Cognitive Interference in Multiple System Categorization

Study Motivation

The ability to observe and organize environmental stimuli into meaningful knowledge is an important behaviour in animal survival. It helps to identify dangerous landscapes and poisonous foods, as well as understand the parameters of environmental features and abstract that to other similar stimuli. Furthermore, this ability has continued to influence higher order cognition in humans. For instance, among taxonomists, the ability to recognize characteristics of species and group them according to their similarities is a necessary professional skill. While many Galapagos finches appear similar, a taxonomist that was unable to tell the difference between them would not be particularly good.

In the COVIS model of category learning, categorization is characterized by two different systems competing simultaneously against each other in order to detect and process incoming information (Ashby, Alfonso-Reese, Turken, & Waldron, 1998). In it, categorization is assumed to be mediated by one of two independent systems. In the first system, a verbal system processes incoming information using learned, easily verbalizable rules and hypothesis testing. Its dependency on hypothesis testing and executive functioning indicates that this process is heavily influenced by working memory components. In particular, it is thought that these are the verbal components of working memory, as interpretted by Baddeley and Hitch in their 1974 paper, and updated by Baddeley in 1986, 2000, and 2013, and is specifically mediated by a central executive supportive system referred to as a the phonological loop. The phonological loop is a rehearsal mechanism responsible for maintain chuncks of temporary verbalizable information. For instance, I could ask you to remember a stream of numbers and you might do so by repeating the numbers to yourself over and over again. In contrast, the second system utilizes a similarity-based II process, where multiple dimensions of an object are integrated at a procedural learning-based level. Because of its reliance on procedural memory, II makes predictions about motor performance during categorization tasks; specifically that II performance will diminish in the presence of an unrelated motor function (Maddox, Bohil, & Ing, 2004). As both of these processes rely on seemingly independent systems in order to function and make different predictions, it would appear that the processes themselves can be differentiated from one another.

A fundamental aspect of multiple system categorization is that different systems are supported by different cognitive structures. In order to demonstrate this, it is necessary to provide instances of structure disruption impacting one system, but not the other. Though it could be said that RB learning is influenced by working memory, the evidence that supports this varies. It is especially important to consider that there is reason to think that RB learning may be affected by executive functioning and mood as well. Rule-based categorization appears to be influenced and mediated by a multitude of factors, the interaction of which is not well understood.

The Current Study

The current study addresses these concerns by having participants complete a Gaussian blur categorization task, where participants learn to categorize either a rule-based categorization set or a non-rule-based (Information Integration) category set. Simultaneously, participants will also be asked to complete one of two concurrent tasks. The first concurrent task will require participants to speak a list of letters out loud while simultaneously completing the categorization task. The second concurrent task will require participants to tap on the desk with their non-dominant hand when a colon appears on the screen during the categorization task. It is hypothesized that those participants who are assigned to the concurrent verbal task will show performance deficits in rule-based category learning. The concurrent verbal task is not expected to impact II category learning. Additionally, as information integration category learning is thought to be influenced by procedural memory and motor function, it is expected that those participants who are assigned to the tapping concurrent task will show performance deficits in information integration category learning, but not rule-based learning. This study’s tasks have been developed on Psychopy2 and involve participants being assigned to one of four groups, (1) rule-defined concurrent tapping, (2) rule-defined concurrent articulation, (3) information integration concurrent tapping, or (4) information integration concurrent articulation.

Data Analysis

Libraries

The first step in any R analysis requires us to prepare the libraries that R will use.

#First install the packages that you don't already have in R. For example, I don't have the packages for 'schoRsch' and 'summary tools'. Once they've been installed, we # them out so that I don't continue to install them every time we run this script.

