Data Analysis example with data from a real study
This webpage was generated with R Markdown.
It is meant to give examples of data analysis and how to interpret it based on real study-data. This webpage is also very much linked to our Alt IHM 2017 paper: La Difference Significative entre Valeurs p et Intervalles de Confiance (available in French here https://hal.inria.fr/hal-01562281/document). An english translation of most of the article is available in the Appendix A of Lonni’s Besancon’s thesis. It is available here: https://tel.archives-ouvertes.fr/tel-01684210/document
If you want to credit this page and its explanations, you can use the following bibtex files:
- The French article: https://hal.inria.fr/hal-01562281v2/bibtex
- The Engligh translation in the Appendix: https://tel.archives-ouvertes.fr/tel-01684210v1/bibtex
Packages, environment and helper functions.
Packages and environment
R and RStudio have been used to generate this webpage and its data analysis. You will need to install at least the packages ggplot2 and PropCIs. They are available in the CRAN repository. You can simply type in the console:
install.packages("ggplot2")
install.packages("PropCIs")Helper Functions
We first need to declare all the helper function that we are going to use in our example.
Confidence Intervals
Here are the helper function for the computation of Bootstrap Confidence Intervals. You can copy/paste into a file for BootstrapCI_macros.
################################################################
# Bootstrap CI Helper Functions.
# Computes bootstrap confidence intervals with the sensible defaults.
# 2014 Pierre Dragicevic
################################################################
# For more details
# See http://www.mayin.org/ajayshah/KB/R/documents/boot.html for boot
# and (Kirby and Gerlanc, 2013) http://web.williams.edu/Psychology/Faculty/Kirby/bootes-kirby-gerlanc-in-press.pdf for bootES and for referencing the bootstrap method in your paper
library(boot)
library(PropCIs)
# If set to TRUE, bootstrap intervals remain the same across executions.
deterministic <- TRUE
# The number of bootstrap resamples. Typically recommended is >= 1,000.
# The higher the number, the more precise the interval but also the slower
# the computation.
replicates <- 10000
# The method for computing intervals. The adjusted bootstrap
# percentile (BCa) method is recommended by (Kirby and Gerlanc, 2013)
# and should work in most cases. For other methods type help(boot.ci).
# FIXME: changing this does not work
intervalMethod <- "bca"
# Number of significant digits used for text output. Using many digits
# is not recommended as it gives a misleading impression of precision.
significantDigits <- 3
#####################################################################
# Statistics
samplemedian <- function(x, d) {
return(median(x[d]))
}
samplemean <- function(x, d) {
return(mean(x[d]))
}
# Data transformations
# No transformation, yields arithmetic means.
identityTransform <- c(
function(x) {return (x)}, # the transformation
function(x) {return (x)}, # the inverse transformation
TRUE # TRUE if increasing, FALSE otherwise
)
# Log transformation, yields geometric means.
logTransform <- c(
function(x) {return (log(x))}, # the transformation
function(x) {return (exp(x))}, # the inverse transformation
TRUE # TRUE if increasing, FALSE otherwise
)
# Inverse transformation, yields harmonic means.
inverseTransform <- c(
function(x) {return (1/x)}, # the transformation
function(x) {return (1/x)}, # the inverse transformation
FALSE # TRUE if increasing, FALSE otherwise
)
# Returns the point estimate and confidence interval in an array of length 3
bootstrapCI <- function(statistic, datapoints) {
# Compute the point estimate
pointEstimate <- statistic(datapoints)
# Make the rest of the code deterministic
if (deterministic) set.seed(0)
# Generate bootstrap replicates
b <- boot(datapoints, statistic, R = replicates, parallel="multicore")
# Compute interval
ci <- boot.ci(b, type = intervalMethod)
# Return the point estimate and CI bounds
# You can print the ci object for more info and debug
lowerBound <- ci$bca[4]
upperBound <- ci$bca[5]
return(c(pointEstimate, lowerBound, upperBound))
}
# Returns the mean and its confidence interval in an array of length 3
bootstrapMeanCI <- function(datapoints) {
return(bootstrapCI(samplemean, datapoints))
}
# Returns the median and its confidence interval in an array of length 3
bootstrapMedianCI <- function(datapoints) {
return(bootstrapCI(samplemedian, datapoints))
