Comparison of size and orientation
for mobile tangible sliders
(improved from IHM 2016 paper)
Juan Rosso, Céline Coutrix
April 1, 2016
Please let us know if you notice any error at Celine.Coutrix (at) imag.fr
Data corresponding to this code
Utility functions
geom_mean <- function(x, na.rm=TRUE){
return(10^mean(log10(x), na.rm=TRUE))
}
ci <- function(x) {
nb = length(x)
icp = mean(x, na.rm=TRUE) + 1.96 * sd(x) / sqrt(nb)
icm = mean(x, na.rm=TRUE) - 1.96 * sd(x) / sqrt(nb)
return(c(icm, icp))
}Loading data
data <- data.frame()
p <- "../data/SizeOrientationLogs/"
files <- list.files(path=p, pattern="*.csv")
for(file in files)
{
df <- read.csv(paste(p, file, sep='/'), sep=";")
data <- rbind(data, df)
}We assign now the right type to variables, make naming more explicit, splitting LengthOrientation into two column – one for each variable
data$Participant <- as.factor(data$Participant)
data$Overshoot <- as.numeric(data$Overshoot)
data$MovementTime <- as.numeric(data$MovementTime)
levels(data$Position) <- c("Down", "Up")
data <- within(data, {
Length <- substr(LengthOrientation, 1, 5)
Orientation <- substr(LengthOrientation, 7, 499)
})
data$Length <- as.factor(data$Length)
data$Orientation <- as.factor(data$Orientation) Checking data
table(data$Participant, data$Grasp)##
## 1H 2H
## 1 64 64
## 2 64 64
## 3 64 64
## 4 64 64
## 5 64 64
## 6 64 64
## 7 64 64
## 8 64 64
## 9 64 64
## 10 64 64table(data$Participant, data$LengthOrientation)##
## large-tilted large-vertical small-tilted small-vertical
## 1 32 32 32 32
## 2 32 32 32 32
## 3 32 32 32 32
## 4 32 32 32 32
## 5 32 32 32 32
## 6 32 32 32 32
## 7 32 32 32 32
## 8 32 32 32 32
## 9 32 32 32 32
## 10 32 32 32 32table(data$Participant, data$Position)##
## Down Up
## 1 64 64
## 2 64 64
## 3 64 64
## 4 64 64
## 5 64 64
## 6 64 64
## 7 64 64
## 8 64 64
## 9 64 64
## 10 64 64table(data$Participant, data$Repetition)##
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 5 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 6 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
## 10 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8Aggregating Overshoot and MovementTime data
dataAggMT <- aggregate(data$MovementTime,
by=list(data$Participant, data$Length, data$Orientation, data$Grasp, data$Position),
FUN=geom_mean)
colnames(dataAggMT) <- c("Participant", "Length", "Orientation", "Grasp", "Position", "MovementTime")
dataAggO <- aggregate(data$Overshoot,
by=list(data$Participant, data$Length, data$Orientation, data$Grasp, data$Position),
FUN=sum)
colnames(dataAggO) <- c("Participant", "Length", "Orientation", "Grasp", "Position", "Overshoot")Plotting movement time
dataAggMT$Mixed <- paste(dataAggMT$Length, dataAggMT$Orientation, sep="-")
library("sciplot")
p <- lineplot.CI(x.factor = dataAggMT$Mixed,
dataAggMT$MovementTime,
group=dataAggMT$Grasp,
type="p",
err.width=0,
ci.fun= ci,
xlab="Conditions",
ylab="Mean Movement Time (s)",
pch = c(18,16,15),
ylim=range(0,2.5))
grid (NA, NULL, lty = 6, col = "cornsilk2")
p## $vals
## 1H 2H
## large-tilted 1.305188 1.274173
## large-vertical 1.343233 1.306857
## small-tilted 1.867981 1.591435
## small-vertical 1.773250 1.438768
##
## $CI
## 1H 2H
## large-tilted Numeric,2 Numeric,2
## large-vertical Numeric,2 Numeric,2
## small-tilted Numeric,2 Numeric,2
## small-vertical Numeric,2 Numeric,2Plotting overshoot
library("sciplot")
dataAggO$Mixed <- paste(dataAggO$Length, dataAggO$Orientation, sep="-")
p <- lineplot.CI(x.factor = dataAggO$Mixed,
dataAggO$Overshoot,
group=dataAggO$Grasp,
type="p",
err.width=0,
ci.fun= ci,
xlab="Conditions",
ylab="Number of overshoots",
pch = c(18,16,15),
ylim=range(0,15))
grid (NA, NULL, lty = 6, col = "cornsilk2")
p## $vals
## 1H 2H
## large-tilted 0.80 1.25
## large-vertical 0.35 0.60
## small-tilted 4.80 3.50
## small-vertical 3.95 3.70
##
## $CI
## 1H 2H
## large-tilted Numeric,2 Numeric,2
## large-vertical Numeric,2 Numeric,2
## small-tilted Numeric,2 Numeric,2
## small-vertical Numeric,2 Numeric,2Impact of independant variables on movement time
Normality and Homogeneity checks
Preview of data distribution
hist(dataAggMT$MovementTime, breaks=seq(0,max(dataAggMT$MovementTime)+1,0.5))
qqnorm(dataAggMT$MovementTime)
qqline(dataAggMT$MovementTime)