#install.packages('schoRsch')
#install.packages('summarytools')
#install.packages('apaTables')
#install.packages('Rmisc')
#install.packages('knitr')
#install.packages('kableExtra')
#install.packages('prettydoc')
#install.packages('tidyverse')
#install.packages("knitr")
#install.packages('ez')
#install.packages('stringi')
#install.packages("ggplot2")
#install.packages("colorspace")
#install.packages('curl')
#install.packages("data.table")
#install.packages("zip")
#install.packages("broom")

library(broom)
library(stringi)
library(ggplot2) #for plotting
library(readxl) #reading in excel docs  
library(ez) #this package is calls the car package and runs basic ANOVAs and other stats
library(apaTables) 
library(RColorBrewer) 
library(schoRsch)
library(Rmisc)
library(summarytools)
library(knitr)
library(plyr)
library(kableExtra)
library(prettydoc)
library(tidyverse)

Data Files

Next, we will need to import the data that we will be using for our analysis.The following data is a set of 20 participants collected as part of a Honours thesis project.

#mydata = readr::read_csv("https://www.dropbox.com/home/Psychopy%20Examples/coarticulation%20gabor%20blur%20task/Data%20Analysis?preview=Cogintcatlearning.csv")

library(readr)
mydata <- read_csv("COVISInteferenceData.csv")
#View(mydata)

Statistical Analysis

Accuracy

Before we can begin our data analysis, we must first create a new data frame. R works best when data has been organized into a long format/matrix. Right now, our data is a ‘short’ format, where each participant has a column for each block. What we want is for each participant to have their own row for each block of each variable, so eight total. Before we can analyse each block, we need to have a single column (that we’ll call performance) with the performance at that block for a subject, and another column (called block) with the numbers 1, 2, 3, and 4 in it. The new data frame will have a column for Subject, Category, Concurrent Task, Block, and Performance.

Step One: Data Visualization

We’ll begin by using our old data file.

Subject <- mydata$`Participant Code`
Category <-mydata$`Category Set`
ConcurrentTask <- mydata$`Concurrent Set`
Condition <- mydata$Condition
#Blocks for Accuracy
Block1 <- mydata$`B1 Accuracy`
Block2 <- mydata$`B2 Accuracy`
Block3 <- mydata$`B3 Accuracy`
Block4 <- mydata$`B4 Accuracy`

#Now that we have collected our data, we can arrange it into a single data frame.
myaccdata_wide <- data.frame(Subject, Category, ConcurrentTask, Condition, Block1, Block2, Block3, Block4)

Next we need to make this taller.

library(tidyr)
myaccdata_wide <- gather(myaccdata_wide, Block, Performance,
                      Block1:Block4, factor_key = TRUE)

Lets make a table of our performance.Below we can we performance broken down by several factors. Though it looks large, remember that it is a representation of the accuracy and response across four blocks, for each of our four conditions (RB/Letters, RB/Tapping, II/Letters, II/Tapping).

mydata_acc <- summarySE(data = myaccdata_wide, measurevar = "Performance", groupvars = c("Category",  "ConcurrentTask", "Condition", "Block"),
                      na.rm = FALSE, conf.interval = 0.95, .drop = TRUE)
kable(mydata_acc, digits = 3,
      caption = "Table 1. Accuracy Performance Summary",
      align = 'c') %>%
  kable_styling(bootstrap_options =
                  c("hover", "responsive", "striped"),
                full_width = F, position = "center")

