# ::Free Statistics and Forecasting Software::

v1.1.23-r7
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### :: Mixed Within-Between Two-Way ANOVA - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Mixed Within-Between Two-Way ANOVA, Mauchly's Sphericity Test, and the Sphericity Corrections using Greenhouse-Geisser values (GG) or Huynh-Feldt (HF). This R module is used in Workshop 10 of the PY2224 statistics course at Aston University, UK. Updated for R v2.12.1 Jan 2011

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

 Send output to: Browser Blue - Charts White Browser Black/White CSV MS Excel MS Word Data X (click to load default data) '1' 'Trt' 'NoCue' 'Neut' 433.5 '1' 'Trt' 'NoCue' 'Cong' 423.9 '1' 'Trt' 'NoCue' 'Inc' 490.9 '1' 'Trt' 'Cent' 'Neut' 385.2 '1' 'Trt' 'Cent' 'Cong' 368.6 '1' 'Trt' 'Cent' 'Inc' 473.4 '1' 'Trt' 'Double' 'Neut' 378.9 '1' 'Trt' 'Double' 'Cong' 378.9 '1' 'Trt' 'Double' 'Inc' 455.4 '1' 'Trt' 'Spatial' 'Neut' 328.1 '1' 'Trt' 'Spatial' 'Cong' 350.2 '1' 'Trt' 'Spatial' 'Inc' 407.2 '2' 'Trt' 'NoCue' 'Neut' 436.4 '2' 'Trt' 'NoCue' 'Cong' 441.9 '2' 'Trt' 'NoCue' 'Inc' 483.3 '2' 'Trt' 'Cent' 'Neut' 374.2 '2' 'Trt' 'Cent' 'Cong' 389.8 '2' 'Trt' 'Cent' 'Inc' 455.7 '2' 'Trt' 'Double' 'Neut' 357.0 '2' 'Trt' 'Double' 'Cong' 384.2 '2' 'Trt' 'Double' 'Inc' 433.0 '2' 'Trt' 'Spatial' 'Neut' 339.4 '2' 'Trt' 'Spatial' 'Cong' 337.6 '2' 'Trt' 'Spatial' 'Inc' 421.0 '3' 'Trt' 'NoCue' 'Neut' 428.7 '3' 'Trt' 'NoCue' 'Cong' 428.1 '3' 'Trt' 'NoCue' 'Inc' 503.3 '3' 'Trt' 'Cent' 'Neut' 371.2 '3' 'Trt' 'Cent' 'Cong' 368.0 '3' 'Trt' 'Cent' 'Inc' 436.5 '3' 'Trt' 'Double' 'Neut' 392.3 '3' 'Trt' 'Double' 'Cong' 356.3 '3' 'Trt' 'Double' 'Inc' 432.7 '3' 'Trt' 'Spatial' 'Neut' 331.3 '3' 'Trt' 'Spatial' 'Cong' 334.6 '3' 'Trt' 'Spatial' 'Inc' 431.4 '4' 'Trt' 'NoCue' 'Neut' 415.5 '4' 'Trt' 'NoCue' 'Cong' 433.3 '4' 'Trt' 'NoCue' 'Inc' 498.5 '4' 'Trt' 'Cent' 'Neut' 384.8 '4' 'Trt' 'Cent' 'Cong' 383.2 '4' 'Trt' 'Cent' 'Inc' 438.5 '4' 'Trt' 'Double' 'Neut' 370.3 '4' 'Trt' 'Double' 'Cong' 399.4 '4' 'Trt' 'Double' 'Inc' 445.9 '4' 'Trt' 'Spatial' 'Neut' 320.7 '4' 'Trt' 'Spatial' 'Cong' 342.8 '4' 'Trt' 'Spatial' 'Inc' 407.0 '5' 'Trt' 'NoCue' 'Neut' 429.1 '5' 'Trt' 'NoCue' 'Cong' 436.9 '5' 'Trt' 'NoCue' 'Inc' 499.0 '5' 'Trt' 'Cent' 'Neut' 378.1 '5' 'Trt' 'Cent' 'Cong' 394.6 '5' 'Trt' 'Cent' 