}
# Returns the mean and its "classical" confidence interval in an array of length 3.
# Uses the t-distribution confidence interval for samples that are approximately normally
# distributed and/or large. Not a bootstrap method but included here for convenience.
exactMeanCI <- function(datapoints, transformation = identityTransform) {
datapoints <- transformation[[1]](datapoints)
pointEstimate <- mean(datapoints)
ttest <- t.test(datapoints)
lowerBound <- ttest[4]$conf.int[1]
upperBound <- ttest[4]$conf.int[2]
if (transformation[[3]])
return(transformation[[2]](c(pointEstimate, lowerBound, upperBound)))
else
return(transformation[[2]](c(pointEstimate, upperBound, lowerBound)))
}
# Returns a percentage and its confidence interval, for binary observations.
# Uses a confidence interval method for proportions. Not a bootstrap method but
# included here for convenience.
percentCI <- function(datapoints, value) {
ncorrect <- length(datapoints[datapoints == value])
total <- length(datapoints)
percent <- 100 * ncorrect / total
proportionCI <- midPci(x = ncorrect, n = total, conf.level = 0.95)
percentCIlow <- 100 * proportionCI$conf.int[1]
percentCIhigh <- 100 * proportionCI$conf.int[2]
return (c(percent, percentCIlow, percentCIhigh))
}
# Returns the point estimate and confidence interval in a human-legible text format
bootstrapCI.text <- function(statistic, datapoints, unit) {
result <- bootstrapCI(statistic, datapoints)
point <- result[1]
interval <- c(result[2], result[3])
# Format results in human-legible format using APA style
text <- paste(
prettyNum(point, digits=significantDigits),
unit,
", 95% CI [",
prettyNum(interval[1], digits=significantDigits),
unit,
", ",
prettyNum(interval[2], digits=significantDigits),
unit,
"]",
sep = "")
return(text)
}
# Returns the mean and its confidence interval in a human-legible text format
bootstrapMeanCI.text <- function(datapoints, unit) {
return(bootstrapCI.text(samplemean, datapoints, unit))
}
# Returns the median and its confidence interval in a human-legible text format
bootstrapMedianCI.text <- function(datapoints, unit) {
return(bootstrapCI.text(samplemedian, datapoints, unit))
}Plotting function helper
This function is designed to plot point estimates and confidence intervals for several factors. It is designed to be generic but has been thoroughly tested.
# 2015--2017 Wesley Willett, Petra Isenberg and Lonni Besancon
library(ggplot2)
library(reshape2)
barChart <- function(resultTable, techniques, nbTechs = -1, ymin, ymax, xAxisLabel = "I am the X axis", yAxisLabel = "I am the Y Label"){
#tr <- t(resultTable)
if(nbTechs <= 0){
stop('Please give a positive number of Techniques, nbTechs');
}
tr <- as.data.frame(resultTable)
nbTechs <- nbTechs - 1 ; # seq will generate nb+1
#now need to calculate one number for the width of the interval
tr$CI2 <- tr$upperBound_CI - tr$mean_time
tr$CI1 <- tr$mean_time - tr$lowerBound_CI
#add a technique column
tr$technique <- factor(seq.int(0, nbTechs, 1));
breaks <- c(as.character(tr$technique));
print(tr)
g <- ggplot(tr, aes(x=technique, y=mean_time)) +
geom_bar(stat="identity",fill = I("#CCCCCC")) +
geom_errorbar(aes(ymin=mean_time-CI1, ymax=mean_time+CI2),
width=0, # Width of the error bars
size = 1.1
) +
#labs(title="Overall time per technique") +
labs(x = xAxisLabel, y = yAxisLabel) +
scale_y_continuous(limits = c(ymin,ymax)) +
scale_x_discrete(name="",breaks,techniques)+
coord_flip() +
theme(panel.background = element_rect(fill = 'white', colour = 'white'),axis.title=element_text(size = rel(1.2), colour = "black"),axis.text=element_text(size = rel(1.2), colour = "black"),panel.grid.major = element_line(colour = "#DDDDDD"),panel.grid.major.y = element_blank(), panel.grid.minor.y = element_blank())+
geom_point(size=4, colour="black") # dots
print(g)
}The data
The data gathered are about 4 different techniques from the paper Pressure-Based Gain Factor Control for Mobile 3D Interaction using Locally-Coupled Devices which is available from: “https://hal.inria.fr/hal-01436172”. The idea was to compare different gain factor manipulations for a 3D docking task. The goal of a 3D docking task is to ask users to match an objet’s position and orientation ot a target position and orientation. We can then use the angular and Euclidean distances between the object and the target as a measure of accuracy.
