS error = (SS e1 + SS )e2 (df e1 + df e2 Measure: MEASURE_1 = (31.10 + 12.50) / (24 + 8) Type III Sum Partial Eta = 43.60 / 32 Source of Squares df Mean Square F Sig. Squared audience Sphericity Assumed 220.500 3 73.500 56.720 .000 .876 = 1.36 Greenhouse-Geisser 220.500 2.171 101.588 56.720 .000 .876 Huynh-Feldt 220.500 3.000 73.500 56.720 .000 .876 Lower-bound 220.500 1.000 220.500 56.720 .000 .876 Step 2: Calculate df for new MS (denominator) error audience * genderSphericity Assumed 20.900 3 6.967 5.376 .006 .402 new df = (SS + SS ) / (SS 2/df + SS 2/df ) Greenhouse-Geisser 20.900 2.171 9.629 5.376 .014 .402 error e1 e2 e1 e1 e2 e2 Huynh-Feldt 20.900 3.000 6.967 5.376 .006 .402 = (31.10+12.50) 2 / (31.102/24 + 12.502/8) Lower-bound = 1900.96 / 59.83 20.900 1.000 20.900 5.376 .049 .402 Error(audience) Sphericity Assumed 31.100 24 1.296 = 31.77 Greenhouse-Geisser 31.100 17.364 1.791 = 31 in this case, round down Huynh-Feldt 31.100 24.000 1.296 Lower-bound 31.100 8.000 3.888 23 24 aud0 aud1 aud2 aud3 Need to pool error terms when doing simple main effects of the males 8.0 6.2 4.2 4.0 independent groups variable at the different levels of the repeated measures variable females 9.8 6.4 3.0 2.0 effects of Gender at different levels of Audience: Gender & interaction have different error terms, so pool them Step 1: Calculate a new pooled MS errordenominator) aud0: F(?, ?) = ?? / 1.36 new MS error = (SS e1 + SS e2/ (df e1+ dfe2 = (31.10 + 12.50) / (24 + 8) Calculate = 43.60 / 32 4 F-ratios aud1: F(?, ?) = ?? / 1.36 = 1.36 aud2: F(?, ?) = ?? / 1.36 Step 2: Calculate df for new MS errordenominator) 2 2 2 new df error = (SS e1 + SS e2/ (SS e1 /dfe1+ SS e2/dfe2 aud3: F(?, ?) = ?? / 1.36 = (31.10+12.50)/ (31.102/24 + 12.502/8) = 1900.96 / 59.83 = 31.77 = 31 in this case, round down 25 26 Need to pool error terms when doing simple main effects of the independent groups variable at the different levels of the repeated measures variable If they have different Error Terms effects of Gender at different levels of Audience: Calculate F-ratio By Hand Gender & interaction have different error terms, so pool them 1)  Calculate a new pooled MS errordenominator) to put into each F-ratio. Step 1: Calculate a new pooled MS errordenominator) new MS = (SS + SS ) / (df + df ) error e1 e2 e1 e2 2)  **Calculate d.f. for new pooled MS errordenominator). = (31.10 + 12.50) / (24 + 8) = 43.60 / 32 3)  Use ONEWAY command to get appropriate MS and d.f. = 1.36 between for them. 4)  Calculate F-ratios by hand Step 2: Calculate df for new MS error(denominator) new df error = (SS e1+ SS )e2 (SS e12/dfe1+ SS e22/dfe2 = (31.10+12.50)/ (31.102/24 + 12.502/8) 5)  Determine critical F-ratio using df MS between and MS error = 1900.96 / 59.83 and compare to obtained F-values = 31.77 = 31 in this case, round down 27 28 Tests of Between-Subjects Effects Measure: MEASURE_1 Transformed Variable: Average Need to pool error terms when doing simple main effects of the independent groups variable at the different levels of the repeated Type III Sum Partial Eta Source of Squares df Mean Square F Sig. Squared measures variable Intercept 1188.100 1 1188.100 760.384 .000 .990 gender .900 1 .900 .576 .470 .067 Error 12.500 8 1.563 effects