anova(md)
anova(mds)
anova(msd)
library(car)
Anova(mds)
drop1(mds,test="F")
tg1 <- aov(len~supp+as.factor(dose),data=ToothGrowth)
summary(tg1)
Anova(tg1)
tg2 <- aov(len~supp*as.factor(dose),data=ToothGrowth)
tg2 <- aov(len~supp + as.factor(dose) + supp:as.factor(dose),data=ToothGrowth)
tg2
summary(tg2)
Anova(tg2)
tg3 <- aov(len~supp:as.factor(dose),data=ToothGrowth)
tg33
tg3
summary(tg3)
Anova(tg3)
anova(tg3,tg2)
##we can obtain complete tables of means. This gives the relative effects:
model.tables(tg2)
model.tables(tg3)
##this gives the absolute mean values
model.tables(tg2,type="means")
model.tables(tg3,type="means")
?Anova
tg3 <- aov(len~supp:as.factor(dose),data=ToothGrowth)
Anova(tg3)
Anova(tg2)
##this gives the absolute mean values
model.tables(tg2,type="means")
model.tables(tg2)
setwd("~/Dropbox/courses/5210-2020/web-5210/psy5210/Projects/Chapter19")
##Exercise Solution
dat.raw <- read.table("tsp-all.txt",header=T)
dat <- dat.raw[ dat.raw$subnum !="B1"&dat.raw$cycle>0,]
dat$cycle <- as.factor(dat$cycle)
contrasts(dat$cycle) <- contr.poly(levels(dat$cycle))
dat$mopp <- as.factor(dat$mopp)
tab1 <- tapply(dat$eff,list(size=dat$numpos,cycle=dat$cycle),mean)
matplot(c(10,20,30),tab1,type="o",pch=c(1:4),xlab="Problem size",ylab="Efficiency")
legend(25,1.08,paste("Cycle", 1:4),lty=1:4,pch=1:4,col=1:4)
matplot(c(10,20,30),tab1,type="o",pch=c(1:4),xlab="Problem size",ylab="Efficiency",lwd=2)
legend(25,1.08,paste("Cycle", 1:4),lty=1:4,pch=1:4,col=1:4)
##Build and test the ANCOVA models:
tsp0 <- aov(eff~numpos,data=dat)
tsp1 <- aov(eff~numpos+cycle,data=dat)
tsp2 <- aov(eff~numpos*cycle,data=dat)
tsp3 <- aov(eff~test+subnum+cycle+(mopp),data=dat)
Anova(tsp3)
Anova(tsp1)
Anova(tsp2, type="II") #test the interaction
Anova(tsp2,type="III") #test the interaction
##These don't differ:
Anova(tsp1, type="II") #test the interaction
Anova(tsp1,type="III") #test the interaction
##what about post-hoc tests:
TukeyHSD(tsp3,which="cycle") ##won't work!
#look at cycle in each case
TukeyHSD(tsp1,which="cycle")
TukeyHSD(tsp2,which="cycle")
TukeyHSD(tsp3,which="cycle")
library(sjstats)
anova_stats(tsp1)
?anova_stats
anova_stats(tsp2)
##Exercise Solution
dat.raw <- read.table("tsp-all.txt",header=T)
dat <- dat.raw[ dat.raw$subnum !="B1"&dat.raw$cycle>0,]
dat$cycle <- as.factor(dat$cycle)
contrasts(dat$cycle) <- contr.poly(levels(dat$cycle))
dat$mopp <- as.factor(dat$mopp)
tab1 <- tapply(dat$eff,list(size=dat$numpos,cycle=dat$cycle),mean)
matplot(c(10,20,30),tab1,type="o",pch=c(1:4),xlab="Problem size",ylab="Efficiency",lwd=2)
legend(25,1.08,paste("Cycle", 1:4),lty=1:4,pch=1:4,col=1:4)
tab1
dat[1:5,]
tsp1
tsp2 <- aov(eff~numpos*cycle,data=dat)   ##interaction
tsp3 <- aov(eff~test+subnum+cycle+(mopp),data=dat)   ##MOPP is the thing we really care about
tsp3
summary(tsp3)
Anova(tsp3)
dat$cycle
table(dat$cycle,dat$test)
Anova(tsp3)
tsp3b <- aov(eff~test+subnum+(mopp)+ mopp:numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsb3b)
Anova(tsp3b)
tsp3b <- aov(eff~subnum+(mopp)+ cycle+ mopp:numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp3b)
tsp4a <- aov(eff~subnum+(mopp)+ cycle+ numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4a)
tsp4a <- aov(eff~subnum+(mopp)+ cycle,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4a)
tsp4a <- aov(eff~subnum+(mopp)+ cycle+ numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4b)
tsp4b <- aov(eff~subnum+(mopp)+ cycle+ numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4b)
tsp4a <- aov(eff~subnum+(mopp)+ cycle,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4a)
tsp4b <- aov(eff~subnum+(mopp)+ cycle+ numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4b)
Anova(tsp4a,tsp4b)
anova(tsp4a,tsp4b)
Anova(tsp4b)
##Is the numpos covariate significant?
