In this experiment, participants performed a visual working-memory task requiring the reproduction of the exact angle of one out of two tilted bars at the end of a memory delay. Depending on the type of block, (1) an interfering item could either appear at a temporally fixed (i.e., predictable) or variable (i.e., unpredictable) time point during the memory delay, and (2) participants either had to ignore it (i.e., distractor) or respond to it (i.e., interrupter).

Dependent variables in this analysis are the reproduction error in the working memory task (DevTargetvsReport) and the reaction time to the interrupter (IntRT). Furthermore, we determine the angular difference between interference and report, the probability of swaps, and response biases.

Independent variables are TrialType (InterferenceTrial vs. DelayTrial), OnsetType (Fixed vs. Random), InterferenceType (Distraction vs. Interruption), and OnsetTimePoint (0 vs. 1 vs. 2).

In the paper, we refer to OnsetType as Temporal Predictability (Fixed = Fixed vs. Random = Variable), to OnsetTimePoint as Interference Onset (0 = 500 ms vs. 1 = 1250 ms vs. 2 = 2000 ms after encoding onset), and to Trial Type as Interference Presentation (DelayTrial = No Interference vs. InterferenceTrial = Interference).

Note regarding orientations: 0° is 3 o’clock, 90° is 12 o’clock, 180° is 9 o’clock, and 270° is 6 o’clock.

1. Set Up

1.1 Load in the libraries

library(dplyr) 
library(ggplot2)
library(Rmisc)
library(ez)
library(lsr)
library(rmarkdown)
library(mixtur)
library(DescTools)

2. Get the data

Get working directory.

getwd()

Check the available data files.

files <- list.files(pattern = ".csv", recursive = T)

Read-in the files, and remove practice trials and empty rows and then concatinate them into one data frame.

#initialize empty data frame 
data <- NULL

#loop through data files, read them in and concatinate
for(file in files){
  jj <- read.csv(file, sep = ",", header = T)
  # bind files into one data frame
  data <- rbind(data, jj)
}

#removes practice trials and empty rows (practice and between blocks)
data <- data[!is.na(data$TrialNumber), ] 

#removes empty columns
data <- data[!sapply(data, function (x) all(is.na(x) | x == ""))]
## Number of subjects:  79

Check if all participants completed all blocks and trials.

CompletedTrials <- NULL
for (sub in unique(data$participant)){
  nTrials         <- length(which(data$participant == sub))
  CompletedTrials  <- append(CompletedTrials, nTrials)
}
## All participants completed the experiment

3. Determine bonus payment

Performances above 80% will receive a bonus payment scaling from £0 at 80% to £5 at 100%.

AverageBonus <- aggregate(data = data,  DevTargetvsReport ~ participant, mean)

#calculate accuracy for each participant
AverageBonus$MeanAcc <- 100 - (1.11111 * AverageBonus$DevTargetvsReport)

#calculate payment for each participant
AverageBonus$Payment <- round(0.25 * (AverageBonus$MeanAcc-80), digits=2)

#participants with negative bonus payments receive £0
AverageBonus$Payment[AverageBonus$Payment < 0] <- 0 
## Mean bonus payment:  0.7596203
## SD bonus payment:  0.8208773

4. Fix RGB values of interfering item

Although displayed correctly, the RGB values for the interfering item were incorrectly logged in the data files. This is fixed here.

data$IntCol[data$TargetCol == "[253,142,253]" & data$NonTargetCol == "[254,163,0]"] <- "[0,225,228]" #blue
data$IntCol[data$TargetCol == "[254,163,0]" & data$NonTargetCol == "[253,142,253]"] <- "[0,225,228]" #blue

data$IntCol[data$TargetCol == "[253,142,253]" & data$NonTargetCol == "[0,225,228]"] <- "[254,163,0]" #orange
data$IntCol[data$TargetCol == "[0,225,228]" & data$NonTargetCol == "[253,142,253]"] <- "[254,163,0]" #orange

data$IntCol[data$TargetCol == "[254,163,0]" & data$NonTargetCol == "[0,225,228]"] <- "[253,142,253]" #pink
data$IntCol[data$TargetCol == "[0,225,228]" & data$NonTargetCol == "[254,163,0]"] <- "[253,142,253]" #pink

data$IntCol[data$TrialType == "DelayTrial"] = "None"

5. Cleaning - Trial and Participant Removal

Check if there’s participant who did not confirm tilt reproduction with space bar. If yes, remove participants.

for (sub in unique(data$participant)){
  NoConfirmation <- length(which(data$participant == sub & data$TooSlowDialing == "Yes"))
  if (NoConfirmation == 384){
  data <- data[!(sub == data$participant),]
  }
}
## Number of subjects:  78
## Number of trials before trial removal:  29952

Convert reaction time from seconds into milliseconds.

data$KeyProbe.rt                 <- data$KeyProbe.rt *1000

data$IntRT[data$IntRT == "None"] <- NA
data$IntRT                       <- as.numeric(as.character(data$IntRT))
data$IntRT                       <- data$IntRT *1000

Remove trials where participants where slower than 5 seconds after probe onset.

CutOff_5s <- NULL

for (sub in unique(data$participant)){
  SlowProbe_5s <- length(which(data$participant == sub & data$KeyProbe.rt > 5000)) #number of trials with reaction time > 5000 ms
  CutOff_5s    <- append(CutOff_5s, SlowProbe_5s)
}

#remove trials
data <- data[data$KeyProbe.rt <= 5000,]
## Number of trials after more than 5s reaction time removal:  29861

Remove trials with slow reaction time to the probe (reaction time +/- 2.5 SD above individual mean reaction time).

CutOff2Remove  <- NULL
CutOff_SD_low  <- NULL
CutOff_SD_high <- NULL

for (sub in unique(data$participant)){
  CutOffSD1      <- mean(data$KeyProbe.rt[data$participant==sub])+(2.5*sd(data$KeyProbe.rt[data$participant==sub])) #mean reaction time + 2.5 SD
  CutOffSD2      <- mean(data$KeyProbe.rt[data$participant==sub])-(2.5*sd(data$KeyProbe.rt[data$participant==sub])) #mean reaction time - 2.5 SD
  CutOff2Remove  <- append(CutOff2Remove, which(data$participant == sub & data$KeyProbe.rt > CutOffSD1))
  CutOff2Remove  <- append(CutOff2Remove, which(data$participant == sub & data$KeyProbe.rt < CutOffSD2))
  
  SlowProbeSD1   <- length(which(data$participant == sub & data$KeyProbe.rt > CutOffSD1)) #number of trials with reaction time > mean reaction time + 2.5 SD
  SlowProbeSD2   <- length(which(data$participant == sub & data$KeyProbe.rt < CutOffSD2)) #number of trials with reaction time < mean reaction time - 2.5 SD
  CutOff_SD_low  <- append(CutOff_SD_low, SlowProbeSD2) 
  CutOff_SD_high <- append(CutOff_SD_high, SlowProbeSD1)
}

#remove trials
data <- data[-c(CutOff2Remove),]
## Number of trials after +/-2.5 SD reaction time removal:  28974

Remove trials where subjects were to slow to use the dial.

Dialling <- NULL

for (sub in unique(data$participant)){
  SlowDial <- length(which(data$participant == sub & data$TooSlowDialing == "Yes")) #number of trials where too slow to reproduce the tilt
  Dialling  <- append(Dialling, SlowDial)
}

#remove trials
data <- data[data$TooSlowDialing == "No",]
## Number of trials after 'too slow dialing' removal:  28500

Remove trials where participants did not respond/responded incorrectly/too slow to interrupter or where they incorrectly responded to distractor.

#interrupter responses
InterrupterResponse <- NULL
for (sub in unique(data$participant)){
  SubsetInterrupter        <- NULL
  SubsetInterrupter        <- data[data$participant == sub & data$InterferenceType == "Interruption" & data$Response2Interruptor == "Yes" & data$CorrectInterruptorResponse == "Yes",] #trials in which participants responded correctly to the interrupter
  tempInterrupterResponse <- length(which(SubsetInterrupter$participant == sub & SubsetInterrupter$IntRT < 1000)) #number of trials with correct responses to interrupter that are faster than 1000 ms
  nTrials                 <- length(which(data$participant == sub & data$InterferenceType == "Interruption" & data$TrialType == "InterferenceTrial")) #number of interrupter trials
  InterrupterResponse     <- append(InterrupterResponse, nTrials-tempInterrupterResponse) #number of trials in which participants did not respond/responded incorrectly/too slow to interrupter
}

#distractor responses
DistractorResponse <- NULL
for (sub in unique(data$participant)){
  tempDistractorResponse <- length(which(data$participant == sub & data$InterferenceType == "Distraction" & data$Response2Distractor == "No")) #number of trials in which participants did not responded to distractor
  nTrials                <- length(which(data$participant == sub & data$InterferenceType == "Distraction" & data$TrialType == "InterferenceTrial")) #number of distractor trials
  DistractorResponse     <- append(DistractorResponse, nTrials-tempDistractorResponse) #number of trials in which participants mistakenly responded to distractor
}

#remove trials
data <- data[!(data$Response2Interruptor == "No" | data$CorrectInterruptorResponse == "No" | data$Response2Distractor == "Yes"),] #trials with no response to interrupter, wrong response to interrupter, response to distractor
data <- data[!(data$TrialType == "InterferenceTrial" & data$InterferenceType == "Interruption" & data$IntRT > 1000),] #RTs to interrupter slower than 1000 ms
## Number of trials after removal of incorrect interference responses:  26343

Table with number of all removed trials per category:

participants                <- unique(factor(data$participant))
BadTrials                   <- data.frame(participants, CutOff_5s, CutOff_SD_low, CutOff_SD_high, Dialling, InterrupterResponse, DistractorResponse)
BadTrials$TotalRemoved      <- rowSums(BadTrials[2:7])
BadTrials$PercentageRemoved <- round(BadTrials$Total/384*100, digits = 2)

BadTrials$Remove <- NULL

#check if more than 10% of trials were removed
for (row in 1:nrow(BadTrials)) {
  if (BadTrials$PercentageRemoved[row] <= 10) {
    BadTrials$Remove[row] <- 'no'
  } else {
    BadTrials$Remove[row] <- 'yes'
  }
}

Remove participants with more than 10% bad trials.