'Inc' 471.4 '5' 'Trt' 'Double' 'Neut' 370.6 '5' 'Trt' 'Double' 'Cong' 370.7 '5' 'Trt' 'Double' 'Inc' 447.1 '5' 'Trt' 'Spatial' 'Neut' 332.5 '5' 'Trt' 'Spatial' 'Cong' 329.9 '5' 'Trt' 'Spatial' 'Inc' 418.3 '6' 'Trt' 'NoCue' 'Neut' 435.3 '6' 'Trt' 'NoCue' 'Cong' 422.7 '6' 'Trt' 'NoCue' 'Inc' 480.0 '6' 'Trt' 'Cent' 'Neut' 390.7 '6' 'Trt' 'Cent' 'Cong' 366.9 '6' 'Trt' 'Cent' 'Inc' 461.5 '6' 'Trt' 'Double' 'Neut' 354.1 '6' 'Trt' 'Double' 'Cong' 385.6 '6' 'Trt' 'Double' 'Inc' 435.4 '6' 'Trt' 'Spatial' 'Neut' 336.3 '6' 'Trt' 'Spatial' 'Cong' 335.0 '6' 'Trt' 'Spatial' 'Inc' 399.6 '7' 'Trt' 'NoCue' 'Neut' 435.4 '7' 'Trt' 'NoCue' 'Cong' 412.3 '7' 'Trt' 'NoCue' 'Inc' 484.9 '7' 'Trt' 'Cent' 'Neut' 387.8 '7' 'Trt' 'Cent' 'Cong' 380.5 '7' 'Trt' 'Cent' 'Inc' 443.4 '7' 'Trt' 'Double' 'Neut' 361.9 '7' 'Trt' 'Double' 'Cong' 346.4 '7' 'Trt' 'Double' 'Inc' 452.1 '7' 'Trt' 'Spatial' 'Neut' 351.1 '7' 'Trt' 'Spatial' 'Cong' 345.6 '7' 'Trt' 'Spatial' 'Inc' 424.7 '8' 'Trt' 'NoCue' 'Neut' 402.9 '8' 'Trt' 'NoCue' 'Cong' 412.7 '8' 'Trt' 'NoCue' 'Inc' 502.4 '8' 'Trt' 'Cent' 'Neut' 387.8 '8' 'Trt' 'Cent' 'Cong' 358.2 '8' 'Trt' 'Cent' 'Inc' 437.8 '8' 'Trt' 'Double' 'Neut' 357.4 '8' 'Trt' 'Double' 'Cong' 401.8 '8' 'Trt' 'Double' 'Inc' 459.5 '8' 'Trt' 'Spatial' 'Neut' 360.1 '8' 'Trt' 'Spatial' 'Cong' 335.6 '8' 'Trt' 'Spatial' 'Inc' 405.1 '9' 'Trt' 'NoCue' 'Neut' 419.2 '9' 'Trt' 'NoCue' 'Cong' 420.1 '9' 'Trt' 'NoCue' 'Inc' 500.0 '9' 'Trt' 'Cent' 'Neut' 386.1 '9' 'Trt' 'Cent' 'Cong' 381.4 '9' 'Trt' 'Cent' 'Inc' 460.0 '9' 'Trt' 'Double' 'Neut' 370.2 '9' 'Trt' 'Double' 'Cong' 369.4 '9' 'Trt' 'Double' 'Inc' 445.4 '9' 'Trt' 'Spatial' 'Neut' 351.2 '9' 'Trt' 'Spatial' 'Cong' 336.6 '9' 'Trt' 'Spatial' 'Inc' 422.3 '10' 'Trt' 'NoCue' 'Neut' 441.6 '10' 'Trt' 'NoCue' 'Cong' 432.2 '10' 'Trt' 'NoCue' 'Inc' 516.9 '10' 'Trt' 'Cent' 'Neut' 382.5 '10' 'Trt' 'Cent' 'Cong' 376.9 '10' 'Trt' 'Cent' 'Inc' 442.9 '10' 'Trt' 'Double' 'Neut' 385.6 '10' 'Trt' 'Double' 'Cong' 385.9 '10' 'Trt' 'Double' 'Inc' 457.8 '10' 'Trt' 'Spatial' 'Neut' 342.2 '10' 'Trt' 'Spatial' 'Cong' 331.5 '10' 'Trt' 'Spatial' 'Inc' 408.1 '11' 'Ctrl' 'NoCue' 'Neut' 446.7 '11' 'Ctrl' 'NoCue' 'Cong' 433.8 '11' 'Ctrl' 'NoCue' 'Inc' 517.3 '11' 'Ctrl' 'Cent' 'Neut' 380.3 '11' 'Ctrl' 'Cent' 'Cong' 371.6 '11' 'Ctrl' 'Cent' 'Inc' 493.7 '11' 'Ctrl' 'Double' 'Neut' 390.9 '11' 'Ctrl' 'Double' 