Table 1. Accuracy Performance Summary

Category	ConcurrentTask	Condition	Block	N	Performance	sd	se	ci
II	Letters	C2	Block1	20	0.623	0.110	0.025	0.052
II	Letters	C2	Block2	20	0.621	0.127	0.028	0.059
II	Letters	C2	Block3	20	0.668	0.112	0.025	0.053
II	Letters	C2	Block4	20	0.694	0.144	0.032	0.068
II	None	Control 2	Block1	19	0.655	0.081	0.018	0.039
II	None	Control 2	Block2	19	0.713	0.073	0.017	0.035
II	None	Control 2	Block3	19	0.694	0.130	0.030	0.063
II	None	Control 2	Block4	19	0.738	0.110	0.025	0.053
II	Tapping	C4	Block1	18	0.601	0.111	0.026	0.055
II	Tapping	C4	Block2	18	0.697	0.104	0.024	0.051
II	Tapping	C4	Block3	18	0.711	0.152	0.036	0.076
II	Tapping	C4	Block4	18	0.712	0.119	0.028	0.059
RB	Letters	C1	Block1	21	0.524	0.080	0.017	0.036
RB	Letters	C1	Block2	21	0.582	0.114	0.025	0.052
RB	Letters	C1	Block3	21	0.610	0.134	0.029	0.061
RB	Letters	C1	Block4	21	0.643	0.151	0.033	0.069
RB	None	Control 1	Block1	19	0.596	0.113	0.026	0.054
RB	None	Control 1	Block2	19	0.668	0.141	0.032	0.068
RB	None	Control 1	Block3	19	0.687	0.151	0.035	0.073
RB	None	Control 1	Block4	19	0.681	0.165	0.038	0.079
RB	Tapping	C3	Block1	20	0.535	0.075	0.017	0.035
RB	Tapping	C3	Block2	20	0.606	0.178	0.040	0.083
RB	Tapping	C3	Block3	20	0.612	0.156	0.035	0.073
RB	Tapping	C3	Block4	20	0.648	0.162	0.036	0.076

Now let’s plot some learning curves using the table we just built as a reference.

AC_Full = ggplot(mydata_acc, aes(x = Block, y = Performance, group = Condition, Colour = Condition))+
  geom_line(aes(colour = Condition, group = Condition), position = position_dodge(width = .4))+
  geom_point(aes(colour = Condition), position = position_dodge(width = .4))+
  geom_errorbar(aes(ymin = Performance-se, ymax = Performance+se), width = 0.1, position = position_dodge(width = .4))+
  ggtitle("Accuracy by Block")+
  scale_fill_discrete(name = "Condition")+
  scale_fill_brewer(palette = "Paired")+
  theme_classic()

AC_Full + scale_color_discrete(
  name = "Condition",
  breaks = c("C1", "C2", "C3", "C4", "Control 1", "Control 2"),
  labels = c("Rule-Based Verbal Concurrent","Information Integration Verbal Concurrent", "Rule-Based Motor Concurrent", "Information Integration Motor Concurrent", "Rule-Based Control", "Information Integration Control")
)

There’s a lot of information in this graph. Again, we see the four different conditions compaired across each block. However, in regards to our hypothesis, we’re most interested in the difference in performance between the two concurrent tasks in the Rule-Based category set and the two concurrent tasks in the Information Integration category set. Let’s make two graphs that depict this.

First, the Rule-Based category set:

acgraph = ggplot(mydata_acc, aes(x = Block, y = Performance, group = Condition, Colour = Condition))+
  geom_line(aes(colour = Condition, group = Condition), position = position_dodge(width = .4))+
  geom_point(aes(colour = Condition), position = position_dodge(width = .4))+
  geom_errorbar(aes(ymin = Performance-se, ymax = Performance+se), width = 0.1, position = position_dodge(width = .4))+
  ggtitle("Accuracy by Block")+
  scale_fill_discrete(name = "Condition")+
  scale_fill_brewer(palette = "Paired")+
  theme_classic()

#Now we'll tell R to break the graphs down by Category Type, which we specified earlier.

acgraph = acgraph + facet_wrap(~ Category) + scale_color_discrete(
  name = "Condition",
  breaks = c("C2", "C4", "Control 2", "C1", "C3", "Control 1"),
  labels = c("Information Integration Verbal Concurrent", "Information Integration Motor Concurrent", "Information Integration Control", "Rule-Based Verbal Concurrent","Rule-Based Motor Concurrent", "Rule-Based Control")
)

print(acgraph)
ggsave("acgraph.pdf")