We used 4 different techniques to manipulate the gain factor:
pressure-based manipulations, slider-based manipulations, rate-control manipulation, and speed-based manipulations.
The names of these techniques will be used in the following example code. Modify these names so that they fit your needs.
We will look at three different performance measures for these 4 techniques:
- Euclidean Distance
- Angular Distance
- Overall Workload
This data does not include time data (which is also very interesting), we will deal with this example later.
Data Analysis
We present here the data analysis for the Euclidean Distance, the Angular Distance, and the workload per technique. For all of these, the distribution of data is far from normal so we use the Bootstrap CIs helper functions presented above.
We first need to read the data with a line like:
################ BOOTSTRAP CI #################
data = read.table("./Info.csv", header=T, sep=",")
data = aggregate(data,by=list(data$pID), FUN=mean, na.rm=TRUE)The data for the Euclidean Distance and the Angular Distance is summarized below:
## Group.1 EucliPressure AngularPressure EucliRate
## Min. : 1.00 Min. : 3.13 Min. : 7.234 Min. : 7.987
## 1st Qu.: 6.75 1st Qu.:11.75 1st Qu.: 25.299 1st Qu.: 29.167
## Median :12.50 Median :26.36 Median : 40.187 Median : 80.384
## Mean :12.50 Mean :31.73 Mean : 45.614 Mean :114.394
## 3rd Qu.:18.25 3rd Qu.:49.43 3rd Qu.: 61.346 3rd Qu.:161.468
## Max. :24.00 Max. :86.47 Max. :105.215 Max. :427.770
## AngularRate EucliSpeed AngularSpeed EucliSlider
## Min. : 13.88 Min. : 3.187 Min. : 9.618 Min. : 2.076
## 1st Qu.: 42.92 1st Qu.:19.007 1st Qu.: 26.425 1st Qu.: 10.895
## Median : 73.53 Median :43.053 Median : 46.461 Median : 34.649
## Mean : 66.90 Mean :45.182 Mean : 52.150 Mean : 43.719
## 3rd Qu.: 95.28 3rd Qu.:67.917 3rd Qu.: 74.324 3rd Qu.: 69.486
## Max. :119.37 Max. :99.690 Max. :125.185 Max. :119.997
## AngularSlider pID
## Min. : 5.613 Min. : 1.00
## 1st Qu.: 18.792 1st Qu.: 6.75
## Median : 35.933 Median :12.50
## Mean : 47.440 Mean :12.50
## 3rd Qu.: 71.374 3rd Qu.:18.25
## Max. :119.719 Max. :24.00Euclidean Distance
Code
Here is the code to compute the means and CIs for each of the 4 techniques.
data = aggregate(data,by=list(data$pID), FUN=mean, na.rm=TRUE)
resultPressure = bootstrapMeanCI(data$EucliPressure)
resultRate = bootstrapMeanCI(data$EucliRate)
resultSpeed = bootstrapMeanCI(data$EucliSpeed)
resultSlider = bootstrapMeanCI(data$EucliSlider)
analysisData = c()
analysisData$ratio = c("Slider","Speed","Rate","Pressure")
analysisData$pointEstimate = c(resultSlider[1],resultSpeed[1],resultRate[1],resultPressure[1])
analysisData$ci.max = c(resultSlider[3], resultSpeed[3], resultRate[3], resultPressure[3])
analysisData$ci.min = c(resultSlider[2], resultSpeed[2], resultRate[2], resultPressure[2])
datatoprint <- data.frame(factor(analysisData$ratio),analysisData$pointEstimate, analysisData$ci.max, analysisData$ci.min)
colnames(datatoprint) <- c("technique", "mean_time", "lowerBound_CI", "upperBound_CI ") #We use the name mean_time for the value of the mean even though it's not a time, it's just to parse the data for the plot
barChart(datatoprint,analysisData$ratio ,nbTechs = 4, ymin = 0, ymax = 170, "", "Euclidean Distance per technique. Error Bars, Bootstrap 95% CIs")## technique mean_time lowerBound_CI upperBound_CI CI2 CI1
## 1 0 43.71918 60.49831 29.43647 -14.282712 -16.779135
## 2 1 45.18153 57.34625 33.60464 -11.576890 -12.164717
## 3 2 114.39352 166.24510 77.10322 -37.290293 -51.851581
## 4 3 31.72767 41.67720 23.08464 -8.643031 -9.949531
Interpretation
While these results can be interpreted using a binary approach based on the spacing of the confidence intervals, estimation calls for more nuance. Here are how the results were interpreted in the paper:
These results show strong evidence for a better performance of pressure-based, speed-based, and slider-based control compared to rate control. There is also weak evidence for a better performance of pressure-control over the slider-based and speed-based methods.