'Cong' 394.2 '11' 'Ctrl' 'Double' 'Inc' 482.1 '11' 'Ctrl' 'Spatial' 'Neut' 345.2 '11' 'Ctrl' 'Spatial' 'Cong' 330.7 '11' 'Ctrl' 'Spatial' 'Inc' 391.5 '12' 'Ctrl' 'NoCue' 'Neut' 420.7 '12' 'Ctrl' 'NoCue' 'Cong' 442.7 '12' 'Ctrl' 'NoCue' 'Inc' 513.3 '12' 'Ctrl' 'Cent' 'Neut' 374.7 '12' 'Ctrl' 'Cent' 'Cong' 373.0 '12' 'Ctrl' 'Cent' 'Inc' 486.7 '12' 'Ctrl' 'Double' 'Neut' 380.0 '12' 'Ctrl' 'Double' 'Cong' 374.9 '12' 'Ctrl' 'Double' 'Inc' 495.7 '12' 'Ctrl' 'Spatial' 'Neut' 352.6 '12' 'Ctrl' 'Spatial' 'Cong' 347.6 '12' 'Ctrl' 'Spatial' 'Inc' 424.4 '13' 'Ctrl' 'NoCue' 'Neut' 422.1 '13' 'Ctrl' 'NoCue' 'Cong' 424.2 '13' 'Ctrl' 'NoCue' 'Inc' 503.6 '13' 'Ctrl' 'Cent' 'Neut' 364.8 '13' 'Ctrl' 'Cent' 'Cong' 364.3 '13' 'Ctrl' 'Cent' 'Inc' 474.6 '13' 'Ctrl' 'Double' 'Neut' 383.8 '13' 'Ctrl' 'Double' 'Cong' 363.6 '13' 'Ctrl' 'Double' 'Inc' 477.1 '13' 'Ctrl' 'Spatial' 'Neut' 338.0 '13' 'Ctrl' 'Spatial' 'Cong' 332.8 '13' 'Ctrl' 'Spatial' 'Inc' 420.3 '14' 'Ctrl' 'NoCue' 'Neut' 431.7 '14' 'Ctrl' 'NoCue' 'Cong' 436.4 '14' 'Ctrl' 'NoCue' 'Inc' 481.9 '14' 'Ctrl' 'Cent' 'Neut' 376.7 '14' 'Ctrl' 'Cent' 'Cong' 388.7 '14' 'Ctrl' 'Cent' 'Inc' 484.4 '14' 'Ctrl' 'Double' 'Neut' 383.4 '14' 'Ctrl' 'Double' 'Cong' 363.5 '14' 'Ctrl' 'Double' 'Inc' 467.4 '14' 'Ctrl' 'Spatial' 'Neut' 315.9 '14' 'Ctrl' 'Spatial' 'Cong' 354.7 '14' 'Ctrl' 'Spatial' 'Inc' 408.6 '15' 'Ctrl' 'NoCue' 'Neut' 430.9 '15' 'Ctrl' 'NoCue' 'Cong' 446.8 '15' 'Ctrl' 'NoCue' 'Inc' 505.1 '15' 'Ctrl' 'Cent' 'Neut' 372.7 '15' 'Ctrl' 'Cent' 'Cong' 382.8 '15' 'Ctrl' 'Cent' 'Inc' 483.5 '15' 'Ctrl' 'Double' 'Neut' 369.3 '15' 'Ctrl' 'Double' 'Cong' 378.1 '15' 'Ctrl' 'Double' 'Inc' 461.1 '15' 'Ctrl' 'Spatial' 'Neut' 342.6 '15' 'Ctrl' 'Spatial' 'Cong' 336.2 '15' 'Ctrl' 'Spatial' 'Inc' 421.7 '16' 'Ctrl' 'NoCue' 'Neut' 425.6 '16' 'Ctrl' 'NoCue' 'Cong' 417.5 '16' 'Ctrl' 'NoCue' 'Inc' 495.2 '16' 'Ctrl' 'Cent' 'Neut' 373.9 '16' 'Ctrl' 'Cent' 'Cong' 378.6 '16' 'Ctrl' 'Cent' 'Inc' 490.9 '16' 'Ctrl' 'Double' 'Neut' 381.9 '16' 'Ctrl' 'Double' 'Cong' 358.5 '16' 'Ctrl' 'Double' 'Inc' 464.4 '16' 'Ctrl' 'Spatial' 'Neut' 340.3 '16' 'Ctrl' 'Spatial' 'Cong' 351.1 '16' 'Ctrl' 'Spatial' 'Inc' 408.4 '17' 'Ctrl' 'NoCue' 'Neut' 421.6 '17' 'Ctrl' 'NoCue' 'Cong' 432.6 '17' 'Ctrl' 'NoCue' 'Inc' 502.8 '17' 'Ctrl' 'Cent' 'Neut' 386.0 '17' 'Ctrl' 'Cent' 'Cong' 389.3 '17' 'Ctrl' 'Cent' 'Inc' 