# ::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' 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'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')
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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
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 To cite Wessa.net in publications use:Wessa, P. (2013), Free Statistics Software, Office for Research Development and Education, version 1.1.23-r7, URL http://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.1.23-r7Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net