RemoveSubs <- NULL

for (sub in unique(BadTrials$participants)){
    if (BadTrials$Remove[BadTrials$participants == sub] == "yes"){
    RemoveSubs <- append(RemoveSubs, sub)
  }
}

#remove participants
data <- data[!data$participant %in% RemoveSubs,]
## Number of subjects:  57

Remove participants that indicated explicit strategy use in the survey at the end of the experiment. Survey results can be found in the “Analysis” folder on OSF.

StrategyUse <- c("5f404a1174f003185c71c0ce", "5ce1b37e71a170001971342c", "5e791235c7d30f00096255e0", "5bc772a554b3bc0001a33bde", "5cc9796d3cc87b0013051b88") #5ce1b37e71a170001971342c & 5bc772a554b3bc0001a33bde already removed in bad trial removal

#remove participants
data <- data[!data$participant %in% StrategyUse,]
## Number of subjects:  54

6. Information about sample

6.1 Age

agg_subInfo <- aggregate(data = data, Age~participant+Gender..male.female., FUN = mean)
## Mean Age:  27.16667
## Min Age:  18
## Max Age:  38

6.2 Sex

aggregate(data = agg_subInfo, participant ~ Gender..male.female., FUN = length)
##   Gender..male.female. participant
## 1               female          18
## 2               Female           9
## 3              Females           1
## 4                 male          18
## 5                 Male           8

6.3 Handedness

aggregate(data = aggregate(data = data, Age~participant+Handedness..right.left., FUN=mean), participant ~ Handedness..right.left., FUN = length)
##        Handedness..right.left. participant
## 1 Ambidextrous, Right primary.           1
## 2                         left           2
## 3                         Left           2
## 4                         None           1
## 5                        right          36
## 6                        Right          12

6.4 Average number of trials of remaining participants (in percent).

TotalNoTrials <- NULL

for (sub in unique(data$participant)){
  nTrials       <- length(which(data$participant == sub))
  TotalNoTrials <- append(TotalNoTrials, nTrials)
}

PerNoTrial <- TotalNoTrials/384
## Mean number of trials across participants (in %):  93.99595
## SD of trials across participants (in %):  1.818642

6.5 Add subject number counting from 1 to 54

data$SubjectNo <- NULL
data           <- transform(data, SubjectNo = as.factor(factor(data$participant))) #number of subjects

7. Main analysis

Transform into factors.

data$TrialType         <- as.factor(data$TrialType)
data$OnsetType         <- as.factor(data$OnsetType)
data$InterferenceType  <- as.factor(data$InterferenceType)
data$OnsetTimePoint    <- as.factor(data$OnsetTimePoint)

7.1 Interference has a detrimental impact on working-memory performance

7.1.1 Reproduction errors as a function of Trial Type and Interference Type

Collapse reproduction errors by factors Trial Type, Interference Type, and SubjectNo. Calculate summary statistics.

agg_Int <- aggregate(data = data,  DevTargetvsReport ~ SubjectNo + TrialType + InterferenceType, mean)
summary_Int <- summarySEwithin(data = agg_Int, measurevar = "DevTargetvsReport", withinvars = c("InterferenceType","TrialType"), idvar = "SubjectNo")

Plot reproduction errors as a function of Trial Type and Interference Type.

ggplot(summary_Int, aes(x = InterferenceType, y = DevTargetvsReport, fill = interaction(TrialType, InterferenceType))) +
 geom_bar(stat = "identity", position = position_dodge(width=0.9), color = "black", width = 0.8, size=0.9) +
  scale_fill_manual(values=c("#DDE8F8", "#4582D9", "#98BBEB","#235BA9")) +
  geom_point(data=agg_Int,aes(group =TrialType), position =position_dodge(width=0.9), size = 1, color = "#1F1F1F",  shape = 1,  alpha = 0.4) +
  geom_errorbar(data=summary_Int, aes(ymin=DevTargetvsReport-se, ymax=DevTargetvsReport+se), width=0.1, position=position_dodge(0.9), size=0.6)+
  labs(fill = "Onset Type", x = "Onset Type", y = "Error (in degrees)") +
  coord_cartesian(ylim= c(6,36.03))+
  labs(fill = "Onset Type", y = "Error (degrees)") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none",  
        axis.line = element_line(colour = "black"),
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.1.2 Interference cost (in degrees)

The interference cost of each Interference Type is calculated by taking the difference in reproduction errors between trials with and without interference (Interference - No Interference).

aggDev_DisRand <- agg_Int[agg_Int$InterferenceType == 'Distraction'  & agg_Int$TrialType == 'DelayTrial',]
aggDev_DisFix  <- agg_Int[agg_Int$InterferenceType == 'Distraction'  & agg_Int$TrialType == 'InterferenceTrial',]
aggDev_IntRand <- agg_Int[agg_Int$InterferenceType == 'Interruption' & agg_Int$TrialType == 'DelayTrial',]
aggDev_IntFix  <- agg_Int[agg_Int$InterferenceType == 'Interruption' & agg_Int$TrialType == 'InterferenceTrial',]

aggDev_DisDiff <- merge(aggDev_DisFix, aggDev_DisRand, by = 'SubjectNo', sort = F)
aggDev_IntDiff <- merge(aggDev_IntFix, aggDev_IntRand, by = 'SubjectNo', sort = F)

aggDev_DisDiff$diff <- aggDev_DisDiff$DevTargetvsReport.x - aggDev_DisDiff$DevTargetvsReport.y #fixed-random for distractors
aggDev_IntDiff$diff <- aggDev_IntDiff$DevTargetvsReport.x - aggDev_IntDiff$DevTargetvsReport.y #fixed-random for interrupters

aggDev_DisDiff$cond <- 'difference'
aggDev_IntDiff$cond <- 'difference'

aggDev_AllDiff       <- rbind(aggDev_DisDiff, aggDev_IntDiff)
names(aggDev_AllDiff )[names(aggDev_AllDiff ) == "InterferenceType.x"] <- "InterferenceType"
names(aggDev_AllDiff )[names(aggDev_AllDiff ) == "TrialType.x"] <- "TrialType"

sum.aggDev_Dis   <- data.frame("InterferenceType" = "Distraction", "cond" = 'difference', 
                                "diff" = mean(aggDev_AllDiff$diff[aggDev_AllDiff$InterferenceType == 'Distraction']), 
                                "se" = sd(aggDev_AllDiff$diff[aggDev_AllDiff$InterferenceType == 'Distraction']) / sqrt(length(aggDev_AllDiff$SubjectNo[aggDev_AllDiff$InterferenceType == 'Distraction'])))

sum.aggDev_Int   <- data.frame("InterferenceType" = "Interruption", "cond" = 'difference', 
                                "diff" = mean(aggDev_AllDiff$diff[aggDev_AllDiff$InterferenceType == 'Interruption']), 
                                "se" = sd(aggDev_AllDiff$diff[aggDev_AllDiff$InterferenceType == 'Interruption']) / sqrt(length(aggDev_AllDiff$SubjectNo[aggDev_AllDiff$InterferenceType == 'Interruption'])))

sum.aggDev_AllDiff <- rbind(sum.aggDev_Dis, sum.aggDev_Int)

Violin plot depicting the cost of interference for both Interference Types.

ggplot(sum.aggDev_AllDiff, aes(x = InterferenceType, y = diff, fill = InterferenceType, color = InterferenceType)) + 
  geom_hline(yintercept=0, linetype="dashed", color = "black") +
  geom_violin(data = aggDev_AllDiff, size = 1) +
  geom_point(size = 2) +
  geom_errorbar(data = sum.aggDev_AllDiff, aes(ymin=(diff-se), ymax=(diff+se)), width = .1, size = 0.6) +
  geom_point(data = aggDev_AllDiff,  size = 1.5, alpha = .3, shape = 1) +
  scale_fill_manual(values=c("#FFFFFF", "#FFFFFF")) +
  scale_color_manual(values=c("#2868C0", "#2868C0"))+
  labs(y = "Interference Cost (degrees)", x= "Interference Type") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none",  
        axis.line = element_line(colour = "black"),
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.1.3 Stats (reproduction error)

Repeated-measures ANOVA with factors Trial Type and Interference Type.

ezANOVA(data = agg_Int, 
              dv = DevTargetvsReport, 
              wid = SubjectNo, 
              within = .(InterferenceType, TrialType),
              detailed = TRUE,
              type = 3)
## $ANOVA
##                       Effect DFn DFd         SSn       SSd         F
## 1                (Intercept)   1  53 47644.97369 4853.5959 520.27067
## 2           InterferenceType   1  53   514.84415  370.4075  73.66681
## 3                  TrialType   1  53   223.70311  220.0991  53.86786
## 4 InterferenceType:TrialType   1  53    48.67688  233.5954  11.04420
##              p p<.05         ges
## 1 4.516436e-29     * 0.893521879
## 2 1.326422e-11     * 0.083139387
## 3 1.282077e-09     * 0.037906780
## 4 1.617936e-03     * 0.008500471

Pairwise comparisons to break down interaction effect between Interference Type and Trial Type.

