Plot of Items*Condition. Symbol is value of Age. 20 ˆ 18 ˆ Y 16 ˆ. Items Y 14 ˆ 12 ˆ O 10 ˆ 8 ˆ Y O O Y 6 ˆ

Transcription

1 Plot of Items*Condition. Symbol is value of Age. 20 ˆ Y 18 ˆ Y 16 ˆ Items Y 14 ˆ O 12 ˆ O O 10 ˆ 8 ˆ Y O O Y 6 ˆ Šƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒ Counting Rhyming Adjective Imagery Intentional Condition

2 proc means NWAY noprint; class Age Condition; var Items; output out=klw2 mean= ; proc plot; plot Items*Condition=Age; PROC GLM data=klw; CLASS Age Condition; MODEL Items=Age Condition / SS1 EFFECTSIZE alpha=0.1; means Age Condition; MEANS Condition / REGWQ; LSMEANS Condition / PDIFF CL ALPHA=.05; LSMEANS Age*Condition / SLICE=Age; LSMEANS Age*Condition / SLICE=Condition; * Note had to specify DATA=KLW -- otherwise PROC ANOVA would use the last created data set (KLW2, the cell means); Omnibus Analysis and Simple Main Effects Using Pooled Error Class Age Condition The GLM Procedure Class Level Information Levels Values 2 Old Young 5 Adjective Counting Imagery Intentional Rhyming Number of ervations Read 100 Number of ervations Used 100 Source DF Sum of s Mean F Value Pr > F Model <.0001 Error Corrected Total R- Coeff Var Root MSE Items Mean Proportion of Variation Accounted for Eta Omega % Confidence Limits (0.62,0.76)

3 Source DF Type I SS Mean F Value Pr > F Total Variation Accounted For Partial Variation Accounted For Semipartial Eta- Semipartial Omega- Conservative 90% Confidence Limits Partial Eta- Partial Omega- 90% Confidence Limits Age < Condition < Age*Condition

4 Omnibus Analysis and Simple Main Effects Using Pooled Error The GLM Procedure Level of Age N Mean Items Std Dev Old Young

5 Level of Condition N Mean Items Std Dev Adjective Counting Imagery Intentional Rhyming

6 Level of Age Level of Condition N Mean Items Std Dev Old Adjective Old Counting Old Imagery Old Intentional Old Rhyming Young Adjective Young Counting Young Imagery Young Intentional Young Rhyming

7 Ryan-Einot-Gabriel-Welsch Multiple Range Test for Items Note: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 90 Error Mean Means with the same letter are not significantly different. REGWQ Grouping A A A Mean N Condition Intentional Imagery B Adjective C C C Rhyming Counting LSMEANS Condition / PDIFF CL ALPHA=.05; Least s Means Condition Items LSMEAN LSMEAN Number Adjective Counting Imagery Intentional Rhyming Least s Means for effect Condition Pr > t for H0: LSMean(i)=LSMean(j) i/j < < <.0001 <.0001 < < < < < < <.0001 <.0001

8 Condition Items LSMEAN 95% Confidence Limits Adjective Counting Imagery Intentional Rhyming Least s Means for Effect Condition i j Difference Between Means 95% Confidence Limits for LSMean(i)-LSMean(j) Note: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used. LSMEANS Age*Condition / SLICE=Age; Least s Means Age Condition Items LSMEAN Old Adjective Old Counting Old Imagery Old Intentional Old Rhyming Young Adjective Young Counting Young Imagery Young Intentional Young Rhyming

9 Age DF Sum of s Mean Simple Main Effect of Condition at Levels of Age F Value Pr > F Total Variation Accounted For Partial Variation Accounted For Semipartial Eta- Semipartial Omega- Conservative 90% Confidence Limits Partial Eta- Partial Omega- 90% Confidence Limits Old < Young < CAUTION: Do not use the eta-squared statistics provided by the simple effects analysis in the table above and that immediately below. For both groups (Old and Young) it includes in the denominator the total variance in both groups, that is, SSTotal = I recommend getting the eta-squared statistics from the individual error terms approach shown later. LSMEANS Age*Condition / SLICE=Condition; Condition DF Sum of s Simple Main Effect of Age at Levels of Depth of Cognitive Processing Mean F Value Pr > F Total Variation Accounted For Partial Variation Accounted For Semipartial Eta- Semipartial Omega- Conservative 90% Confidence Limits Partial Eta- Partial Omega- 90% Confidence Limits Adjective Counting Imagery Intentional < Rhyming DATA ETA; F= 29.94; df_num = 1; df_den = 90; %CI F and df from the omnibus ANOVA. %CI calls up my macro, which is included in the program. 90% Confidence interval on PARTIAL eta-squared for the main effect of Age eta_2 eta2_lower eta2_upper My macro produces a less conservative CI than does GLM. GLM produced [.119,.363]. *********************************************************************************** Construct 90% Confidence Interval for Eta-d for Age -- used Proc ANOVA to get the adjusted F with effects of Condition and the interaction put in the error term. **********************************************************************************; title '90% Confidence interval on eta-squared for the effect of Age'; run; PROC ANOVA data=klw; CLASS Age; Model Items = Age; run; DATA ETA; F= 9.699; df_num = 1; df_den = 98; %CI