Now we can see performance (accuracy) broken down by category set. On the left, we can see the performance of conditions C2 and C4 in the Information Integration category set (II). If we’re familiar with the original data set, we will know that the C2 group completed an II category set while completing a concurrent letter articulation task, and the C4 group completed an II category set while completing a concurrent tapping task. It was expected that for the II category set, participants who were in the tapping condition would perform worse than those participants in the letter task. This was thought to occur because II category learning requires the use of procedural memory, which is also thought to be used in motor function tasks. A diversion in resources because of a concurrent motor task, should move resources away from II category learning, resulting in poorer performance. As we can see, this does not appear to be the case in our II

Step Two: Data Analysis

To set up a between subjects ANOVA using ez, we need to specify the data file (that we created above), the dependent variable, the error term and the factors.

Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().Collapsing data to cell means. IF the requested effects are a subset of the full design, you must use the “within_full” argument, else results may be inaccurate.

Table 2. Mixed ANOVA on performance across block by category set and concurrent task.

	Effect	DFn	DFd	SSn	SSd	F	p	p<.05	ges
1	(Intercept)	1	110	193.7890	5.5038	3873.0819	0.0000	*	0.9640
2	Category	1	110	0.4540	5.5038	9.0731	0.0032	*	0.0590
3	ConcurrentTask	2	110	0.2932	5.5038	2.9304	0.0576		0.0389
5	Block	3	330	0.6062	1.7395	38.3368	0.0000	*	0.0772
4	Category:ConcurrentTask	2	110	0.0214	5.5038	0.2139	0.8078		0.0029
6	Category:Block	3	330	0.0067	1.7395	0.4218	0.7375		0.0009
7	ConcurrentTask:Block	6	330	0.0418	1.7395	1.3229	0.2462		0.0057
8	Category:ConcurrentTask:Block	6	330	0.0365	1.7395	1.1529	0.3314		0.0050

Block Main Effect Based on an alpha level of 0.05, a main effect of Block was found with F(3, 210) = 24.3511, p < 0.0000, n^2 = 0.0801. A post hoc bonferroni correction confirms a significant difference between block 1 and block 4 in the rule-based category sets (p = 0.0142).

#Define RB data sets:

RB_Perf = subset(mydata_acc, Category == "RB")

#Create a pairwise t test with bonferroni correction:

RB_post = pairwise.t.test(RB_Perf$Performance, RB_Perf$Block, p.adjust.method = "bonferroni", paired = T)

#Round the results to 4 decimal points:

RB_post = data.frame(round(RB_post$p.value,4))

#Format the results table so that significant p-values with be bolded:

RB_posthoc = RB_post %>%
  mutate(
    Block1 = text_spec(Block1, bold = (ifelse(Block1 < .05, "TRUE", "FALSE"))),
    Block2 = text_spec(Block2, bold = (ifelse(Block2 < .05, "TRUE", "FALSE"))),
    Block3 = text_spec(Block3, bold = (ifelse(Block3 < .05, "TRUE", "FALSE")))
  )

#Add row labels:

RB_posthocL = data.frame("Comparison" = c("Block2", "Block3", "Block4"))
RB_posthoc = cbind(RB_posthocL, RB_posthoc)

#Create a table to display the results:
kable(RB_posthoc, digits = 4,
      caption = "Table 4. Post-hoc test of rule-defined performance across block.",
      align = 'c', escape = FALSE) %>%
  kable_styling(bootstrap_options = 
                  c("hover", "responsive", "striped"),
                full_width = F, position = "center")

Table 4. Post-hoc test of rule-defined performance across block.