#distraction: interference vs no interference
(DisInt   <- pairedSamplesTTest(data = agg_Int[agg_Int$InterferenceType == "Distraction",], DevTargetvsReport ~ TrialType, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   DevTargetvsReport 
## Grouping variable:  TrialType 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##             DelayTrial InterferenceTrial difference
##    mean         12.765            13.851     -1.086
##    std dev.      4.552             4.380      2.457
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -3.248 
##    degrees of freedom:  53 
##    p-value:  0.002 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-1.756, -0.415] 
##    estimated effect size (Cohen's d):  0.442
#interruption: interference vs no interference
(IrInt   <- pairedSamplesTTest(data = agg_Int[agg_Int$InterferenceType == "Interruption",], DevTargetvsReport ~ TrialType, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   DevTargetvsReport 
## Grouping variable:  TrialType 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##             DelayTrial InterferenceTrial difference
##    mean         14.903            17.888     -2.985
##    std dev.      5.503             6.078      3.329
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -6.588 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-3.894, -2.076] 
##    estimated effect size (Cohen's d):  0.897
#bonferroni correction
p.adjust(c(DisInt$p.value, IrInt$p.value), method = "bonferroni")
## [1] 4.037828e-03 4.150309e-08

7.2 Temporal expectations mitigate interference

Subset data into trials in which interference was presented.

data_noDelay <- data[data$TrialType != "DelayTrial", ]

7.2.1 Reproduction errors as a function of Onset Type and Interference Type

Collapse reproduction errors by factors Onset Type, Interference Type, and SubjectNo. Calculate summary statistics.

aggDev     <- aggregate(data = data_noDelay ,DevTargetvsReport ~ SubjectNo + OnsetType + InterferenceType, mean)
summaryDev <- summarySEwithin(data = aggDev, measurevar = "DevTargetvsReport", withinvars = c("OnsetType", "InterferenceType"), idvar = "SubjectNo")

Plot reproduction errors as a function of Interference Type and Onset Type.

ggplot(summaryDev, aes(x = InterferenceType, y = DevTargetvsReport, fill = interaction(OnsetType, InterferenceType))) +
  geom_bar(stat = "identity", position = position_dodge(width=0.9), color = "black", width = 0.8, size=0.9) +
  scale_fill_manual(values=c("#E66062","#A3A3A3", "#B01C1E", "#666666")) +
  geom_point(data=aggDev,aes(group =OnsetType), position =position_dodge(width=0.9), size = 1, color = "#1F1F1F",  shape = 1,  alpha = 0.4) +
  coord_cartesian(ylim = c(8, 37))+
  geom_errorbar(data=summaryDev, aes(ymin=DevTargetvsReport-se, ymax=DevTargetvsReport+se), width=0.1, position=position_dodge(0.9), size=0.6)+
  labs(fill = "Onset Type", y = "Error (degrees)") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none",  
        axis.line = element_line(colour = "black"),
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.2.2 Temporal expectation benefit (in degrees)

The temporal expectation benefit of each Interference Type is calculated by taking the difference in reproduction errors between variable-onset blocks and fixed-onset blocks (Fixed - Variable).

aggDev_DisRand <- aggDev[aggDev$InterferenceType == 'Distraction'  & aggDev$OnsetType == 'Random',]
aggDev_DisFix  <- aggDev[aggDev$InterferenceType == 'Distraction'  & aggDev$OnsetType == 'Fixed',]
aggDev_IntRand <- aggDev[aggDev$InterferenceType == 'Interruption' & aggDev$OnsetType == 'Random',]
aggDev_IntFix  <- aggDev[aggDev$InterferenceType == 'Interruption' & aggDev$OnsetType == 'Fixed',]

aggDev_DisDiff <- merge(aggDev_DisFix, aggDev_DisRand, by = 'SubjectNo', sort = F)
aggDev_IntDiff <- merge(aggDev_IntFix, aggDev_IntRand, by = 'SubjectNo', sort = F)

aggDev_DisDiff$diff <- aggDev_DisDiff$DevTargetvsReport.x - aggDev_DisDiff$DevTargetvsReport.y #fixed-random for distractors
aggDev_IntDiff$diff <- aggDev_IntDiff$DevTargetvsReport.x - aggDev_IntDiff$DevTargetvsReport.y #fixed-random for interrupters

aggDev_DisDiff$cond <- 'difference'
aggDev_IntDiff$cond <- 'difference'

aggDev_AllDiff       <- rbind(aggDev_DisDiff, aggDev_IntDiff)
names(aggDev_AllDiff )[names(aggDev_AllDiff ) == "InterferenceType.x"] <- "InterferenceType"
names(aggDev_AllDiff )[names(aggDev_AllDiff ) == "OnsetType.x"] <- "OnsetType"

sum.aggDev_Dis   <- data.frame("InterferenceType" = "Distraction", "cond" = 'difference', 
                                "diff" = mean(aggDev_AllDiff$diff[aggDev_AllDiff$InterferenceType == 'Distraction']), 
                                "se" = sd(aggDev_AllDiff$diff[aggDev_AllDiff$InterferenceType == 'Distraction']) / sqrt(length(aggDev_AllDiff$SubjectNo[aggDev_AllDiff$InterferenceType == 'Distraction'])))

sum.aggDev_Int   <- data.frame("InterferenceType" = "Interruption", "cond" = 'difference', 
                                "diff" = mean(aggDev_AllDiff$diff[aggDev_AllDiff$InterferenceType == 'Interruption']), 
                                "se" = sd(aggDev_AllDiff$diff[aggDev_AllDiff$InterferenceType == 'Interruption']) / sqrt(length(aggDev_AllDiff$SubjectNo[aggDev_AllDiff$InterferenceType == 'Interruption'])))

sum.aggDev_AllDiff <- rbind(sum.aggDev_Dis, sum.aggDev_Int)

Violin plots depicting the temporal expectation benefit for both distractors and interrupters.

ggplot(sum.aggDev_AllDiff, aes(x = InterferenceType, y = diff, fill = InterferenceType, color = InterferenceType)) + 
  geom_hline(yintercept=0, linetype="dashed", color = "black") +
  geom_violin(data = aggDev_AllDiff, size = 1) +
  geom_point(size = 2) +
  geom_errorbar(data = sum.aggDev_AllDiff, aes(ymin=(diff-se), ymax=(diff+se)), width = .1, size = 0.6) +
  geom_point(data = aggDev_AllDiff,  size = 1.5, alpha = .3, shape = 1) +
  scale_fill_manual(values=c("#FFFFFF", "#FFFFFF")) +
  scale_color_manual(values=c("#DE2B2E", "#DE2B2E"))+
  labs(y = "Temporal Expectation Benefit (degrees)", x= "Interference Type") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none",  
        axis.line = element_line(colour = "black"),
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.2.3 Reproduction errors as a function of Onset Type, Interference Type, and Onset Time Point

Collapse reproduction errors by factors Onset Type, Interference Type, Onset Time Point, and SubjectNo. Calculate summary statistics.

agg_Dev_TP <- aggregate(data = data_noDelay,  DevTargetvsReport ~ SubjectNo + OnsetType + InterferenceType + OnsetTimePoint, mean)
agg_Dev_TP[] <- lapply(agg_Dev_TP, function(x) if(is.factor(x)) factor(x) else x)
summary_Dev_TP <- summarySEwithin(data = agg_Dev_TP, measurevar = "DevTargetvsReport", withinvars = c("OnsetType", "InterferenceType", "OnsetTimePoint"), idvar = "SubjectNo")

Plot reproduction errors as a function of Onset Type, Interference Type, and Onset Time Point.

label_names =c('0' = "500 ms", "1" = "1250 ms",'2' = "2000 ms") #change labels for onset time point 

ggplot(summary_Dev_TP, aes(x = InterferenceType, y = DevTargetvsReport, fill = interaction(OnsetType, InterferenceType))) +
  geom_bar(stat = "identity", position = position_dodge(0.9), color= "black", size = 0.9, width =0.8) +
  geom_point(data=aggDev,aes(group =OnsetType), position  = position_dodge(0.9), size = 1, color = "#1F1F1F", shape = 1,  alpha = 0.4) +
  geom_errorbar(data=summary_Dev_TP,aes(ymin=DevTargetvsReport-se, ymax=DevTargetvsReport+se), width=0.1, position=position_dodge(0.9), size=0.6)+
  scale_fill_manual("Onset Type", values=c("#E66062", "#A3A3A3","#B01C1E","#666666")) +
  facet_wrap(~OnsetTimePoint,  scales="free_x",  labeller = as_labeller(label_names)) +
  coord_cartesian(ylim = c(8, 37))+
  labs(fill = "Onset Type", x = "Interference Type", y = "Error (degrees)") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none", 
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        strip.text.x = element_text(size = 15),
        strip.background = element_blank(),
        axis.line = element_line(colour = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.2.4 Stats (reproduction error)

Repeated-measures ANOVA with factors Interference Type, Onset Type, and Onset Time Point.