487.0 '17' 'Ctrl' 'Double' 'Neut' 369.5 '17' 'Ctrl' 'Double' 'Cong' 368.7 '17' 'Ctrl' 'Double' 'Inc' 482.0 '17' 'Ctrl' 'Spatial' 'Neut' 350.8 '17' 'Ctrl' 'Spatial' 'Cong' 333.9 '17' 'Ctrl' 'Spatial' 'Inc' 421.7 '18' 'Ctrl' 'NoCue' 'Neut' 432.5 '18' 'Ctrl' 'NoCue' 'Cong' 413.6 '18' 'Ctrl' 'NoCue' 'Inc' 484.4 '18' 'Ctrl' 'Cent' 'Neut' 388.4 '18' 'Ctrl' 'Cent' 'Cong' 374.6 '18' 'Ctrl' 'Cent' 'Inc' 475.4 '18' 'Ctrl' 'Double' 'Neut' 380.8 '18' 'Ctrl' 'Double' 'Cong' 372.6 '18' 'Ctrl' 'Double' 'Inc' 464.2 '18' 'Ctrl' 'Spatial' 'Neut' 337.4 '18' 'Ctrl' 'Spatial' 'Cong' 338.3 '18' 'Ctrl' 'Spatial' 'Inc' 407.7 '19' 'Ctrl' 'NoCue' 'Neut' 436.6 '19' 'Ctrl' 'NoCue' 'Cong' 421.7 '19' 'Ctrl' 'NoCue' 'Inc' 494.7 '19' 'Ctrl' 'Cent' 'Neut' 393.5 '19' 'Ctrl' 'Cent' 'Cong' 393.9 '19' 'Ctrl' 'Cent' 'Inc' 482.2 '19' 'Ctrl' 'Double' 'Neut' 368.6 '19' 'Ctrl' 'Double' 'Cong' 384.2 '19' 'Ctrl' 'Double' 'Inc' 477.8 '19' 'Ctrl' 'Spatial' 'Neut' 344.0 '19' 'Ctrl' 'Spatial' 'Cong' 339.6 '19' 'Ctrl' 'Spatial' 'Inc' 392.7 '20' 'Ctrl' 'NoCue' 'Neut' 412.5 '20' 'Ctrl' 'NoCue' 'Cong' 424.3 '20' 'Ctrl' 'NoCue' 'Inc' 488.2 '20' 'Ctrl' 'Cent' 'Neut' 372.9 '20' 'Ctrl' 'Cent' 'Cong' 393.0 '20' 'Ctrl' 'Cent' 'Inc' 475.3 '20' 'Ctrl' 'Double' 'Neut' 384.2 '20' 'Ctrl' 'Double' 'Cong' 366.5 '20' 'Ctrl' 'Double' 'Inc' 460.0 '20' 'Ctrl' 'Spatial' 'Neut' 338.1 '20' 'Ctrl' 'Spatial' 'Cong' 372.3 '20' 'Ctrl' 'Spatial' 'Inc' 418.3 Names of X columns: sid group cue flanker mean_rt Sample Range:(leave blank to include all observations) From: To: Response : Variable 1 Within Ss Factor : Variable 2 Within Ss Factor : Variable 3 Between Ss Factor : Variable 4 Subject Identifier Column : Variable 5 Chart options Width: Height: Title: Label y-axis: Label x-axis:

 Source code of R module cat1 <- as.numeric(par1) # cat2<- as.numeric(par2) # cat3 <- as.numeric(par3) cat4 <-as.numeric(par4) cat5 <-as.numeric(par5) x <- t(x) x1<-as.numeric(x[,cat1]) wf1<-as.character(x[,cat2]) wf2 <- as.character(x[,cat3]) bf1 <- as.character(x[,cat4]) sid<- as.character(x[,cat5]) # author of ez changed within subjects variable name from sid to wid xdf<-data.frame(x1,wf1, wf2, bf1, sid) (V1<-dimnames(y)[[1]][cat1]) (V2<-dimnames(y)[[1]][cat2]) (V3 <-dimnames(y)[[1]][cat3]) (V4 <-dimnames(y)[[1]][cat4]) (V5 <-dimnames(y)[[1]][cat5]) names(xdf)<-c(V1, V2, V3, V4, V5) library(ez) library(Cairo) (ezout <- ezANOVA(data=xdf, dv=.