anova(tsp4a,tsp4b)
Anova(tsb4b,type="III")
Anova(tsp4b,type="III")
Anova(tsp4b)
Anova(tsp4b,type="III")
Anova(tsp2, type="II") #test the interaction
Anova(tsp2,type="III") #test the interaction
Anova(tsp4b,type="II")
Anova(tsp4b,type="III")
Anova(tsp1)
Anova(tsp2, type="II") #test the interaction
Anova(tsp2,type="III") #test the interaction
Anova(tsp1)
##These don't differ:
Anova(tsp1, type="II") #test the interaction
Anova(tsp1,type="III") #test the interaction
Anova(tsp2, type="II") #test the interaction
Anova(tsp2,type="III") #test the interaction
tsp3 <- aov(eff~test+subnum+cycle+(mopp),data=dat)   ##MOPP is the thing we really care about
##subnum is a factor accounting for consistency within people (repeated measures)
## Although this is not exactly the right way to hand that predictor.
## test is the problem number, sort of like subnum.
##cycle and test were confounded intentionally, so adding cycle won't do anything
table(dat$cycle,dat$test)
Anova(tsp3)
tsp3 <- aov(eff~test+subnum+cycle+(mopp),data=dat)   ##MOPP is the thing we really care about
##subnum is a factor accounting for consistency within people (repeated measures)
## Although this is not exactly the right way to hand that predictor.
## test is the problem number, sort of like subnum.
##cycle and test were confounded intentionally, so adding cycle won't do anything
table(dat$cycle,dat$test)
Anova(tsp3)
tsp4a <- aov(eff~subnum+(mopp)+ cycle,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4a)
#Here we add problem size as an independent covariate:
tsp4b <- aov(eff~subnum+(mopp)+ cycle+ numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
##Is the numpos covariate significant?  Comparing type-II and type-III, the main effects actually have the same values
anova(tsp4a,tsp4b)
Anova(tsp4b,type="II")
Anova(tsp4b,type="III")
tsp4c <- aov(eff~subnum+(mopp)+ cycle+ mopp:numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4c)
anova(tsp4c,tsp4b)
tsp4b <- aov(eff~subnum+(mopp)+ cycle+ numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
##Is the numpos covariate significant?  Comparing type-II and type-III, the main effects actually have the same values
anova(tsp4a,tsp4b)
Anova(tsp4b,type="II")
Anova(tsp4b,type="III")
##  Problem size is significant, and so are the other main effects (and these no longer depend on type-II vs. type-III)
##
#What if we added an interaction term?
tsp4c <- aov(eff~subnum+(mopp)+ cycle+ mopp:numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4c)
anova(tsp4c,tsp4b)
Anova(tsp4c,type="I")
Anova(tsp4c,type="II")
Anova(tsp4c,type="III")
anova(tsp4c,tsp4b)
tsp4c <- aov(eff~subnum+(mopp)+ cycle+ +numpos+ mopp:numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4c,type="II")
Anova(tsp4c,type="III")
tsp4c <- aov(eff~subnum+(mopp)+ cycle+ numpos*mopp,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4c,type="II")
Anova(tsp4c,type="III")
anova(tsp4c,tsp4b)
##what about post-hoc tests:
TukeyHSD(tsp3,which="cycle") ##won't work!