of Gender at different levels of Audience: Gender & interaction have different error terms, so pool them Step 1: Calculate a new pooled MS error(denominator) Tests of Within-Subjects Effects Measure: MEASURE_1 new MS error = (SS e1+ SS ) e2(df e1 + df e2 = (31.10 + 12.50) / (24 + 8) Type III Sum Partial Eta Source of Squares df Mean Square F Sig. Squared = 43.60 / 32 audience Sphericity Assumed 220.500 3 73.500 56.720 .000 .876 =1.36 Greenhouse-Geisser 220.500 2.171 101.588 56.720 .000 .876 Huynh-Feldt 220.500 3.000 73.500 56.720 .000 .876 Lower-bound 220.500 1.000 220.500 56.720 .000 .876 audience * gendeSphericity Assumed 20.900 3 6.967 5.376 .006 .402 Step 2: Calculate df for new MS error(denominator) Greenhouse-Geisser 20.900 2.171 9.629 5.376 .014 .402 2 2 2 new df error = (SS e1+ SS ) e2(SS e1 /df e1 + SS e2 /dfe2 Huynh-Feldt 20.900 3.000 6.967 5.376 .006 .402 = (31.10+12.50) 2/ (31.10 /24 + 12.50 /8) Lower-bound 20.900 1.000 20.900 5.376 .049 .402 Error(audience) Sphericity Assumed 31.100 24 1.296 = 1900.96 / 59.83 = 31.77 Greenhouse-Geisser 31.100 17.364 1.791 Huynh-Feldt 31.100 24.000 1.296 =31 in this case, round down Lower-bound 31.100 8.000 3.888 29 30 aud0 aud1 aud2 aud3 aud0 aud1 aud2 aud3 males 8.0 6.2 4.2 4.0 males 8.0 6.2 4.2 4.0 females 9.8 6.4 3.0 2.0 females 9.8 6.4 3.0 2.0 aud0: F(?, 31) = ?? / 1.36 aud0: F(?, 31) = ?? / 1.36 Calculate Now find a 4 F-ratios numerator aud1: F(?, 31) = ?? / 1.36 aud1: F(?, 31) = ?? / 1.36 for each SME aud2: F(?, 31) = ?? / 1.36 aud2: F(?, 31) = ?? / 1.36 aud3: F(?, 31) = ?? / 1.36 aud3: F(?, 31) = ?? / 1.36 31 32 Split-Plot Analysis of Variance Part II: Exploring the Interaction! 1)  Interaction Overview! " If they have different Error Terms 2)  Two types of situations with different error terms" ! 3)  Situation 1: Comparing effect of the between-subjects factor at a particular level of Calculate F-ratio By Hand the within-subjects factor! 4)  Situation 1: Denominator calculations! 1)  Calculate a new pooled MS errordenominator) to put into each 5)  Situation 1: Numerator calculations**! F-ratio. 6)  Situation 1: F-values and significance! 2)  Calculate d.f. for new pooled MS (denominator). error 7)  Situation 1: Effect size calculation! 8)  Situation 1: Sample Results Paragraph! 3)  **Use ONEWAY command to get appropriate MS between and d.f. for them. 9)  Situation 2: Comparing effect of the within-subjects factor at a particular level of the 4)  Calculate F-ratios by hand between-subjects factor! 10)  Situation 2: Understanding the SPSS syntax! 5)  Determine critical F-ratio using df MS between and MS error and compare to obtained F-values 11)  Situation 2: Understanding SPSS Output! 12)  Situation 2: Effect size calculation! 33 34 Step 3: Use ONEWAY command to get appropriate MS between ONEWAY aud0 aud1 aud2 aud3 BY gender /MISSING ANALYSIS. Gender at: Oneway From ONEWAY command New Pooled MS error aud0: F(?, 31) = ?? / 1.36 aud1: F(?, 31) = ?? / 1.36 aud2: F(?, 31) = ?? / 1.36 aud3: F(?, 31) = ?? / 1.36 35 36 aud0 aud1 aud2 aud3 Split-Plot Analysis of Variance Part II: Exploring the Interaction! males 8.0 6.2 4.2 4.0 females 9.8 6.4 3.0 2.0 1)  Interaction Overview! "
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