ezANOVA(data = agg_Dev_TP, 
              dv = DevTargetvsReport, 
              wid = SubjectNo, 
              within = .(OnsetType, InterferenceType, OnsetTimePoint),
              detailed = TRUE,
              type = 3)
## $ANOVA
##                                      Effect DFn DFd          SSn        SSd
## 1                               (Intercept)   1  53 1.636379e+05 16175.8625
## 2                                 OnsetType   1  53 1.137356e+02   686.9912
## 3                          InterferenceType   1  53 2.726460e+03  1919.3080
## 4                            OnsetTimePoint   2 106 1.154915e+02  1803.0091
## 5                OnsetType:InterferenceType   1  53 5.703386e+00   602.6364
## 6                  OnsetType:OnsetTimePoint   2 106 3.093759e+00  1583.5413
## 7           InterferenceType:OnsetTimePoint   2 106 1.101176e+02  1480.0605
## 8 OnsetType:InterferenceType:OnsetTimePoint   2 106 1.071849e+01  1369.4309
##             F            p p<.05          ges
## 1 536.1574481 2.185874e-29     * 0.8646253339
## 2   8.7744729 4.564823e-03     * 0.0044195631
## 3  75.2887902 9.427470e-12     * 0.0961805860
## 4   3.3949083 3.723117e-02     * 0.0044874896
## 5   0.5015951 4.819034e-01       0.0002225578
## 6   0.1035459 9.017257e-01       0.0001207371
## 7   3.9432401 2.229389e-02     * 0.0042795772
## 8   0.4148293 6.615205e-01       0.0004181755
## 
## $`Mauchly's Test for Sphericity`
##                                      Effect         W           p p<.05
## 4                            OnsetTimePoint 0.9198161 0.113821877      
## 6                  OnsetType:OnsetTimePoint 0.9832806 0.645081022      
## 7           InterferenceType:OnsetTimePoint 0.9929855 0.832752525      
## 8 OnsetType:InterferenceType:OnsetTimePoint 0.7986064 0.002888365     *
## 
## $`Sphericity Corrections`
##                                      Effect       GGe      p[GG] p[GG]<.05
## 4                            OnsetTimePoint 0.9257683 0.04103452         *
## 6                  OnsetType:OnsetTimePoint 0.9835555 0.89883630          
## 7           InterferenceType:OnsetTimePoint 0.9930344 0.02256113         *
## 8 OnsetType:InterferenceType:OnsetTimePoint 0.8323667 0.62441903          
##         HFe      p[HF] p[HF]<.05
## 4 0.9578291 0.03934636         *
## 6 1.0211454 0.90172570          
## 7 1.0315586 0.02229389         *
## 8 0.8560937 0.63010303

Pairwise comparisons to break down main effect of Onset Time Point.

agg_Dev_TP_sep <- aggregate(data = data_noDelay,  DevTargetvsReport ~ SubjectNo + OnsetTimePoint, mean)
agg_Dev_TP_sep$OnsetTimePoint <- as.factor(agg_Dev_TP_sep$OnsetTimePoint)
agg_Dev_TP_sep$SubjectNo <- as.factor(agg_Dev_TP_sep$SubjectNo)

#500 ms vs 1250 ms
(Del500_1250   <- pairedSamplesTTest(data = agg_Dev_TP_sep[agg_Dev_TP_sep$OnsetTimePoint != 2,], DevTargetvsReport ~ OnsetTimePoint, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   DevTargetvsReport 
## Grouping variable:  OnsetTimePoint 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##                  0      1 difference
##    mean     15.894 15.265      0.628
##    std dev.  4.907  5.366      2.386
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  1.936 
##    degrees of freedom:  53 
##    p-value:  0.058 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-0.023, 1.28] 
##    estimated effect size (Cohen's d):  0.263
#500 ms vs 2000 ms
(Del500_2000   <- pairedSamplesTTest(data = agg_Dev_TP_sep[agg_Dev_TP_sep$OnsetTimePoint != 1,], DevTargetvsReport ~ OnsetTimePoint, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   DevTargetvsReport 
## Grouping variable:  OnsetTimePoint 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##                  0      2 difference
##    mean     15.894 16.190     -0.297
##    std dev.  4.907  5.415      3.022
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -0.722 
##    degrees of freedom:  53 
##    p-value:  0.474 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-1.122, 0.528] 
##    estimated effect size (Cohen's d):  0.098
#1250 ms vs 2000 ms
(Del1250_2000  <- pairedSamplesTTest(data = agg_Dev_TP_sep[agg_Dev_TP_sep$OnsetTimePoint != 0,], DevTargetvsReport ~ OnsetTimePoint, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   DevTargetvsReport 
## Grouping variable:  OnsetTimePoint 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##                  1      2 difference
##    mean     15.265 16.190     -0.925
##    std dev.  5.366  5.415      3.102
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -2.192 
##    degrees of freedom:  53 
##    p-value:  0.033 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-1.772, -0.079] 
##    estimated effect size (Cohen's d):  0.298
#bonferroni correction
p.adjust(c(Del500_1250$p.value, Del500_2000$p.value, Del1250_2000$p.value), method = "bonferroni") 
## [1] 0.17475373 1.00000000 0.09839738

Pairwise comparisons to break down interaction effect of Interference Type and Onset Time Point.

agg_Dev_TPI  <- aggregate(data = data_noDelay,  DevTargetvsReport ~ SubjectNo + InterferenceType + OnsetTimePoint, mean)
agg_Dev_TPI[] <- lapply(agg_Dev_TPI, function(x) if(is.factor(x)) factor(x) else x)

#500 ms: distraction vs interruption
(Int500   <- pairedSamplesTTest(data = agg_Dev_TPI[agg_Dev_TPI$OnsetTimePoint == 0,], DevTargetvsReport ~ InterferenceType, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   DevTargetvsReport 
## Grouping variable:  InterferenceType 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##             Distraction Interruption difference
##    mean          14.087       17.953     -3.866
##    std dev.       4.474        6.338      4.657
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -6.101 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-5.137, -2.595] 
##    estimated effect size (Cohen's d):  0.83
#1250 ms: distraction vs interruption
(Int1250  <- pairedSamplesTTest(data = agg_Dev_TPI[agg_Dev_TPI$OnsetTimePoint == 1,], DevTargetvsReport ~ InterferenceType, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   DevTargetvsReport 
## Grouping variable:  InterferenceType 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##             Distraction Interruption difference
##    mean          13.711       16.918     -3.207
##    std dev.       4.952        6.570      4.230
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -5.572 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-4.362, -2.053] 
##    estimated effect size (Cohen's d):  0.758
#2000 ms: distraction vs interruption
(Int2000  <- pairedSamplesTTest(data = agg_Dev_TPI[agg_Dev_TPI$OnsetTimePoint == 2,], DevTargetvsReport ~ InterferenceType, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   DevTargetvsReport 
## Grouping variable:  InterferenceType 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##             Distraction Interruption difference
##    mean          13.747       18.871     -5.124
##    std dev.       4.680        7.082      4.803
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -7.839 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-6.435, -3.813] 
##    estimated effect size (Cohen's d):  1.067
#bonferroni correction
p.adjust(c(Int500$p.value, Int1250$p.value, Int2000$p.value), method = "bonferroni")
## [1] 3.744715e-07 2.582430e-06 6.066810e-10

7.3 The benefit on the working-memory task does not occur at the expense of the intervening task

Subset data in only interrupter-trials.

data_onlyIR <- data[data$InterferenceType == "Interruption" & data$TrialType == "InterferenceTrial", ]

7.3.1 Reaction time to interrupter task as a function of Onset Type

Collapse reaction time to interrupter by factor Onset Type and SubjectNo. Calculate summary statistics.

agg_RT_IR     <- aggregate(data = data_onlyIR,  IntRT ~ SubjectNo + OnsetType, mean)
summary_RT_IR <- summarySEwithin(data = agg_RT_IR, measurevar = "IntRT", withinvars = c("OnsetType"), idvar = "SubjectNo")

Plot reaction time to interrupter as a function of Onset Type.

ggplot(summary_RT_IR, aes(x = OnsetType, y = IntRT, fill = OnsetType)) +
  geom_bar(stat = "identity", position = position_dodge(0.9), color= "black", size = 0.9, width = 0.75) +
  geom_point(data=agg_RT_IR,aes(group =OnsetType), position = position_dodge(0.9), size = 1.5, color = "#1F1F1F", shape=1, alpha = 0.4) +
  geom_errorbar(data=summary_RT_IR, aes(ymin=IntRT-se, ymax=IntRT+se), width=0.1, position=position_dodge(0.5), size=0.6)+
  scale_fill_manual("Onset Type", values=c("#B01C1E", "#666666")) +
  scale_x_discrete(breaks=c("Fixed","Random"), labels=c("Fixed", "Variable"))+
  coord_cartesian(ylim= c(430,740))+
  labs(x = "Onset Type", y = "RT to interrupter (ms)") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none", 
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        strip.text.x = element_text(size = 15),
        strip.background = element_blank(),
        axis.line = element_line(colour = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.3.2 Temporal expectation benefit in the interrupter task (in ms)

The temporal expectation benefit in the interrupter task is calculated by taking the difference in reproduction errors between variable-onset blocks and fixed-onset blocks (Fixed - Variable).

aggFixRan_Fix   <- agg_RT_IR[agg_RT_IR$OnsetType == 'Fixed',]
aggFixRan_Ran    <- agg_RT_IR[agg_RT_IR$OnsetType == 'Random',]

aggFixRan_Diff    <- merge(aggFixRan_Fix, aggFixRan_Ran, by = 'SubjectNo', sort = F)

aggFixRan_Diff$diff     <- aggFixRan_Diff$IntRT.x - aggFixRan_Diff$IntRT.y 

aggFixRan_Diff$cond    <- 'difference'

names(aggFixRan_Diff)[names(aggFixRan_Diff ) == "OnsetType.x"] <- "OnsetType"

sum.aggFixRan   <- data.frame("cond" = 'difference', 
                                "diff" = mean(aggFixRan_Diff$diff), 
                                "se" = sd(aggFixRan_Diff$diff) / sqrt(length(aggFixRan_Diff$SubjectNo)))