#look at cycle in each case
TukeyHSD(tsp1,which="cycle")
TukeyHSD(tsp2,which="cycle")
TukeyHSD(tsp2,which="cycle")
TukeyHSD(tsp2,which="cycle")  #ditto
TukeyHSD(tsp3,which="cycle")
tsp3
summary(tsp3)
library(sjstats)
anova_stats(tsp1)
anova_stats(tsp3)
knitr::opts_chunk$set(echo = TRUE)
data <- read.csv("spokenduration.csv")
data$length <- as.factor(rowSums(data[,2:12]))
setwd("~/Dropbox/courses/5210-2020/problemsets/ps11")
knitr::opts_chunk$set(echo = TRUE)
data <- read.csv("spokenduration.csv")
data$length <- as.factor(rowSums(data[,2:12]))
data[1:5,]
m1 <- aov(time~length,data=data)
l1 <- lm(time~length,data=data)
summary(m1)
summary(l1)
sjstats::anova_stats(m1)
sjstats::anova_stats(l1)
m1 <- aov(time~length,data=data)
l1 <- lm(time~length,data=data)
summary(m1)
summary(l1)
library(agricolae)
HSD.test(m1,trt="length",group=T,console=T)
library(sjstats)
sjstats::anova_stats(m1)
sjstats::anova_stats(l1)
eta_sq(m1)
omega_sq(m1,partial=F)
anova(l1,m1)
l2 <- lm(time~as.numeric(length),data=data)
anova(l1,m2)
l2 <- lm(time~as.numeric(length),data=data)
anova(l1,l2)
dat[1:5,]
data[1:5,]
m2a <- lm(time~cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal,data=data)
m2a <- lm(time~cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal + as.numeric(length),data=data)
m2a
m2a <- lm(time~(cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal)* as.numeric(length),data=data)
m2b <- lm(time~(cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal)* as.numeric(length),data=data)
m2a <- lm(time~cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal,data=data)
m2b <- lm(time~(cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal)* as.numeric(length),data=data)
m2b
m2b <- lm(time~(cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal):as.numeric(length),data=data)
m2b
m2b <- lm(time~as.numeric(length) +(cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal):as.numeric(length),data=data)
m2b
summary(m2b)
m2b <- lm(time~(cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal):as.numeric(length),data=data)
summary(m2b)
anova(m2a,m2b)
anova(m2a,m2b,test="F")
m2b <- lm(time~(cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal)*as.numeric(length),data=data)
anova(m2a,m2b,test="F")
lm(time~length*cult,data=data)
summary(lm(time~length*cult,data=data))
summary(lm(time~length*dare,data=data))
summary(lm(time~length*hint,data=data))
summary(lm(time~length*hint*cult,data=data))
summary(lm(time~length*zeal,data=data))
summary(lm(time~length*truth,data=data))
summary(lm(time~length*verb,data=data))
data <- read.csv("spokenduration.csv")
data$length <- rowSums(data[,2:12])
data$lengthC <- as.factor(rowSums(data[,2:12]))
m1 <- aov(time~lengthC,data=data)
l1 <- lm(time~lengthC,data=data)
summary(m1)
summary(l1)
l2 <- lm(time~length,data=data)
anova(l1,l2)
##there is no difference between these, so we would probably prefer the smaller model treating length as a numeric
library(agricolae)
HSD.test(m1,trt="lengthC",group=T,console=T)
library(sjstats)
sjstats::anova_stats(m1)
sjstats::anova_stats(l1)
eta_sq(m1)
omega_sq(m1,partial=F)
contrasts(data$lengthC) <- contr.sum(levels(data$lengthC))