The second sentence is a bit risky given the rather large overlaps but we will see that it’s confirmed by an analysis of effect sizes.
Going further with a pair-wise difference to show effect sizes
While we managed to avoid binary analysis of the previous results, this is still not enough because we haven’t talked about effect sizes just yet.
We decide to compute the difference between pressure-based control (which seems to be our best technique) and all the other techniques. Since it’s a within-subject design, we compute the difference for every subject individually
data = aggregate(data,by=list(data$pID), FUN=mean, na.rm=TRUE)
data$EucliPR = (data$EucliRate-data$EucliPressure)
data$EucliPSp = (data$EucliSpeed-data$EucliPressure)
data$EucliPSl = (data$EucliSlider-data$EucliPressure)
resultPR = bootstrapMeanCI(data$EucliPR)
resultPSp = bootstrapMeanCI(data$EucliPSp)
resultPSl = bootstrapMeanCI(data$EucliPSl)
analysisData = c()
analysisData$ratio = c("Slider-Pressure","Speed-Pressure","Rate-Pressure")
analysisData$pointEstimate = c(resultPSl[1],resultPSp[1], resultPR[1])
analysisData$ci.max = c(resultPSl[3], resultPSp[3], resultPR[3])
analysisData$ci.min = c(resultPSl[2], resultPSp[2], resultPR[2])
datatoprint <- data.frame(factor(analysisData$ratio),analysisData$pointEstimate, analysisData$ci.max, analysisData$ci.min)
colnames(datatoprint) <- c("technique", "mean_time", "lowerBound_CI", "upperBound_CI ")
barChart(datatoprint,analysisData$ratio ,nbTechs = 3, ymin = 0 , ymax = 150, "", "Pair-wise differences. Error Bars, Bootstrap 95% CIs")## technique mean_time lowerBound_CI upperBound_CI CI2 CI1
## 1 0 11.99151 25.40051 1.963988 -10.027519 -13.409003
## 2 1 13.45386 21.02514 6.187039 -7.266819 -7.571285
## 3 2 82.66585 132.93559 50.898956 -31.766890 -50.269748
We can now interpret these results.
The fact that none of the confidence intervals for these differences overlaps with 0 supports our finding that pressure-based control of the gain factor is more accurate than all other techniques. Analyzing the ratios between the techniques leads to errors about 4 times smaller on average (in terms of Euclidean distances) than rate-control, and about 2 times smaller than speed-based control.
The results are clearer than before (when we compared technique means) because it’s a within-subjects design.
Angular Distance
Code
Similarly we can compute the mean and CIs for each of the techniques for the angular distance with the following code.
resultPressure = bootstrapMeanCI(data$AngularPressure)
resultRate = bootstrapMeanCI(data$AngularRate)
resultSpeed = bootstrapMeanCI(data$AngularSpeed)
resultSlider = bootstrapMeanCI(data$AngularSlider)
analysisData = c()
analysisData$ratio = c("Slider","Speed","Rate","Pressure")
analysisData$pointEstimate = c(resultSlider[1],resultSpeed[1],resultRate[1],resultPressure[1])
analysisData$ci.max = c(resultSlider[3], resultSpeed[3], resultRate[3], resultPressure[3])
analysisData$ci.min = c(resultSlider[2], resultSpeed[2], resultRate[2], resultPressure[2])
datatoprint <- data.frame(factor(analysisData$ratio),analysisData$pointEstimate, analysisData$ci.max, analysisData$ci.min)
colnames(datatoprint) <- c("technique", "mean_time", "lowerBound_CI", "upperBound_CI ")
barChart(datatoprint,analysisData$ratio ,nbTechs = 4, ymin = 0, ymax = 85, "", "Angular Distances Per Technique. Error Bars, Bootstrap 95% CIs")## technique mean_time lowerBound_CI upperBound_CI CI2 CI1
## 1 0 47.44002 61.61774 35.57512 -11.864900 -14.17772
## 2 1 52.14977 66.97297 39.94621 -12.203564 -14.82319
## 3 2 66.90453 79.29061 53.55713 -13.347401 -12.38608
## 4 3 45.61402 56.61330 36.03621 -9.577812 -10.99928
Additionally and following the previous example, we can compute the pair-wise comparisons between the techniques. The code can easily be derived from the previous example and the figure is: 
Interpretation
The only clear result in the first figure is pressure control being less error-prone than rate control. As before, it is more informative to look at the effect size (either the ratio or the difference between the techniques), especially since the data is from a within-subject design.