Violin plots depicting the temporal expectation benefit for fixed as compared to random onsets of the interrupter.

ggplot(sum.aggFixRan, aes(x = cond, y = diff, fill = cond, color = cond)) + 
  geom_hline(yintercept=0, linetype="dashed", color = "black") +
  geom_violin(data = aggFixRan_Diff, size = 1) +
  scale_fill_manual("cond", values="#FFFFFF") +
  scale_color_manual("cond", values="#B01C1E") +
  geom_point(size = 2) +
  geom_errorbar(data = sum.aggFixRan, aes(ymin=(diff-se), ymax=(diff+se)), width = .1, size = 0.6) +
  geom_point(data = aggFixRan_Diff,  size = 1.5, alpha = .3, shape =1) +
  labs(y = "Temporal Expectation Benefit (ms)") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none",  
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        axis.ticks.x=element_blank(),
        axis.line = element_line(colour = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.3.3 Reaction time to interrupter task as a function of Onset Type and Onset Time Point

Collapse reaction times to the interrupter by factors Onset Type, Onset Time Point, and SubjectNo. Calculate summary statistics.

agg_RT_IR_TP  <- aggregate(data = data_onlyIR,  IntRT ~ SubjectNo + OnsetTimePoint + OnsetType, mean)
agg_RT_IR_TP[] <- lapply(agg_RT_IR_TP, function(x) if(is.factor(x)) factor(x) else x)
summary_RT_IR_TP <- summarySEwithin(data = agg_RT_IR_TP, measurevar = "IntRT", withinvars = c("OnsetTimePoint", "OnsetType"), idvar = "SubjectNo")

Plot reaction times to interrupter as a function of Onset Type and Onset Time Point.

label_names =c('0' = "500 ms", "1" = "1250 ms",'2' = "2000 ms") 

ggplot(summary_RT_IR_TP, aes(x = OnsetType, y = IntRT, fill = OnsetType)) +
  geom_bar(stat = "identity", position = position_dodge(0.9), color= "black", width = 0.85,  size = 0.9) +
  geom_point(data=agg_RT_IR_TP,aes(group =OnsetType), position = position_dodge(0.9), size = 1, color = "#1F1F1F", shape = 1,  alpha = 0.4) +
  geom_errorbar(data = summary_RT_IR_TP, aes(ymin=IntRT-se, ymax=IntRT+se), width=0.1, position=position_dodge(0.9), size=0.6)+
  scale_fill_manual("Onset Type", values=c("#B01C1E", "#666666")) +
  facet_wrap(~OnsetTimePoint,  scales="free_x",  labeller = as_labeller(label_names)) +
  scale_x_discrete(breaks=c("Fixed","Random"), labels=c("Fixed", "Variable"))+
  coord_cartesian(ylim= c(420,830))+
  labs(x = "Onset Type", y = "RT to interrupter (ms)") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none", 
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        strip.text.x = element_text(size = 15),
        strip.background = element_blank(),
        axis.line = element_line(colour = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.3.4 Stats (interrupter task)

Repeated-measures ANOVA with factors Onset Type and Onset Time Point.

ezANOVA(data = agg_RT_IR_TP, 
              dv = IntRT, 
              wid = SubjectNo, 
              within = .(OnsetType, OnsetTimePoint),
              detailed = TRUE,
              type = 3)
## $ANOVA
##                     Effect DFn DFd          SSn        SSd          F
## 1              (Intercept)   1  53 103774089.98 1456781.62 3775.46415
## 2                OnsetType   1  53     46028.32   76146.68   32.03687
## 3           OnsetTimePoint   2 106     74613.71  252611.52   15.65458
## 4 OnsetType:OnsetTimePoint   2 106     52135.12  175048.76   15.78510
##              p p<.05        ges
## 1 6.078957e-51     * 0.98145747
## 2 6.254886e-07     * 0.02293827
## 3 1.104428e-06     * 0.03666157
## 4 9.986675e-07     * 0.02590277
## 
## $`Mauchly's Test for Sphericity`
##                     Effect         W          p p<.05
## 3           OnsetTimePoint 0.8959843 0.05751893      
## 4 OnsetType:OnsetTimePoint 0.8425218 0.01161741     *
## 
## $`Sphericity Corrections`
##                     Effect       GGe        p[GG] p[GG]<.05       HFe
## 3           OnsetTimePoint 0.9057842 2.995524e-06         * 0.9359996
## 4 OnsetType:OnsetTimePoint 0.8639471 4.276799e-06         * 0.8904090
##          p[HF] p[HF]<.05
## 3 2.174652e-06         *
## 4 3.221678e-06         *

Pairwise comparisons to break down main effect of Onset Time Point.

agg_Dev_IR_TP_sep                <- aggregate(data = data_onlyIR,  IntRT ~ SubjectNo + OnsetTimePoint, mean)
agg_Dev_IR_TP_sep[]              <- lapply(agg_Dev_IR_TP_sep, function(x) if(is.factor(x)) factor(x) else x)
agg_Dev_IR_TP_sep$OnsetTimePoint <- as.factor(agg_Dev_IR_TP_sep$OnsetTimePoint)
agg_Dev_IR_TP_sep$SubjectNo      <- as.factor(agg_Dev_IR_TP_sep$SubjectNo)

#500 ms vs 1250 ms
(IntRT500_1250   <- pairedSamplesTTest(data = agg_Dev_IR_TP_sep[agg_Dev_IR_TP_sep$OnsetTimePoint != 2,], IntRT ~ OnsetTimePoint, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   IntRT 
## Grouping variable:  OnsetTimePoint 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##                   0       1 difference
##    mean     586.411 553.756     32.655
##    std dev.  83.456  73.333     46.845
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  5.123 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [19.869, 45.442] 
##    estimated effect size (Cohen's d):  0.697
#500 ms vs 2000 ms
(IntRT500_2000   <- pairedSamplesTTest(data = agg_Dev_IR_TP_sep[agg_Dev_IR_TP_sep$OnsetTimePoint != 1,], IntRT ~ OnsetTimePoint, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   IntRT 
## Grouping variable:  OnsetTimePoint 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##                   0       2 difference
##    mean     586.411 555.827     30.584
##    std dev.  83.456  59.842     54.965
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  4.089 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [15.582, 45.587] 
##    estimated effect size (Cohen's d):  0.556
#1250 ms vs 2000 ms
(IntRT1250_2000  <- pairedSamplesTTest(data = agg_Dev_IR_TP_sep[agg_Dev_IR_TP_sep$OnsetTimePoint != 0,], IntRT ~ OnsetTimePoint, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   IntRT 
## Grouping variable:  OnsetTimePoint 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##                   1       2 difference
##    mean     553.756 555.827     -2.071
##    std dev.  73.333  59.842     41.372
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -0.368 
##    degrees of freedom:  53 
##    p-value:  0.714 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-13.363, 9.221] 
##    estimated effect size (Cohen's d):  0.05
#bonferroni correction
p.adjust(c(IntRT500_1250$p.value, IntRT500_2000$p.value, IntRT1250_2000$p.value), method = "bonferroni") #bonferroni correction
## [1] 1.291806e-05 4.436956e-04 1.000000e+00

Pairwise comparisons to break down interaction effect of Onset Type and Onset Time Point.

agg_Dev_IR_TPI                <- aggregate(data = data_noDelay,  IntRT ~ SubjectNo + OnsetType + OnsetTimePoint, mean)
agg_Dev_IR_TPI[]              <- lapply(agg_Dev_IR_TPI, function(x) if(is.factor(x)) factor(x) else x)
agg_Dev_IR_TPI$OnsetTimePoint <- as.factor(agg_Dev_IR_TPI$OnsetTimePoint)
agg_Dev_IR_TPI$OnsetType      <- as.factor(agg_Dev_IR_TPI$OnsetType)
agg_Dev_IR_TPI$SubjectNo      <- as.factor(agg_Dev_IR_TPI$SubjectNo)

#500 ms: fixed vs random
(IntRT_Int500   <- pairedSamplesTTest(data = agg_Dev_IR_TPI[agg_Dev_IR_TPI$OnsetTimePoint == 0,], IntRT ~ OnsetType, id = "SubjectNo")) #change sign of t-value in text for consistency 
## 
##    Paired samples t-test 
## 
## Outcome variable:   IntRT 
## Grouping variable:  OnsetType 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##               Fixed  Random difference
##    mean     557.715 616.968    -59.253
##    std dev.  97.288  86.078     71.794
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -6.065 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-78.849, -39.657] 
##    estimated effect size (Cohen's d):  0.825
#1250 ms: fixed vs random
(IntRT_Int1250  <- pairedSamplesTTest(data = agg_Dev_IR_TPI[agg_Dev_IR_TPI$OnsetTimePoint == 1,], IntRT ~ OnsetType, id = "SubjectNo")) #change sign of t-value in text for consistency
## 
##    Paired samples t-test 
## 
## Outcome variable:   IntRT 
## Grouping variable:  OnsetType 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##               Fixed  Random difference
##    mean     553.255 554.407     -1.152
##    std dev.  81.678  71.808     45.200
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -0.187 
##    degrees of freedom:  53 
##    p-value:  0.852 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-13.489, 11.185] 
##    estimated effect size (Cohen's d):  0.025
#2000 ms: fixed vs random
(IntRT_Int2000  <- pairedSamplesTTest(data = agg_Dev_IR_TPI[agg_Dev_IR_TPI$OnsetTimePoint == 2,], IntRT ~ OnsetType, id = "SubjectNo")) #change sign of t-value in text for consistency
## 
##    Paired samples t-test 
## 
## Outcome variable:   IntRT 
## Grouping variable:  OnsetType 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##               Fixed  Random difference
##    mean     551.099 562.208    -11.109
##    std dev.  63.170  65.573     47.767
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  -1.709 
##    degrees of freedom:  53 
##    p-value:  0.093 
## 
## Other information: 
##    two-sided 95% confidence interval:  [-24.147, 1.929] 
##    estimated effect size (Cohen's d):  0.233
#bonferroni correction
p.adjust(c(IntRT_Int500$p.value, IntRT_Int1250$p.value, IntRT_Int2000$p.value), method = "bonferroni") #bonferroni correction
## [1] 4.281413e-07 1.000000e+00 2.799406e-01