lm(time~lengthC,data=data)
lm2a <- lm(time~lengthC,data=data)
#contrasts(data$lengthC) <- contr.sum(levels(data$lengthC))
lm2a <- lm(time~cult+dare+fate+guess+hint+mood+oath+plea=rush+verb+zeal,data=data)
#contrasts(data$lengthC) <- contr.sum(levels(data$lengthC))
lm2a <- lm(time~cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal,data=data)
lm2a <- lm(time~cult+dare+fate+guess+hint+mood+oath+plea+rush+verb+zeal+0,data=data)
lm2a
barplot(lm2a$coefficients)
barplot(lm2a$coefficients,ylab="Duration per word (s)")
m2a <- lm(time~verb,data=data)
m2a
summary(m2a)
data.verb <- data[data$verb,]
m3a <- lm(time~verb,data=data.verb)
m3a <- lm(time~verb*length,data=data)
m3b <- lm(time~verb*length,data=data)
summary(m3a)
m3b
data.verb$length <- contr.poly(data.verb$length)
m3a <- lm(time~verb,data=data.verb)
m3b <- lm(time~verb*length,data=data)
anova(m3a,m3b)
summar(m3a)
summary(m3a)
summary(m3b)
data$length <- contr.poly(data$length)
data$length <- contr.poly(data$length)
data$lengthC <- contr.poly(data$lengthC)
data$lengthC
data$lengthC <- contr.poly(levels(data$lengthC))
contrasts(data$lengthC) <- contr.poly(levels(data$lengthC))
m3a <- lm(time~verb,data=data.verb)
m3b <- lm(time~verb*length,data=data)
anova(m3a,m3b)
m3a <- lm(time~verb,data=data)
m3b <- lm(time~verb*length,data=data)
anova(m3a,m3b)
summary(m3b)
m3a <- lm(time~verb+length,data=data)
m3b <- lm(time~verb*length,data=data)
summary(m3b)
anova(m3a,m3b)
m3a
summary(m3a)
anova(m3a)
summary(m3b)
library(car)
contrasts(data$subject) <- contr.sum(levels(data$subject))
data$subject
contrasts(data$subject) <- contr.sum(levels(as.factor(data$subject)))
data$subject <- factor(data$subject, contrasts= contr.sum(levels(as.factor(data$subject))))
contrasts(data$subject) <- contr.sum(levels(as.factor(data$subject))))
data$subject <- factor(data$subject)
contrasts(data$subject) <- contr.sum(levels(as.factor(data$subject)))
m2 <- aov(time~length+subject,data=data)
Anova(m2)
model.tables(m2)
model.tables(m2)
m2 <- aov(time~lengthC+subject,data=data)
Anova(m2)
model.tables(m2)
library(car)
data$subject <- factor(data$subject)
contrasts(data$subject) <- contr.sum(levels(as.factor(data$subject)))
m2 <- aov(time~lengthC+subject,data=data)
Anova(m2)
model.tables(m2)
eta_sq(m2)
omega_sq(m2,partial=F)
TukeyHSD(m2)
anova_stats(m2)
l3 <- lm(time~lengthC*subject,data=data)
m3 <- aov(time~lengthC*subject,data=data)
sjstats::anova_stats(m3)
Anova(l3)
summary(l3)
TukeyHSD(m3)
options(max.print=500)
tapply(data$time[data$length==6],list(data$subject[data$length==6]),mean)
?TukeyHSD
TukeyHSD(m3,ordered=F,which="subject:lengthC")
HSD.test(m3,console=T,group=T)
data[1:5,]
TukeyHSD(m3,ordered=F)
HSD.test(m3,"console=T,group=T)
HSD.test(m3,"",console=T,group=T)
)
)
)"
HSD.test(m3,"",console=T,group=T)
HSD.test(m3,"lengthC:subject",console=T,group=T)
HSD.test(m3,"lengthC",console=T,group=T)
TukeyHSD(m3,which="lengthC:subject",ordered=F)
tuk <- TukeyHSD(m3,which="lengthC:subject",ordered=F)
options(max.print=500)
tuk
tuk$`lengthC:subject`[1,]
rowNames(tuk$`lengthC:subject`)
rownames(tuk$`lengthC:subject`)
