1 Packages

2 Read in data

# read data 
tdata_between <- read.delim("tdata_between.txt", header=TRUE, sep="\t", na.strings="NA", dec=".", strip.white=TRUE) # Exp1a

tdata_within <- read.delim("tdata_within.txt", header=TRUE, sep="\t", na.strings="NA", dec=".", strip.white=TRUE) # Exp1b

tdata_manip <- read.delim("tdata_manip.txt", header=TRUE, sep="\t", na.strings="NA", dec=".", strip.white=TRUE) # Exp2

tdata_2d <- read.delim("tdata_between_2d.txt", header=TRUE, sep="\t", na.strings="NA", dec=".", strip.white=TRUE) # Exp3

3 Plot Results

3.1 Plot Results of Exp. 1a

tdata <- tdata_between

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_between <- tdata %>%
  group_by(Dimensions, Transformation, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions', 'Transformation'. You can override using the `.groups` argument.

## Warning: Ignoring unknown aesthetics: y

3.2 Plot Results of Exp. 1b

tdata <- tdata_within

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_within <- tdata %>%
  group_by(Dimensions, Transformation, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions', 'Transformation'. You can override using the `.groups` argument.

## Warning: Ignoring unknown aesthetics: y

3.3 Plot Results of Exp. 2

tdata <- tdata_manip

# declare factors and their levels 
#$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)


tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_2d <- tdata %>%
  group_by(Transformation, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Transformation'. You can override using the `.groups` argument.

## Warning: Ignoring unknown aesthetics: y

3.4 Plot Results of Exp. 3

tdata <- tdata_2d

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)


tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_2d <- tdata %>%
  group_by(Dimensions, Transformation, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions', 'Transformation'. You can override using the `.groups` argument.

## Warning: Ignoring unknown aesthetics: y

4 Main effect of Dimensions

4.1 Exp 1a

tdata <- tdata_between

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_between <- tdata %>%
  group_by(Dimensions, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions'. You can override using the `.groups` argument.

## Warning: Ignoring unknown aesthetics: y

## Warning: Unknown or uninitialised column: `Transformation`.

library(scales)
theme_set(theme_light(base_size = 12, base_family = "Poppins"))

g<- ggplot(plotdata, 
       aes(x = "3D (between)",
           y = pct,
           fill = selection_rec)) +
  geom_bar(stat = "identity",
           position = "fill") +
  scale_y_continuous(breaks = seq(0, 1, .25), 
                     label = percent) +
  geom_text(aes(label = lbl), 
            size = 4, 
            position = position_stack(vjust = 0.5)) +
  scale_fill_brewer(palette = "Pastel1") +
  labs(y = "Percentage", 
       fill = "Selec. Obj.",
       x = "Test condition",
       title = "3D Context a (N = 854)")+
  annotate(geom = "hline",yintercept = 0.5, y = 0.5, color = "black", size = 1, linetype='dotted')+
  annotate("pointrange", x = 1, y = 1 - plotdata_sub$pct, 
           ymin = 1 - plotdata_sub$pct - plotdata_sub$CI, 
           ymax = 1- plotdata_sub$pct + plotdata_sub$CI, 
           colour = "black", size = 0.8, shape = 22, fill = "lightblue", fatten = 1)+
  theme(legend.position = "top", axis.title = element_text(size = 15), axis.text = element_text(size = 13, color = "black"),
        legend.text = element_text(size = 13))

## Warning: Ignoring unknown aesthetics: y

#ggsave("selections_between_main.pdf",width=3.5,height=5)
#ggsave("selections_between_main.svg",width=3.5,height=5)

4.2 Exp. 1b

tdata <- tdata_within

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_within <- tdata %>%
  group_by(Dimensions, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions'. You can override using the `.groups` argument.