7.4 Temporal expectations shield internal representations instead of averting external interference

7.4.1 Angular difference between interference and report

Collapse the angular difference between the orientation of the interfering item and the reported orientation by factor SubjectNo. Calculate summary statistics.

data_noDelay$InterferencevsReport <- as.numeric(data_noDelay$InterferencevsReport)
agg_IntDev                        <- aggregate(data = data_noDelay, InterferencevsReport ~ SubjectNo, mean)

agg_IntDevChance                      <- aggregate(data = data_noDelay, InterferencevsReport ~ SubjectNo, mean)
agg_IntDevChance$InterferencevsReport <- 45

agg_IntDevChance$cond <- 'chance'
agg_IntDev$cond       <- 'error'

aggChanceError      <- rbind(agg_IntDevChance, agg_IntDev)
aggChanceError$cond <- as.factor(aggChanceError$cond)
sum_ChanceError     <- summarySEwithin(data = aggChanceError, measurevar = 'InterferencevsReport', withinvars = 'cond', idvar = 'SubjectNo')

Plot angular difference between interference and report and chance level (dashed line = chance level).

ggplot(sum_ChanceError[sum_ChanceError$cond == "error",], aes(x =cond, y = InterferencevsReport)) +
  geom_bar(stat = "identity", position = position_dodge(width=0.9), color= "black", width = 0.8, size=0.9, fill = "white")+
  geom_hline(yintercept=sum_ChanceError$InterferencevsReport[sum_ChanceError$cond == "chance"], color = "#979797", linetype = "dashed") +
  geom_point(data=agg_IntDev, position =position_dodge(width=0.9), size = 1, color = "#1F1F1F",  shape = 1,  alpha = 0.4) +
  geom_errorbar(data=sum_ChanceError[sum_ChanceError$cond == "error",], aes(ymin=InterferencevsReport-se, ymax=InterferencevsReport+se), width=0.1, position=position_dodge(0.9), size=0.6)+
  coord_cartesian(ylim = c(40, 49))+
  labs(fill = "Onset Type", y = "Interference vs. Report (degrees)") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none",  
        axis.line = element_line(colour = "black"),
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        axis.ticks.x=element_blank(),
        legend.text=element_text(size=11),
        legend.title=element_text(size=13),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.4.2 Stats (angular difference between interference and report)

Pairwise comparisons to compare angular difference between interference and report versus chance level.

agg_allChance <- rbind(agg_IntDevChance, agg_IntDev)

#actual error vs chance error
(ErrorChance   <- pairedSamplesTTest(data = agg_allChance, InterferencevsReport ~ cond, id = "SubjectNo"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   InterferencevsReport 
## Grouping variable:  cond 
## ID variable:        SubjectNo 
## 
## Descriptive statistics: 
##             chance  error difference
##    mean     45.000 44.121      0.879
##    std dev.  0.000  1.478      1.478
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  4.372 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [0.476, 1.282] 
##    estimated effect size (Cohen's d):  0.595

7.4.3 Swaps between memory target and interfering item

Fit mixture model to data. Here, we are only interested in the swaps.

data_noDelay$IntOri<- as.numeric(as.character(data_noDelay$IntOri))

MM.data <- NULL
MM.data <-data.frame(data_noDelay$participant, data_noDelay$InterferenceType, data_noDelay$OnsetType, data_noDelay$TargetOri, data_noDelay$ReportOri, data_noDelay$IntOri)

names(MM.data)[names(MM.data) == "data_noDelay.participant"]      <- "id"
names(MM.data)[names(MM.data) == "data_noDelay.InterferenceType"] <- "InterferenceType"
names(MM.data)[names(MM.data) == "data_noDelay.OnsetType"]        <- "OnsetType"
names(MM.data)[names(MM.data) == "data_noDelay.TargetOri"]        <- "TargetOri"
names(MM.data)[names(MM.data) == "data_noDelay.ReportOri"]        <- "ReportOri"
names(MM.data)[names(MM.data) == "data_noDelay.IntOri"]           <- "IntOri"

#convert factors into characters (model doesn't like conditions as factors)
MM.data$InterferenceType <- as.character(MM.data$InterferenceType)
MM.data$OnsetType        <- as.character(MM.data$OnsetType)
MM.data$id               <- as.character(MM.data$id)

#subset into different conditions 
MM.data_IF <- MM.data[MM.data$InterferenceType == 'Interruption' & MM.data$OnsetType == 'Fixed',]
MM.data_IR <- MM.data[MM.data$InterferenceType == 'Interruption' & MM.data$OnsetType == 'Random',]
MM.data_DF <- MM.data[MM.data$InterferenceType == 'Distraction' & MM.data$OnsetType == 'Fixed',]
MM.data_DR<- MM.data[MM.data$InterferenceType == 'Distraction' & MM.data$OnsetType == 'Random',]

#fit model to each condition
#fixed interruption
estimates_IF <- fit_mixtur(data = MM.data_IF, 
                           components = 3,
                           unit = "degrees_180",
                           id_var = "id",
                           response_var = "ReportOri", 
                           target_var = "TargetOri", 
                           non_target_var = "IntOri", 
                           set_size_var = NULL, 
                           condition_var = NULL, 
                           return_fit = FALSE)
estimates_IF$InterferenceType <-  "Interruption"
estimates_IF$OnsetType        <- "Fixed"

#random interruption
estimates_IR <- fit_mixtur(data = MM.data_IR, 
                           components = 3,
                           unit = "degrees_180",
                           id_var = "id",
                           response_var = "ReportOri", 
                           target_var = "TargetOri", 
                           non_target_var = "IntOri", 
                           set_size_var = NULL, 
                           condition_var = NULL, 
                           return_fit = FALSE)
estimates_IR$InterferenceType <-  "Interruption"
estimates_IR$OnsetType        <- "Random"

#fixed distraction
estimates_DF <- fit_mixtur(data = MM.data_DF, 
                           components = 3,
                           unit = "degrees_180",
                           id_var = "id",
                           response_var = "ReportOri", 
                           target_var = "TargetOri", 
                           non_target_var = "IntOri", 
                           set_size_var = NULL, 
                           condition_var = NULL, 
                           return_fit = FALSE)
estimates_DF$InterferenceType <-  "Distraction"
estimates_DF$OnsetType        <- "Fixed"

#random distraction
estimates_DR <- fit_mixtur(data = MM.data_DR, 
                           components = 3,
                           unit = "degrees_180",
                           id_var = "id",
                           response_var = "ReportOri", 
                           target_var = "TargetOri", 
                           non_target_var = "IntOri", 
                           set_size_var = NULL, 
                           condition_var = NULL, 
                           return_fit = FALSE)
estimates_DR$InterferenceType <-  "Distraction"
estimates_DR$OnsetType        <- "Random"

#bind into one data frame
estimates_allCond <- rbind(estimates_IF, estimates_IR, estimates_DF, estimates_DR)

#convert into factors
estimates_allCond$InterferenceType <- as.factor(estimates_allCond$InterferenceType)
estimates_allCond$OnsetType        <- as.factor(estimates_allCond$OnsetType)
estimates_allCond$id               <- as.factor(estimates_allCond$id)

Calculate summary statistics for swaps.

MM_Pn <- summarySEwithin(data = estimates_allCond , measurevar ="p_n", withinvars = c("InterferenceType", "OnsetType"), idvar = "id")

Plot probability of swaps as a function of Onset Type and Interference Type.

ggplot(MM_Pn, aes(x = InterferenceType, y = p_n, fill = interaction(OnsetType,InterferenceType))) +
  geom_bar(stat = "identity", position = position_dodge(width=0.9), color= "black", width = 0.8, size=0.9) +
  geom_point(data=estimates_allCond, aes(group =OnsetType), position =position_dodge(width=0.9), size = 1, color = "#1F1F1F",  shape = 1,  alpha = 0.4)+
  geom_errorbar(data=MM_Pn,aes(ymin=p_n-se, ymax=p_n+se), width=0.1, position=position_dodge(0.9), size=0.6, color="#172A3A")+
  scale_y_continuous(limits = c(0,0.22), expand = c(0, 0)) +
  scale_fill_manual(values=c("#E66062","#A3A3A3", "#B01C1E", "#666666")) +
  labs(fill = "Onset Type", x = "Interference Type", y = "Probability of Swaps") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none",  
        axis.line = element_line(colour = "black"),
        axis.text.x  = element_text(size = 15, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_blank(),
        axis.title.y = element_text(size = 15, color = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.4.4 Stats (swaps)

Repeated-measures ANOVA with factors Onset Type and Interference Type.

ezANOVA(data = estimates_allCond, 
              dv = p_n, 
              wid = id, 
              within = .(InterferenceType, OnsetType),
              detailed = TRUE,
              type = 3)
## $ANOVA
##                       Effect DFn DFd          SSn        SSd          F
## 1                (Intercept)   1  53 0.1305866713 0.14507558 47.7068135
## 2           InterferenceType   1  53 0.0091650417 0.07459621  6.5116876
## 3                  OnsetType   1  53 0.0008205602 0.05717969  0.7605793
## 4 InterferenceType:OnsetType   1  53 0.0009167824 0.05992247  0.8108723
##              p p<.05         ges
## 1 6.365918e-09     * 0.279413085
## 2 1.363670e-02     * 0.026493232
## 3 3.870811e-01       0.002430609
## 4 3.719361e-01       0.002714858