keep <- substr(rownames(tuk$`lengthC:subject`),1,1)="6"
tuk[keep,]
keep <- substr(rownames(tuk$`lengthC:subject`),1,1)=="6"
tuk[keep,]
tuk$`lengthC:subject`[keep,]
keep <- (substr(rownames(tuk$`lengthC:subject`),1,1)=="6") & (substr(rownames(tuk$`lengthC:subject`),7,7)=="6")
tuk$`lengthC:subject`[keep,]
tukey6 <- tuk$`lengthC:subject`[keep,]
tukey6
tukey6[,4]
tukey6[tukey6[,4]<.01,]
l4 <- lm(time~length*subject,data=data)
m4 <- aov(time~length*subject,data=data)
Anova(l4)
summary(l4)
options(max.print=2000)
#TukeyHSD(m4)
options(max.print=500)
HSD.test(m4,trt="subject",console=T,group=T)
eta_sq(m4)
knitr::opts_chunk$set(echo = TRUE)
data <- read.csv("spokenduration.csv")
data$length <- rowSums(data[,2:12])   #numerical list-length
data$lengthC <- as.factor(rowSums(data[,2:12]))  #categorical listlength
set.seed(100)
gender <- as.factor(c("M","M","M","M","M","M","M","M","M","M",
"F","F", "F","F", "F","F", "F","F", "F","F"))
##we are worried about interactions, so be sure we have an orthogonal set of contrasts:
contrasts(gender)<- contr.poly(2)
experience <- c(4,6,10,5,3,8,12,15,9,19,
5,3,5, 6,1,3,5, 9,10,2)
salary1<-c(52.26,59.28,71.10,56.69,49.40,65.80,77.43,85.94,68.99,98.21,56.22,50.42,
55.12,59.74,43.51,50.91,55.69,67.65,70.18,46.30) + rnorm(20)*5
salary2 <- c(53.43,59.39,70.65,55.74,49.68,65.52,76.47,85.92,67.31,97.41,50.49,
45.23,50.3,53.17,39.92,45.93,50.55,63.53,66.77,41.81)+rnorm(20)*2
salary3 <- c(46.6,55.01,71.21,51.82,42.83,62.5,78.35,90.98,67.6,107.52,40.54,37.25,
41.83,42.81,33.34,36.46,40.47,48.37,51.42,34.56)+rnorm(20)*2
#pdf("c19-salaries.pdf",width=8,height=5)
par(mfrow=c(1,3))
boxplot(salary1~gender,col="gold",main="Salary group 1")
boxplot(salary2~gender,col="gold",main="Salary group 2")
boxplot(salary3~gender,col="gold",main="Salary group 3")
t.test(salary1~gender)
t.test(salary2~gender)
t.test(salary3~gender)
par(mfrow=c(1,3))
plot(experience,salary1,col=as.numeric(gender),pch=16,cex=2)
plot(experience,salary2,col=as.numeric(gender),pch=16,cex=2)
plot(experience,salary3,col=as.numeric(gender),pch=16,cex=2)
m1.0 <- lm(salary1~experience)
Anova(m1.0) ##experience matters!
m1 <- lm(salary1~gender+experience)
Anova(m1,type="II")
Anova(m1,type="II")
summary(aov(salary1~experience+gender)) ## Type 1--wrong
summary(aov(salary1~gender+experience))## type 1 -- wrong
Anova(m1,type="II")
m2.0 <- lm(salary2~experience) ##experience matters!
Anova(m2.0)
m2 <- lm(salary2~gender+experience)
Anova(m2,type="II")
m2.0
m2
summary(m2)
##how about the third company?
m3.0 <- lm(salary3~experience)
Anova(m3.0)
m3 <- lm(salary3~gender+experience)
Anova(m3,type="II") ##experience+gender matter
plot(experience,salary1,col=as.numeric(gender),pch=16)
abline(m1$coef[1]+m1$coef[2],m1$coef[3],col=2)
abline(m1$coef[1]-m1$coef[2],m1$coef[3],col=1)
plot(experience,salary2,col=as.numeric(gender),pch=16)
abline(m2$coef[1]+sqrt(.5)*m2$coef[2],m2$coef[3],col=2)
abline(m2$coef[1]-sqrt(.5)*m2$coef[2],m2$coef[3],col=1)
plot(experience,salary3,col=as.numeric(gender),pch=16)
abline(m3$coef[1]+sqrt(.5)*m3$coef[2],m3$coef[3],col=2)
abline(m3$coef[1]-sqrt(.5)*m3$coef[2],m3$coef[3],col=1)
##what about the interactions?