Normality tests
shapiro.test(dataAggMT$MovementTime)##
## Shapiro-Wilk normality test
##
## data: dataAggMT$MovementTime
## W = 0.97024, p-value = 0.00158Normality of Movement Time cannot be assumed.
Homogeneity tests
For each independant variable
bartlett.test(MovementTime~Length, dataAggMT)##
## Bartlett test of homogeneity of variances
##
## data: MovementTime by Length
## Bartlett's K-squared = 13.323, df = 1, p-value = 0.0002622bartlett.test(MovementTime~Orientation, dataAggMT)##
## Bartlett test of homogeneity of variances
##
## data: MovementTime by Orientation
## Bartlett's K-squared = 0.012641, df = 1, p-value = 0.9105bartlett.test(MovementTime~Grasp, dataAggMT)##
## Bartlett test of homogeneity of variances
##
## data: MovementTime by Grasp
## Bartlett's K-squared = 0.0069136, df = 1, p-value = 0.9337Variances cannot be considered equal for Length, but it can for Orientation and Grasp.
Impact of Length
We further analyze Length, as it seems to cause an important difference in the previous graphs.
Friedman test
dataTest <- aggregate(data$MovementTime,
by=list(data$Participant, data$Length),
FUN=geom_mean)
colnames(dataTest) <- c("Participant", "Length", "MovementTime")
dataTest <- cbind(dataTest[dataTest$Length=='small',]$MovementTime, dataTest[dataTest$Length=='large',]$MovementTime)
friedman.test(dataTest)##
## Friedman rank sum test
##
## data: dataTest
## Friedman chi-squared = 10, df = 1, p-value = 0.001565There is indeed a significant impact of Length on Movement Time.
Post-hoc comparisons
From the graph, it seems that there is an interaction between Length and Orientation. We first analyze movement time for small sliders, and then for large sliders.
Is there a significant impact of orientation on movement time for small sliders?
dataTest <- aggregate(data[data$Length=='small',]$MovementTime,
by=list(data[data$Length=='small',]$Participant, data[data$Length=='small',]$Orientation),
FUN=geom_mean)
colnames(dataTest) <- c("Participant", "Orientation", "MovementTime")
pairwise.wilcox.test(dataTest$MovementTime, dataTest$Orientation, p.adj="bonferroni", exact=F, paired=T)##
## Pairwise comparisons using Wilcoxon signed rank test
##
## data: dataTest$MovementTime and dataTest$Orientation
##
## tilted
## vertical 0.041
##
## P value adjustment method: bonferroniThere is a significant impact of orientation on movement time for small sldiers.
Is there a significant impact of orientation on movement time for large sliders?
dataTest <- aggregate(data[data$Length=='large',]$MovementTime,
by=list(data[data$Length=='large',]$Participant, data[data$Length=='large',]$Orientation),
FUN=geom_mean)
colnames(dataTest) <- c("Participant", "Orientation", "MovementTime")
pairwise.wilcox.test(dataTest$MovementTime, dataTest$Orientation, p.adj="bonferroni", exact=F, paired=T)##
## Pairwise comparisons using Wilcoxon signed rank test
##
## data: dataTest$MovementTime and dataTest$Orientation
##
## tilted
## vertical 0.54
##
## P value adjustment method: bonferroniThere is no significant impact of orientation on movement time for large sliders.