7.4.5 Response bias

Transform reproduction errors into -90 to +90 space.

data_noDelay$DevReportvsTargetNew <- NULL
tempTargetDev                     <- data_noDelay$ReportOri - data_noDelay$TargetOri

TargetDev <- NULL
for (i in 1:length(tempTargetDev)) {
  if (0 <= tempTargetDev[i] && tempTargetDev[i] <= 90){
    TargetDev[i] <- tempTargetDev[i]
  } else if (-90 <= tempTargetDev[i] && tempTargetDev[i] < 0) {
    TargetDev[i] <- tempTargetDev[i]
  } else if (90 < tempTargetDev[i] && tempTargetDev[i] <= 270) {
    TargetDev[i] <- tempTargetDev[i] - 180
  } else if (-270 < tempTargetDev[i] && tempTargetDev[i] <= -90) {
    TargetDev[i] <- tempTargetDev[i] + 180  
  }
}

data_noDelay$DevReportvsTargetNew <- TargetDev

Transform angular difference between interference and memory target into -90 to +90 space.

data_noDelay$DevIntvsTargetNew <- NULL
data_noDelay$IntOri            <- as.numeric(as.character(data_noDelay$IntOri))
tempIntDev                     <- data_noDelay$IntOri - data_noDelay$TargetOri

IntDev <- NULL
for (i in 1:length(tempIntDev)) {
  if (0 <= tempIntDev[i] && tempIntDev[i] <= 90){
    IntDev[i] <- tempIntDev[i]
  } else if (-90 <= tempIntDev[i] && tempIntDev[i] < 0) {
    IntDev[i] <- tempIntDev[i]
  } else if (90 < tempIntDev[i] && tempIntDev[i] <= 270) {
    IntDev[i] <- tempIntDev[i] - 180
  } else if (-270 < tempIntDev[i] && tempIntDev[i] <= -90) {
    IntDev[i] <- tempIntDev[i] + 180  
  }
}

data_noDelay$DevIntvsTargetNew <- IntDev

Add column with all conditions.

data_noDelay$allCond <- NULL

data_noDelay$allCond <- ifelse(data_noDelay$InterferenceType == "Distraction" & data_noDelay$OnsetType == "Fixed", "Fixed Distraction",
                                 ifelse(data_noDelay$InterferenceType == "Distraction" & data_noDelay$OnsetType == "Random", "Random Distraction",
                                        ifelse(data_noDelay$InterferenceType == "Interruption" & data_noDelay$OnsetType == "Fixed", "Fixed Interruption", "Random Interruption")))

Demeaning of reproduction errors by subtracting the overall mean response error of a participant from each individual response error.

for(s in unique(data_noDelay$SubjectNo)){
  data_noDelay$MeanError[s == data_noDelay$SubjectNo] <-  mean(data_noDelay$DevReportvsTargetNew[s == data_noDelay$SubjectNo])
  }   

data_noDelay$DMeanDevReportvsTargetNew <- data_noDelay$DevReportvsTargetNew - data_noDelay$MeanError

Bin reproduction errors (i.e., moving-window approach, step size = 1, bin width = 45 degrees) according to the relative orientation of the target angle with respect to the interference angle per subject.

range        <- c(-90, 90)
binwidth     <- 45
halfbinwidth <- binwidth / 2
stepsize     <- 5
bincentres   <- seq(range[1]+halfbinwidth, range[2]-halfbinwidth, by = stepsize)
conditions   <- c("Fixed Distraction", "Random Distraction", "Fixed Interruption", "Random Interruption") # conditions

bindata_x     <- array(0, dim = c(length(unique(data_noDelay$SubjectNo)), length(bincentres)))
bindata_dev_y <- array(0, dim = c(length(unique(data_noDelay$SubjectNo)), length(conditions), length(bincentres)))

DisFixIdx <- data_noDelay$allCond == "Fixed Distraction"
DisRanIdx <- data_noDelay$allCond == "Random Distraction"
IntFixIdx <- data_noDelay$allCond == "Fixed Interruption"
IntRanIdx <- data_noDelay$allCond == "Random Interruption"

s = 0

for(sub in unique(data_noDelay$SubjectNo)) {

    b = 0
    s = s + 1
  
    for(bincentre in bincentres){
      
      b = b+1
      
      binsel               <- data_noDelay$DevIntvsTargetNew <= bincentre + halfbinwidth & data_noDelay$DevIntvsTargetNew >= bincentre - halfbinwidth
      bindata_x[s,b]       <- bincentre
      bindata_dev_y[s,1,b] <- mean(data_noDelay$DMeanDevReportvsTargetNew[DisFixIdx == TRUE & binsel == TRUE & data_noDelay$SubjectNo == sub])
      bindata_dev_y[s,2,b] <- mean(data_noDelay$DMeanDevReportvsTargetNew[DisRanIdx == TRUE & binsel == TRUE & data_noDelay$SubjectNo == sub])
      bindata_dev_y[s,3,b] <- mean(data_noDelay$DMeanDevReportvsTargetNew[IntFixIdx == TRUE & binsel == TRUE & data_noDelay$SubjectNo == sub])
      bindata_dev_y[s,4,b] <- mean(data_noDelay$DMeanDevReportvsTargetNew[IntRanIdx == TRUE & binsel == TRUE & data_noDelay$SubjectNo == sub])
      
       }
    }

Create data frame (curve_data) including response bias, angular difference between interference and memory item, subject number, and conditions.

curve_data <- NULL

for(c in 1:length(conditions)){
  
  s = 1
  
  for(sub in unique(data_noDelay$SubjectNo)){
    
    bias         <- bindata_dev_y[s,c,]
    ii           <- data.frame(bias)
    subbindata_x <- bindata_x[s,]
    ii$bindata_x <- subbindata_x
    ii$subnum    <- rep(s, nrow(ii))
    ii$condition <- conditions[c]
    curve_data   <- rbind(curve_data, ii)
    
    s = s+1
  }
}

Add factors Onset Type and Interference Type to curve_data.

curve_data$InterferenceType <- NULL
curve_data$InterferenceType <- ifelse(curve_data$condition == "Fixed Distraction", "Distraction",
                                 ifelse(curve_data$condition == "Random Distraction", "Distraction",
                                        ifelse(curve_data$condition == "Fixed Interruption", "Interruption", "Interruption")))

curve_data$OnsetType <- NULL
curve_data$OnsetType <- ifelse(curve_data$condition == "Fixed Distraction", "Fixed",
                                 ifelse(curve_data$condition == "Random Distraction", "Random",
                                        ifelse(curve_data$condition == "Fixed Interruption", "Fixed", "Random")))

Collapse response bias by factor Onset Type, Interference Type, angular difference between interference and report, and subnum. Calculate summary statistics.

agg_bias               <- aggregate(data = curve_data,  bias ~ OnsetType + InterferenceType + bindata_x + subnum, mean)
summary_bias           <- summarySEwithin(data = agg_bias, measurevar = "bias", withinvars = c("OnsetType","InterferenceType", "bindata_x"), idvar = "subnum")
summary_bias$bindata_x <- as.numeric(as.character(summary_bias$bindata_x))

Plot response bias as a function of Interference Type and Onset Type.

scaleFUN <- function(x) sprintf("%.1f", x)

ggplot(summary_bias, aes(x=bindata_x, y=bias, color =interaction(OnsetType, InterferenceType),  fill = interaction(OnsetType, InterferenceType))) + 
  scale_y_continuous(labels=scaleFUN, breaks=c(-3, -1.5, 0, 1.5, 3)) + 
  geom_point(aes(x=bindata_x, y=bias)) +
  geom_line(aes(x=bindata_x, y=bias)) +
  facet_wrap(~InterferenceType, scales = 'free_x') +
  geom_ribbon(aes(ymin=bias-se, ymax=bias+se), alpha = 0.2)+
  scale_fill_manual(values=c("#E66062","#A3A3A3", "#B01C1E", "#666666")) +
  scale_color_manual(values=c("#E66062","#A3A3A3", "#B01C1E", "#666666"))+
  geom_hline(aes(yintercept=0), colour="#808080", linetype="dashed")+
  geom_vline(aes(xintercept=0), colour="#808080", linetype="dashed")+
  labs(x = "Interference vs. Target (degrees)", y = "Report vs. Target (degrees)") +
  theme_bw() + 
  theme(text=element_text(family = "Avenir"), 
        legend.position="none", 
        axis.text.x  = element_text(size = 13, color = "black"),
        axis.text.y  = element_text(size = 13, color = "black"),
        axis.title.x = element_text(size = 15, color = "black"),
        axis.title.y = element_text(size = 15, color = "black"),
        strip.text.x = element_text(size = 15),
        strip.background = element_blank(),
        axis.line = element_line(colour = "black"),
        panel.border = element_blank(),
        panel.grid.major=element_blank(),
        panel.grid.minor=element_blank())

7.4.5 Stats (response bias)

To test whether the interfering item biases memory reports (i.e., attractive bias towards or repulsive bias from interfering item), the area under the bias curve was integrated – separately for negative and positive target-to-interference angles – and subsequently compared.

subjects = 1:54

curve_data_negative <- curve_data[curve_data$bindata_x < 0,] #left side, negative interference-target angular differences
curve_data_postive  <- curve_data[curve_data$bindata_x > 0,] #right side, positive interference-target angular differences

#integrate right area under the curve
AreaR <- NULL
i = 1
for(s in 1:54){
AreaR[i] <- AUC(curve_data_postive$bindata_x[curve_data_postive$subnum == s], curve_data_postive$bias[curve_data_postive$subnum == s], method = "trapezoid") 
i = i+1
}
AreaRightG                                      <- data.frame(subjects,AreaR)
AreaRightG$condition                            <- "right"
names(AreaRightG)[names(AreaRightG) == "AreaR"] <- "Area"

#integrate left area under the curve  
AreaL <- NULL
i = 1
for(s in 1:54){
AreaL[i] <- AUC(curve_data_negative$bindata_x[curve_data_negative$subnum == s], curve_data_negative$bias[curve_data_negative$subnum == s], method = "trapezoid") 
i = i+1
}
AreaLeftG                                     <- data.frame(subjects,AreaL)
AreaLeftG$condition                           <- "left"
names(AreaLeftG)[names(AreaLeftG) == "AreaL"] <- "Area"

#bind area left and right into data frame
agg_AUCG <- rbind(AreaRightG, AreaLeftG)
## Mean area under the curve (left side):  -52.69941
## Mean area under the curve (right side):  76.59877
## Indicator for attractive bias (left side = negative, right side = positive)

Pairwise comparisons to compare left and right area under the curve.