Comparison	Block1	Block2	Block3
Block2	0.0337	NA	NA
Block3	0.0031	0.3839	NA
Block4	0.0567	0.8343	1

#Repeat this process for II Blocks. Define data set for II:
II_Perf = subset(mydata_acc, Category == "II")

#Create a pairwise t test with bonferroni correction:

II_post = pairwise.t.test(II_Perf$Performance, II_Perf$Block, p.adjust.method = "bonferroni", paired = T)

#Round the results to 4 decimal points:

II_post = data.frame(round(II_post$p.value,4))

#Format the results table so that significant p-values with be bolded:

II_posthoc = II_post %>%
  mutate(
    Block1 = text_spec(Block1, bold = (ifelse(Block1 < .05, "TRUE", "FALSE"))),
    Block2 = text_spec(Block2, bold = (ifelse(Block2 < .05, "TRUE", "FALSE"))),
    Block3 = text_spec(Block3, bold = (ifelse(Block3 < .05, "TRUE", "FALSE")))
  )

#Add row labels:

II_posthocL = data.frame("Comparison" = c("Block2", "Block3", "Block4"))
II_posthoc = cbind(II_posthocL, II_posthoc)

#Create a table to display the results:
kable(II_posthoc, digits = 4,
      caption = "Table 5. Post-hoc test of information integration performance across block.",
      align = 'c', escape = FALSE) %>%
  kable_styling(bootstrap_options = 
                  c("hover", "responsive", "striped"),
                full_width = F, position = "center")

Table 5. Post-hoc test of information integration performance across block.

Comparison	Block1	Block2	Block3
Block2	1	NA	NA
Block3	0.682	1	NA
Block4	0.1632	0.7195	1

Response Time

The following data is for response time values. To being, we’ll have to edit our wide data frame that we were using before to include response time for blocks, rather than accuracy.

Subject <- mydata$`Participant Code`
Category <-mydata$`Category Set`
ConcurrentTask <- mydata$`Concurrent Set`
Condition <- mydata$Condition
#Blocks for Response Time
Block1 <- mydata$`B1 Response Time`
Block2 <- mydata$`B2 Response Time`
Block3 <- mydata$`B3 Response Time`
Block4 <- mydata$`B4 Response Time`

#Now that we have collected our data, we can arrange it into a single data frame.
myRTdata_wide <- data.frame(Subject, Category, ConcurrentTask, Condition, Block1, Block2, Block3, Block4)

#We'll gather the values that we want for our visualization and analysis:
myRTdata_wide <- gather(myRTdata_wide, Block, Performance,
                      Block1:Block4, factor_key = TRUE)

Step One: Data Visualization

Here is our table of data:

#And then visualize it:
mydata_RT <- summarySE(data = myRTdata_wide, measurevar = "Performance", groupvars = c("Category",  "ConcurrentTask", "Condition", "Block"),
                      na.rm = FALSE, conf.interval = 0.95, .drop = TRUE)

kable(mydata_RT, digits = 3,
      caption = "Table 3. Response Time Performance Summary",
      align = 'c') %>%
  kable_styling(bootstrap_options =
                  c("hover", "responsive", "striped"),
                full_width = F, position = "center")

Table 3. Response Time Performance Summary

Category	ConcurrentTask	Condition	Block	N	Performance	sd	se	ci
II	Letters	C2	Block1	19	1.719	1.297	0.298	0.625
II	Letters	C2	Block2	19	0.834	0.335	0.077	0.162
II	Letters	C2	Block3	19	0.817	0.391	0.090	0.188
II	Letters	C2	Block4	19	0.869	0.420	0.096	0.202
II	None	Control 2	Block1	19	1.277	0.811	0.186	0.391
II	None	Control 2	Block2	19	0.920	0.284	0.065	0.137
II	None	Control 2	Block3	19	0.825	0.242	0.055	0.116
II	None	Control 2	Block4	19	0.877	0.308	0.071	0.149
II	Tapping	C4	Block1	16	1.473	0.471	0.118	0.251
II	Tapping	C4	Block2	16	1.063	0.413	0.103	0.220
II	Tapping	C4	Block3	16	1.005	0.327	0.082	0.174
II	Tapping	C4	Block4	16	1.005	0.320	0.080	0.171
RB	Letters	C1	Block1	20	1.297	0.755	0.169	0.353
RB	Letters	C1	Block2	20	0.877	0.446	0.100	0.209
RB	Letters	C1	Block3	20	0.764	0.280	0.063	0.131
RB	Letters	C1	Block4	20	0.757	0.325	0.073	0.152
RB	None	Control 1	Block1	17	1.478	0.465	0.113	0.239
RB	None	Control 1	Block2	17	1.218	0.458	0.111	0.235
RB	None	Control 1	Block3	17	1.138	0.427	0.104	0.220
RB	None	Control 1	Block4	17	0.999	0.408	0.099	0.210
RB	Tapping	C3	Block1	19	1.699	0.737	0.169	0.355
RB	Tapping	C3	Block2	19	1.108	0.489	0.112	0.235
RB	Tapping	C3	Block3	19	1.044	0.438	0.100	0.211
RB	Tapping	C3	Block4	19	0.907	0.322	0.074	0.155