(mean_rt), wid=.(sid), within=.(cue, flanker), between=.(group) ) ) load(file='createtable') a<-table.start() nr <- nrow(ezout\$ANOVA) nc <- ncol(ezout\$ANOVA) a<-table.row.start(a) a<-table.element(a,'Repeated Measures ANOVA', nc+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'effect', 1,TRUE) a<-table.element(a,'Dfn',1,TRUE) a<-table.element(a,'DFd', 1,TRUE) a<-table.element(a, 'F', 1,TRUE) a<-table.element(a,'p', 1,TRUE) a<-table.element(a,'p<0.05', 1,TRUE) a<-table.element(a, 'ges', 1,TRUE) # generalized eta-sq - was partial eta-sq in earlier version a<-table.row.end(a) for ( i in 1:nr){ a<-table.row.start(a) a<-table.element(a,ezout\$ANOVA\$Effect[i], 1, TRUE) for(j in 2:nc){ if ( j != 6) # author of ez reduced number of columns in output from 8 a<-table.element(a,round(ezout\$ANOVA[[j]][i], digits=3), 1, FALSE) else a<-table.element(a, ezout\$ANOVA[[j]][i], 1, FALSE) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() nr <- nrow(ezout\$Mauchly) nc <- ncol(ezout\$Mauchly) a<-table.row.start(a) a<-table.element(a,'Mauchlys Test for Sphericity', nc+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'effect', 1,TRUE) a<-table.element(a,'W',1,TRUE) a<-table.element(a,'p', 1,TRUE) a<-table.element(a,'p<0.05', 1,TRUE) a<-table.row.end(a) for ( i in 1:nr){ a<-table.row.start(a) a<-table.element(a,ezout\$Mauchly\$Effect[i], 1, TRUE) for(j in 2:nc){ if (j != 4) a<-table.element(a,round(ezout\$Mauchly[[j]][i], digits = 3), 1, FALSE) else a<-table.element(a,ezout\$Mauchly[[j]][i], 1, FALSE) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() nr <- nrow(ezout\$Spher) nc <- ncol(ezout\$Sphe) a<-table.row.start(a) a<-table.element(a,'Sphericity Corrections', nc+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'effect', 1,TRUE) a<-table.element(a,'GGe',1,TRUE) a<-table.element(a,'p[GG]', 1,TRUE) a<-table.element(a,'p[GG]<0.05', 1,TRUE) a<-table.element(a,'HFe', 1,TRUE) a<-table.element(a,'p[HF]', 1,TRUE) a<-table.element(a,'p[HF]<0.05', 1,TRUE) a<-table.row.end(a) for ( i in 1:nr){ a<-table.row.start(a) a<-table.element(a,ezout\$Spher\$Effect[i], 1, TRUE) for(j in 2:nc){ if ( ! ((j == 4) | (j == 7)) ) a<-table.element(a,round(ezout\$Spher[[j]][i], digits=3), 1, FALSE) else a<-table.element(a,ezout\$Spher[[j]][i], 1, FALSE) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') ezP.between<-ezPlot(data = xdf, dv = .