#right vs. left area under the curve
(BiasTest <- pairedSamplesTTest(data = agg_AUCG, Area ~ condition, id = "subjects"))
## 
##    Paired samples t-test 
## 
## Outcome variable:   Area 
## Grouping variable:  condition 
## ID variable:        subjects 
## 
## Descriptive statistics: 
##                left   right difference
##    mean      76.599 -52.699    129.298
##    std dev. 140.484 162.477    251.460
## 
## Hypotheses: 
##    null:        population means equal for both measurements
##    alternative: different population means for each measurement
## 
## Test results: 
##    t-statistic:  3.779 
##    degrees of freedom:  53 
##    p-value:  <.001 
## 
## Other information: 
##    two-sided 95% confidence interval:  [60.663, 197.934] 
##    estimated effect size (Cohen's d):  0.514

Next, we examine whether the factors Onset Type or Interference Type might influence the magnitude of the response bias. We equate the average response biases for the negative and positive interference-target angular differences of each participant and condition and then compare the resulting equated biases between factors.

subjects = 1:54

curve_data_negative <- curve_data[curve_data$bindata_x < 0,]
curve_data_postive  <- curve_data[curve_data$bindata_x > 0,]

#integrate area right - fixed distraction
AreaR <- NULL
i = 1
for(s in 1:54){
AreaR[i] <- AUC(curve_data_postive$bindata_x[curve_data_postive$subnum == s & curve_data_postive$condition == "Fixed Distraction"], curve_data_postive$bias[curve_data_postive$subnum == s & curve_data_postive$condition == "Fixed Distraction"], method = "trapezoid") 
i = i+1
}
AreaRight1                  <- data.frame(subjects,AreaR)
AreaRight1$condition        <- "Fixed Distraction"
AreaRight1$InterferenceType <- "Distraction"
AreaRight1$OnsetType        <- "Fixed"

#integrate area right - random distraction
AreaR <- NULL
i = 1
for(s in 1:54){
AreaR[i] <- AUC(curve_data_postive$bindata_x[curve_data_postive$subnum == s & curve_data_postive$condition == "Random Distraction"], curve_data_postive$bias[curve_data_postive$subnum == s & curve_data_postive$condition == "Random Distraction"], method = "trapezoid")  
i = i+1
}
AreaRight2                  <- data.frame(subjects,AreaR)
AreaRight2$condition        <- "Random Distraction"
AreaRight2$InterferenceType <- "Distraction"
AreaRight2$OnsetType        <- "Random"

#integrate area right - fixed interruption
AreaR <- NULL
i = 1
for(s in 1:54){
AreaR[i] <- AUC(curve_data_postive$bindata_x[curve_data_postive$subnum == s & curve_data_postive$condition == "Fixed Interruption"], curve_data_postive$bias[curve_data_postive$subnum == s & curve_data_postive$condition == "Fixed Interruption"], method = "trapezoid")  
i = i+1
}
AreaRight3                  <- data.frame(subjects,AreaR)
AreaRight3$condition        <- "Fixed Interruption"
AreaRight3$InterferenceType <- "Interruption"
AreaRight3$OnsetType        <- "Fixed"

#integrate area right - random interruption
AreaR <- NULL
i = 1
for(s in 1:54){
AreaR[i] <- AUC(curve_data_postive$bindata_x[curve_data_postive$subnum == s & curve_data_postive$condition == "Random Interruption"], curve_data_postive$bias[curve_data_postive$subnum == s & curve_data_postive$condition == "Random Interruption"], method = "trapezoid")  
i = i+1
}
AreaRight4                  <- data.frame(subjects,AreaR)
AreaRight4$condition        <- "Random Interruption"
AreaRight4$InterferenceType <- "Interruption"
AreaRight4$OnsetType        <- "Random"

#bind data frames area right
agg_AUC_right <- bind_rows(AreaRight1, AreaRight2, AreaRight3, AreaRight4)

#integrate area left - fixed distraction
AreaL <- NULL
i = 1
for(s in 1:54){
AreaL[i] <- AUC(curve_data_negative$bindata_x[curve_data_negative$subnum == s & curve_data_negative$condition == "Fixed Distraction"], curve_data_negative$bias[curve_data_negative$subnum == s & curve_data_negative$condition == "Fixed Distraction"], method = "trapezoid") 
i = i+1
}
AreaLeft1                  <- data.frame(subjects,AreaL)
AreaLeft1$condition        <- "Fixed Distraction"
AreaLeft1$InterferenceType <- "Distraction"
AreaLeft1$OnsetType        <- "Fixed"

#integrate area left - random distraction
AreaL <- NULL
i = 1
for(s in 1:54){
AreaL[i] <- AUC(curve_data_negative$bindata_x[curve_data_negative$subnum == s & curve_data_negative$condition == "Random Distraction"], curve_data_negative$bias[curve_data_negative$subnum == s & curve_data_negative$condition == "Random Distraction"], method = "trapezoid") 
i = i+1
}
AreaLeft2                  <- data.frame(subjects,AreaL)
AreaLeft2$condition        <- "Random Distraction"
AreaLeft2$InterferenceType <- "Distraction"
AreaLeft2$OnsetType        <- "Random"

#integrate area left - fixed interruption
AreaL <- NULL
i = 1
for(s in 1:54){
AreaL[i] <- AUC(curve_data_negative$bindata_x[curve_data_negative$subnum == s & curve_data_negative$condition == "Fixed Interruption"], curve_data_negative$bias[curve_data_negative$subnum == s & curve_data_negative$condition == "Fixed Interruption"], method = "trapezoid") 
i = i+1
}
AreaLeft3                  <- data.frame(subjects,AreaL)
AreaLeft3$condition        <- "Fixed Interruption"
AreaLeft3$InterferenceType <- "Interruption"
AreaLeft3$OnsetType        <- "Fixed"

#integrate area left - random interruption
AreaL <- NULL
i = 1
for(s in 1:54){
AreaL[i] <- AUC(curve_data_negative$bindata_x[curve_data_negative$subnum == s & curve_data_negative$condition == "Random Interruption"], curve_data_negative$bias[curve_data_negative$subnum == s & curve_data_negative$condition == "Random Interruption"], method = "trapezoid") 
i = i+1
}
AreaLeft4                  <- data.frame(subjects,AreaL)
AreaLeft4$condition        <- "Random Interruption"
AreaLeft4$InterferenceType <- "Interruption"
AreaLeft4$OnsetType        <- "Random"

#bind data frames area left
agg_AUC_left <- bind_rows(AreaLeft1, AreaLeft2, AreaLeft3, AreaLeft4)

#combine area left and right into data frame
agg_AUC <- bind_cols(agg_AUC_left, agg_AUC_right)

#rename headers
names(agg_AUC)[names(agg_AUC) == "condition...3"]        <- "condition"
names(agg_AUC)[names(agg_AUC) == "InterferenceType...4"] <- "InterferenceType"
names(agg_AUC)[names(agg_AUC) == "OnsetType...5"]        <- "OnsetType"
names(agg_AUC)[names(agg_AUC) == "subjects...1"]         <- "subjects"

#get relevant columns
agg_AUC <- agg_AUC[c("subjects", "AreaL", "AreaR","InterferenceType", "OnsetType")]

#get mean response bias
agg_AUC$AreaL_flipped <-  agg_AUC$AreaL * (-1)
agg_AUC$mean          <- (agg_AUC$AreaL_flipped + agg_AUC$AreaR)/2

Repeated-measures ANOVA with factors Onset Type and Interference Type.

ezANOVA(data = agg_AUC, 
              dv = mean, 
              wid = subjects, 
              within = .(OnsetType, InterferenceType),
              detailed = TRUE,
              type = 3)
## $ANOVA
##                       Effect DFn DFd         SSn     SSd          F
## 1                (Intercept)   1  53 1083522.912 1831357 31.3574622
## 2                  OnsetType   1  53   17459.617 1307961  0.7074827
## 3           InterferenceType   1  53   43185.075 1750197  1.3077439
## 4 OnsetType:InterferenceType   1  53    3504.243 1587902  0.1169624
##              p p<.05          ges
## 1 7.783999e-07     * 0.1433053219
## 2 4.040598e-01       0.0026882138
## 3 2.579426e-01       0.0066228663
## 4 7.337051e-01       0.0005407013