m1b <- lm(salary1~gender * experience)
Anova(m1b,type="III")
anova(m1b,m1)  ##no difference--interaction does not matter.
m2b <- lm(salary2~gender * experience)
Anova(m2b,type="III")
m3b <- lm(salary3~gender * experience)
Anova(m3b,type="III")
plot(experience,salary3,col=as.numeric(gender),pch=16)
abline(m3b$coef[1]+sqrt(.5)*m3b$coef[2],m3b$coef[3]+sqrt(.5)*m3b$coef[4],col=2)
abline(m3b$coef[1]-sqrt(.5)*m3b$coef[2],m3b$coef[3]-sqrt(.5)*m3b$coef[4],col=1)
Anova(m3b,type="II")
m3b
summary(m3b)
##Exercise Solution
dat.raw <- read.table("tsp-all.txt",header=T)
setwd("~/Dropbox/courses/5210-2020/web-5210/psy5210/Projects/Chapter19")
##Exercise Solution
dat.raw <- read.table("tsp-all.txt",header=T)
dat <- dat.raw[ dat.raw$subnum !="B1"&dat.raw$cycle>0,]
dat$cycle <- as.factor(dat$cycle)
dat[1:5,]
dat$cycle <- as.factor(dat$cycle)
contrasts(dat$cycle) <- contr.poly(levels(dat$cycle))
dat$mopp <- as.factor(dat$mopp)
tab1 <- tapply(dat$eff,list(size=dat$numpos,cycle=dat$cycle),mean)
matplot(c(10,20,30),tab1,type="o",pch=c(1:4),xlab="Problem size",ylab="Efficiency",lwd=2)
legend(25,1.08,paste("Cycle", 1:4),lty=1:4,pch=1:4,col=1:4)
matplot(c(10,20,30),tab1,type="o",pch=c(1:4),xlab="Problem size",ylab="Efficiency",lwd=2)
legend(25,1.08,paste("Cycle", 1:4),lty=1:4,pch=1:4,col=1:4)
##Build and test the ANCOVA models:
tsp0 <- aov(eff~numpos,data=dat)   ##predict efficiency by problem size alone; essentially a regression
tsp1 <- aov(eff~numpos+cycle,data=dat)   ##problem size + cycle; cycle is categorical
tsp2 <- aov(eff~numpos*cycle,data=dat)   ##interaction
Anova(tsp0)
Anova(tsp1)
tsp2 <- aov(eff~numpos*cycle,data=dat)   ##interaction
Anova(tsp2, type="II") #test the interaction
dat[1:10,]
nrow(dat)
Anova(tsp2,type="III") #test the interaction
Anova(tsp2, type="II") #test the interaction
Anova(tsp1)
Anova(tsp2, type="II") #test the interaction
Anova(tsp2,type="III") #test the interaction
tsp2
dat[1:5,]
tsp3 <- aov(eff~test+subnum+cycle+(mopp),data=dat)   ##MOPP is the thing we really care about
##subnum is a factor accounting for consistency within people (repeated measures)
## Although this is not exactly the right way to hand that predictor.
## test is the problem number, sort of like subnum.
Anova(tsp3)
##cycle and test were confounded intentionally, so adding cycle won't do anything
table(dat$cycle,dat$test)
Anova(tsp3)
tsp4a <- aov(eff~subnum+ as.factor(mopp)+ cycle,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4a)
tsp4a <- aov(eff~subnum+ (mopp)+ cycle,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4a)
#Here we add problem size as an independent covariate:
tsp4b <- aov(eff~subnum+(mopp)+ cycle+ numpos,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4b,type="III")
Anova(tsp4b,type="II")
tsp4c <- aov(eff~subnum+(mopp)+ cycle+ numpos*mopp,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4c,type="II")
Anova(tsp4c,type="III")
tsp4c <- aov(eff~subnum*numpos+(mopp)+ cycle+ mopp,data=dat)   ##MOPP is the thing we really care about; we will include problem size as a covariate
Anova(tsp4c,type="II")
library(sjstats)
anova_stats(tsp1)
sjstats::eta_sq(tsp1)