Again, there is a strong evidence that rate control is outperformed by all three other techniques. While there is no evidence for a difference in performance between speed-based and slider-based control or pressure-based and slider-based control, there is slight evidence that pressure-based control may also perform better than speed-based control for rotational distances. Similar to the analysis of the Euclidean distance, we computed the pair-wise differences between pressure-based control and the other techniques and show them in Fig. 6(b). These values confirm that pressure-based control of the gain factor allowed participants to obtain a better angular accuracy than rate-control and speed-based controls. The confidence interval of the difference between slider-based and pressured-based control, however, overlaps 0 so that we cannot claim a difference between these two modalities.
Workload
In our experiment we asked participants to estimate the workload for each technique using NASA’s TLX. Here is how to we compute the means and CIs:
Code
data = read.table("./TLX.csv", header=T, sep=",")
resultPressure = bootstrapMeanCI(data$TPressure)
resultRate = bootstrapMeanCI(data$TRate)
resultSpeed = bootstrapMeanCI(data$TSpeed)
resultSlider = bootstrapMeanCI(data$TSlider)
analysisData = c()
analysisData$ratio = c("Slider","Speed","Rate","Pressure")
analysisData$pointEstimate = c(resultSlider[1],resultSpeed[1],resultRate[1],resultPressure[1])
analysisData$ci.max = c(resultSlider[3],resultSpeed[3],resultRate[3],resultPressure[3])
analysisData$ci.min = c(resultSlider[2],resultSpeed[2],resultRate[2],resultPressure[2])
datatoprint <- data.frame(factor(analysisData$ratio),analysisData$pointEstimate, analysisData$ci.max, analysisData$ci.min)
colnames(datatoprint) <- c("technique", "mean_time", "lowerBound_CI", "upperBound_CI ")
barChart(datatoprint,analysisData$ratio ,nbTechs = 4, ymin = 0, ymax = 100, "", "Total Workload Per Technique, Error Bars, 95% Bootstrap CIs")## technique mean_time lowerBound_CI upperBound_CI CI2 CI1
## 1 0 49.44444 56.14583 42.33523 -7.109213 -6.701389
## 2 1 54.30556 61.27694 47.95004 -6.355511 -6.971385
## 3 2 66.63194 73.40278 59.27083 -7.361111 -6.770833
## 4 3 42.32639 48.50694 36.49306 -5.833333 -6.180556
Interpretation
From our paper:
The overall TLX workload is shown in Fig. 8. There is strong evidence for a higher workload of the use of rate-control compared to the other techniques. While we cannot find evidence for differences in workload between speed-based and slider-based control, there is evidence that pressure-based control is overall less demanding than all the other techniques.
We further discuss in the discussion section of the paper the fact that the difference between slider-based and pressure-based control is not so clear. Our paper thus also focuses on several sub-aspect of the workload to distinguish between them.
Time Data
Time data is a bit specific. It is recommended to first log all the results and present them anti-logged (using the exponential function). By doing so, we can correct for positive skewness in time measurements (see http://dx.doi.org/10.1145/1753326.1753679). We thus arrive at geometric means. Contrary to arithmetic means which use the sum of a set of value to obtean the mean, geometric means use the product of the set of values. Geometric means dampen the effect of potential extreme trial completion times which would bias an arithmetic mean. Other advantages are discussed in https://www.lri.fr/~dragice/fairstats-last.pdf, Tip 12.