Now let’s create three graphs. The first should be with all of the conditions and the second and third should be broken down into their respective category sets.

rtplot = ggplot(mydata_RT, aes(x = Block, y = Performance, group = Condition, Colour = Condition))+
  geom_line(aes(colour = Condition, group = Condition), position = position_dodge(width = .4))+
  geom_point(aes(colour = Condition), position = position_dodge(width = .4))+
  geom_errorbar(aes(ymin = Performance-se, ymax = Performance+se), width = 0.1, position = position_dodge(width = .4))+
  ggtitle("Response Time by Block")+
  ylab("Response Time")+
  scale_fill_discrete(name = "Condition")+
  scale_fill_brewer(palette = "Paired")+
  theme_classic()

rtplot + scale_color_discrete(
  name = "Condition",
  breaks = c("C1", "C2", "C3", "C4", "Control 1", "Control 2"),
  labels = c("Rule-Based Verbal Concurrent","Information Integration Verbal Concurrent", "Rule-Based Motor Concurrent", "Information Integration Motor Concurrent", "Rule-Based Control", "Information Integration Control")
)

#Now we'll tell R to break the graph down by Category Type, which we specified earlier.

rtplot + facet_wrap(~ Category) + facet_wrap(~ Category) + scale_color_discrete(
  name = "Condition",
  breaks = c("C2", "C4", "Control 2", "C1", "C3", "Control 1"),
  labels = c("Information Integration Verbal Concurrent", "Information Integration Motor Concurrent", "Information Integration Control", "Rule-Based Verbal Concurrent","Rule-Based Motor Concurrent", "Rule-Based Control")
)

Step Two: Data Analysis

rt = ezANOVA(myRTdata_wide,
              dv = .(Performance), #DV
              wid = .(Subject), #Subject as within Independent Variable means subject is the error term
              between = .(Category, ConcurrentTask), #Condition as the Independent Variable
              within = .(Block),
              detailed = TRUE,
              return_aov = TRUE,
              type = 3)
#apa.ezANOVA.table(rt, table.title = "Table 4. Mixed ANOVA on response time across block by category set and concurrent task.")
kable(rt$ANOVA, digits = 4,
      caption = "Table 6. Mixed ANOVA on response time across block by category set and concurrent task.",
      
      align = 'c') %>%
  kable_styling(bootstrap_options =
                  c("hover", "responsive", "striped"),
                full_width = TRUE, position = "center")

Table 6. Mixed ANOVA on response time across block by category set and concurrent task.