(mean_rt), between = .(group), wid = .(sid), do_lines=FALSE, x_lab="group", y_lab="RT" , x=.(group)) bitmap(file = "between.cairo") print(ezP.between) dev.off() ezstats_between<-ezStats(data = xdf, dv = .(mean_rt), between =.(group), wid = .(sid)) a<-table.start() nr <- nrow(ezstats_between) nc <- ncol(ezstats_between) a<-table.row.start(a) a<-table.element(a,'Between Effects Comparisons', nc+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) for(i in 1:nc){ a<-table.element(a, names(ezstats_between)[i], 1,TRUE) } a<-table.row.end(a) for ( i in 1:nr){ a<-table.row.start(a) a<-table.element(a,ezstats_between[[1]][i], 1, TRUE) for(j in 2:nc){ a<-table.element(a,ezstats_between[[j]][i], 1, FALSE) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable3.tab') ezP.within<-ezPlot(data = xdf, dv = .(mean_rt), within = .(cue, flanker), wid = .(sid), do_lines=TRUE, x_lab="flanker", y_lab="RT" , x=.(flanker), split=.(cue), split_lab = "cue") bitmap(file = "within.cairo") print(ezP.within) dev.off() ezstats_within <- ezStats(data = xdf, dv = .(mean_rt), within = .(cue, flanker), wid = .(sid)) a<-table.start() nr <- nrow(ezstats_within) nc <- ncol(ezstats_within) a<-table.row.start(a) a<-table.element(a,'Within Effects Comparisons', nc+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) for(i in 1:nc){ a<-table.element(a, names(ezstats_within)[i], 1,TRUE) } a<-table.row.end(a) for ( i in 1:nr){ a<-table.row.start(a) a<-table.element(a,ezstats_within[[1]][i], 1, TRUE) for(j in 2:nc){ a<-table.element(a, ezstats_within[[j]][i], 1, FALSE) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') -SERVER-vre.aston.ac.uk
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 Cite this software as: Ian E. Holliday, 2012, Mixed Within-Between Two-Way ANOVA (v1.0.3) in Free Statistics Software (v1.1.23-r7), Office for Research Development and Education, URL http://www.wessa.net/Ian.Holliday/rwasp_Mixed%20Model%20ANOVA.wasp/ The R code is based on : Mauchly, John W. (June 1940). Significance Test for Sphericity of a Normal n-Variate Distribution. The Annals of Mathematical Statistics 11 (2): 204–209
 Top | Output | Charts | References | History | Feedback
 Top | Output | Charts | References | History | Feedback