Code
data = read.table("./Time.csv", header=T, sep=",")
data$TimeSecs = data$Time/1000
data$TimeLog = log(data$TimeSec)
TimeLogMouse = subset(data, Condition=="Mouse")$TimeLog
TimeLogTactile = subset(data, Condition=="Touch")$TimeLog
TimeLogTangible = subset(data, Condition=="Tangible")$TimeLog
TMouse = t.test(TimeLogMouse, conf.level = 0.95)
TTactile = t.test(TimeLogTactile, conf.level = 0.95)
TTangible = t.test(TimeLogTangible, conf.level = 0.95)
meanM = mean(TimeLogMouse)
meanT = mean(TimeLogTactile)
meanTle = mean(TimeLogTangible)
cimaxM = exp(TMouse$conf.int[2])
cimaxT = exp(TTactile$conf.int[2])
cimaxTle = exp(TTangible$conf.int[2])
ciminM = exp(TMouse$conf.int[1])
ciminT = exp(TTactile$conf.int[1])
ciminTle = exp(TTangible$conf.int[1])
meanM = exp(meanM)
meanT = exp(meanT)
meanTle = exp(meanTle)
analysisData$ratio = c("Tangible","Touch","Mouse")
analysisData$pointEstimate = c(meanTle,meanT,meanM)
analysisData$ci.max = c(cimaxTle,cimaxT,cimaxM)
analysisData$ci.min = c(ciminTle,ciminT,ciminM)
datatoprint <- data.frame(factor(analysisData$ratio),analysisData$pointEstimate, analysisData$ci.max, analysisData$ci.min)
colnames(datatoprint) <- c("technique", "mean_time", "lowerBound_CI", "upperBound_CI ")
barChart(datatoprint,analysisData$ratio ,nbTechs = 3, ymin = 0, ymax = 70, "", "Completion Time per Technique in s. Error Bars, 95% CIs")## technique mean_time lowerBound_CI upperBound_CI CI2 CI1
## 1 0 26.82775 28.26160 25.46664 -1.361104 -1.433850
## 2 1 47.75014 50.69672 44.97482 -2.775316 -2.946576
## 3 2 61.39100 64.78873 58.17146 -3.219539 -3.397726
Interpretation
It took participants about 60 s to complete the task in the mouse condition, about 50 s in the touch condition, and about 25 s in the tangible condition. We can see strong evidence of the mouse being slower than touch interaction which in turn is slower than tangible interaction.
Now for the effect sizes (pair-wise comparisons). The differences in these pair-wise comparisons are also anti-logged, thus they correspond to ratios between each of the geometric means.
#Effect Size Computation
DiffMouseTouch = TimeLogMouse - TimeLogTactile
DiffMouseTangible = TimeLogMouse - TimeLogTangible
DiffTactileTangible = TimeLogTactile - TimeLogTangible
T1 = t.test(DiffMouseTouch, conf.level = 0.95)
T2 = t.test(DiffMouseTangible, conf.level = 0.95)
T3 = t.test(DiffTactileTangible, conf.level = 0.95)
mean1 = mean(DiffMouseTouch)
mean2 = mean(DiffMouseTangible)
mean3 = mean(DiffTactileTangible)
cimax1 = exp(T1$conf.int[2])
cimax2 = exp(T2$conf.int[2])
cimax3 = exp(T3$conf.int[2])
cimin1 = exp(T1$conf.int[1])
cimin2 = exp(T2$conf.int[1])
cimin3 = exp(T3$conf.int[1])
mean1 = exp(mean1)
mean2 = exp(mean2)
mean3 = exp(mean3)
analysisData$ratio = c("Touch/Tangible","Mouse/Tangible","Mouse/Touch")
analysisData$pointEstimate = c(mean3,mean2,mean1)
analysisData$ci.max = c(cimax3,cimax2,cimax1)
analysisData$ci.min = c(cimin3,cimin2,cimin1)
datatoprint <- data.frame(factor(analysisData$ratio),analysisData$pointEstimate, analysisData$ci.max, analysisData$ci.min)
colnames(datatoprint) <- c("technique", "mean_time", "lowerBound_CI", "upperBound_CI ")
barChart(datatoprint,analysisData$ratio ,nbTechs = 3, ymin = 1, ymax = 3, "", "Pair-wise differences. Error Bars, 95% CIs")## technique mean_time lowerBound_CI upperBound_CI CI2 CI1
## 1 0 1.779879 1.902909 1.664803 -0.11507625 -0.12303067
## 2 1 2.288340 2.429307 2.155553 -0.13278700 -0.14096698
## 3 2 1.285672 1.367732 1.208535 -0.07713691 -0.08206031
Interpretation
All ratios are clearly greater than 1, thus there is strong evidence that the techniques differ in average completion time. The tangible condition clearly outperforms the mouse condition: it is more than twice as fast. The difference between the tangible condition and the touch condition is also quite strong: the tangible condition is almost twice as fast as the touch condition. The difference between mouse and touch is not as strong; yet, the touch condition is still clearly faster on average than the mouse condition.
Conclusion
This concludes this small introduction to scripts that generate 95% (Bootstrap) CIs and examples on how to interpret them. If you have further questions on the content of this page, the Alt. IHM (French) paper of the explanation in the appendix of the thesis, feel free to contact the main investigator @ lonni.besancon@gmail.com