10 Value of F and df from the one-way ANOVA below. 90% Confidence interval on eta-squared for the main effect of Age The ANOVA Procedure Source DF Sum of s Mean F Value Pr > F Model Error Corrected Total eta_2 eta2_lower eta2_upper DATA ETA; F= 47.19; df_num = 4; df_den = 90; %CI 90% Confidence interval on PARTIAL eta-squared for the main effect of Condition eta_2 eta2_lower eta2_upper PROC ANOVA data=klw; CLASS Condition; Model Items = Condition; run; DATA ETA; F= 31.21; df_num = 4; df_den = 95; %CI 90% Confidence interval on eta-squared for the main effect of Condition Source DF Sum of s Mean F Value Pr > F Model <.0001 Error Corrected Total eta_2 eta2_lower eta2_upper DATA ETA; F= 5.93; df_num = 4; df_den = 90; %CI 90% Confidence interval on PARTIAL eta-squared for the interaction eta_2 eta2_lower eta2_upper

11 Construct Confidence Interval for Eta-d for Age x Condition Interaction Adjust F by hand: From the factorial ANOVA, MSE = (SS_Total - SS_AxC)/(df_Total - df_axc) = ( )/(99-4) = The F = MS_AxC/MSE = / = on 4 and 95 df. *******************************************************************************; title 'Confidence Interval on Eta-d for Age x Conditon Interaction'; run; Data CI; F= 1.824; df_num = 4; df_den = 95; %CI Confidence Interval on Eta-d for Age x Condition Interaction eta_2 eta2_lower eta2_upper ******************************************************************************** Construct confidence interval for d, main effect of Age. *******************************************************************************; PROC TTEST data=klw; CLASS Age; VAR Items; title 'Comparing Oldsters with Youngsters'; run; Data CI; t= 3.11; df = 98; n1 = 50; n2 = 50; %CIt %CIt calls up my macro to put confidence intervals on Cohen s d. Comparing Oldsters with Youngsters Method Variances DF t Value Pr > t Pooled Equal Satterthwaite Unequal d d_lower d_upper PROC SORT data=klw; BY Age; PROC ANOVA data=klw; CLASS Condition; MODEL Items=Condition; BY Age; title 'Simple Main Effects of Recall Condition Using Individual Error Terms'; run; Simple Main Effects of Recall Condition Using Individual Error Terms Class Condition Levels Values The ANOVA Procedure Age=Old Class Level Information 5 Adjective Counting Imagery Intentional Rhyming Number of ervations Read 50 Number of ervations Used 50

12 The ANOVA Procedure Age=Old Source DF Sum of s Mean F Value Pr > F Model <.0001 Error Corrected Total R- Coeff Var Root MSE Items Mean The ANOVA Procedure Age=Young Source DF Sum of s Mean F Value Pr > F Model <.0001 Error Corrected Total title2 'Oldsters'; Data CI; F= 9.08; df_num = 4; df_den = 45; %CI title2 'Youngsters'; Data CI; F= 53.06; df_num = 4; df_den = 45; %CI R- Coeff Var Root MSE Items Mean Oldsters eta_2 eta2_lower eta2_upper Youngsters eta_2 eta2_lower eta2_upper

13 PROC SORT data=klw; BY Condition; PROC ANOVA data=klw; CLASS Age; MODEL Items=Age; BY Condition; title 'Simple Main Effects of Age Using Individual Error Terms'; run; Source Simple Main Effects of Age Using Individual Error Terms Condition=Counting DF Sum of s Mean F Value Pr > F Model Error Corrected Total Condition=Rhyming Source DF Sum of s Mean F Value Pr > F Model Error Corrected Total Condition=Adjective Source DF Sum of s Mean F Value Pr > F Model Error Corrected Total Condition=Imagery Source DF Sum of s Mean F Value Pr > F Model Error Corrected Total Condition=Intentional Source DF Sum of s Mean F Value Pr > F Model <.0001 Error Corrected Total

14 title2 'Counting'; run; Data CI; t=.678; df = 18; n1 = 10; n2 = 10; %CIt title2 'Rhyming'; run; Data CI; t=.768; df = 18; n1 = 10; n2 = 10; %CIt title2 'Adjective'; run; Data CI; t= 2.80; df = 18; n1 = 10; n2 = 10; %CIt title2 'Imagery'; run; Data CI; t= 2.56; df = 18; n1 = 10; n2 = 10; %CIt title2 'Intentional'; run; Data CI; t= 5.02; df = 18; n1 = 10; n2 = 10; %CIt Note: the value of t is simply the square root of the simple effect F, and the df are simply the error df for that F. Confidence Intervals for Cohen s d Counting d d_lower d_upper Rhyming d d_lower d_upper Adjective d d_lower d_upper Imagery d d_lower d_upper Intentional d d_lower d_upper proc gplot data=klw2; symbol1 interpol=join width=4 value=triangle height=2 color=red; symbol2 interpol=join width=4 value=square height=2 color=green; plot Items*Condition=Age; title 'Figure 1. Recall by Age and Condition'; run; quit;

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