	Effect	DFn	DFd	SSn	SSd	F	p	p<.05	ges
1	(Intercept)	1	103	509.0611	55.5503	943.8882	0.0000	*	0.8183
2	Category	1	103	0.2422	55.5503	0.4491	0.5042		0.0021
3	ConcurrentTask	2	103	2.2102	55.5503	2.0490	0.1341		0.0192
5	Block	3	309	24.9367	57.4651	44.6964	0.0000	*	0.1808
4	Category:ConcurrentTask	2	103	2.4009	55.5503	2.2259	0.1131		0.0208
6	Category:Block	3	309	0.4936	57.4651	0.8847	0.4493		0.0043
7	ConcurrentTask:Block	6	309	1.3574	57.4651	1.2165	0.2974		0.0119
8	Category:ConcurrentTask:Block	6	309	1.3417	57.4651	1.2024	0.3047		0.0117

Block Main Effects Based on an alpha level of 0.05, a main effect of Block was found with F(3, 210) = 31.9265, p < 0.0000, n^2 = 0.1941. In the Rule-Based category set, a bonferroni correction indicated a significant difference between Block 2 and Block 4 in Rule-Based Category sets (p = 0.0275).

#Define RB data sets:

RB_Perf = subset(mydata_RT, Category == "RB")

#Create a pairwise t test with bonferroni correction:

RB_post = pairwise.t.test(RB_Perf$Performance, RB_Perf$Block, p.adjust.method = "bonferroni", paired = T)

#Round the results to 4 decimal points:

RB_post = data.frame(round(RB_post$p.value,4))

#Format the results table so that significant p-values with be bolded:

RB_posthoc = RB_post %>%
  mutate(
    Block1 = text_spec(Block1, bold = (ifelse(Block1 < .05, "TRUE", "FALSE"))),
    Block2 = text_spec(Block2, bold = (ifelse(Block2 < .05, "TRUE", "FALSE"))),
    Block3 = text_spec(Block3, bold = (ifelse(Block3 < .05, "TRUE", "FALSE")))
  )

#Add row labels:

RB_posthocL = data.frame("Comparison" = c("Block2", "Block3", "Block4"))
RB_posthoc = cbind(RB_posthocL, RB_posthoc)

#Create a table to display the results:
kable(RB_posthoc, digits = 4,
      caption = "Table 7. Post-hoc test of rule-defined performance across block.",
      align = 'c', escape = FALSE) %>%
  kable_styling(bootstrap_options = 
                  c("hover", "responsive", "striped"),
                full_width = F, position = "center")

Table 7. Post-hoc test of rule-defined performance across block.

Comparison	Block1	Block2	Block3
Block2	0.2818	NA	NA
Block3	0.185	0.1594	NA
Block4	0.1445	0.1659	0.9716

#Repeat this process for II Blocks. Define data set for II:
II_Perf = subset(mydata_RT, Category == "II")

#Create a pairwise t test with bonferroni correction:

II_post = pairwise.t.test(II_Perf$Performance, II_Perf$Block, p.adjust.method = "bonferroni", paired = T)

#Round the results to 4 decimal points:

II_post = data.frame(round(II_post$p.value,4))

#Format the results table so that significant p-values with be bolded:

II_posthoc = II_post %>%
  mutate(
    Block1 = text_spec(Block1, bold = (ifelse(Block1 < .05, "TRUE", "FALSE"))),
    Block2 = text_spec(Block2, bold = (ifelse(Block2 < .05, "TRUE", "FALSE"))),
    Block3 = text_spec(Block3, bold = (ifelse(Block3 < .05, "TRUE", "FALSE")))
  )

#Add row labels:

II_posthocL = data.frame("Comparison" = c("Block2", "Block3", "Block4"))
II_posthoc = cbind(II_posthocL, II_posthoc)

#Create a table to display the results:
kable(II_posthoc, digits = 4,
      caption = "Table 8. Post-hoc test of information integration performance across block.",
      align = 'c', escape = FALSE) %>%
  kable_styling(bootstrap_options = 
                  c("hover", "responsive", "striped"),
                full_width = F, position = "center")

Table 8. Post-hoc test of information integration performance across block.

Comparison	Block1	Block2	Block3
Block2	0.4892	NA	NA
Block3	0.3249	0.7846	NA
Block4	0.3287	1	1