## Warning: Ignoring unknown aesthetics: y

## Warning: Unknown or uninitialised column: `Transformation`.

library(scales)
theme_set(theme_light(base_size = 12, base_family = "Poppins"))

g<- ggplot(plotdata, 
       aes(x = "3D (within)",
           y = pct,
           fill = selection_rec)) +
  geom_bar(stat = "identity",
           position = "fill") +
  scale_y_continuous(breaks = seq(0, 1, .25), 
                     label = percent) +
  geom_text(aes(label = lbl), 
            size = 4, 
            position = position_stack(vjust = 0.5)) +
  scale_fill_brewer(palette = "Pastel1") +
  labs(y = "Percentage", 
       fill = "Selec. Obj.",
       x = "Test condition",
       title = "3D Context b (N = 854)")+
  annotate(geom = "hline",yintercept = 0.5, y = 0.5, color = "black", size = 1, linetype='dotted')+
  annotate("pointrange", x = 1, y = 1 - plotdata_sub$pct, 
           ymin = 1 - plotdata_sub$pct - plotdata_sub$CI, 
           ymax = 1- plotdata_sub$pct + plotdata_sub$CI, 
           colour = "black", size = 0.8, shape = 22, fill = "lightblue", fatten = 1)+
  theme(legend.position = "top", axis.title = element_text(size = 15), axis.text = element_text(size = 13, color = "black"),
        legend.text = element_text(size = 13))

## Warning: Ignoring unknown aesthetics: y

#ggsave("selections_within_main.pdf",width=3.5,height=5)
#ggsave("selections_within_main.svg",width=3.5,height=5)

4.3 Exp. 2

tdata <- tdata_manip

# declare factors and their levels 
#tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_within <- tdata %>%
  group_by(selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## Warning: Ignoring unknown aesthetics: y

## Warning: Unknown or uninitialised column: `Transformation`.

library(scales)
theme_set(theme_light(base_size = 12, base_family = "Poppins"))

g<- ggplot(plotdata, 
       aes(x = "3D with manipul. obj.",
           y = pct,
           fill = selection_rec)) +
  geom_bar(stat = "identity",
           position = "fill") +
  scale_y_continuous(breaks = seq(0, 1, .25), 
                     label = percent) +
  geom_text(aes(label = lbl), 
            size = 4, 
            position = position_stack(vjust = 0.5)) +
  scale_fill_brewer(palette = "Pastel1") +
  labs(y = "Percentage", 
       fill = "Selec. Obj.",
       x = "Test condition",
       title = "3D Context c (N = 868)")+
  annotate(geom = "hline",yintercept = 0.5, y = 0.5, color = "black", size = 1, linetype='dotted')+
  annotate("pointrange", x = 1, y = 1 - plotdata_sub$pct, 
           ymin = 1 - plotdata_sub$pct - plotdata_sub$CI, 
           ymax = 1- plotdata_sub$pct + plotdata_sub$CI, 
           colour = "black", size = 0.8, shape = 22, fill = "lightblue", fatten = 1)+
  theme(legend.position = "top", axis.title = element_text(size = 15), axis.text = element_text(size = 13, color = "black"),
        legend.text = element_text(size = 13))

## Warning: Ignoring unknown aesthetics: y

ggsave("selections_within_main.pdf",width=3.5,height=5)
#ggsave("selections_within_main.svg",width=3.5,height=5)

4.4 Exp. 3

tdata <- tdata_2d

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_2d <- tdata %>%
  group_by(Dimensions, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions'. You can override using the `.groups` argument.

library(scales)
theme_set(theme_light(base_size = 12, base_family = "Poppins"))

g<- ggplot(plotdata, 
       aes(x = Dimensions,
           y = pct,
           fill = selection_rec)) +
  geom_bar(stat = "identity",
           position = "fill") +
  scale_y_continuous(breaks = seq(0, 1, .25), 
                     label = percent) +
  geom_text(aes(label = lbl), 
            size = 4, 
            position = position_stack(vjust = 0.5)) +
  scale_fill_brewer(palette = "Pastel1") +
  labs(y = "Percentage", 
       fill = "Selec. Obj.",
       x = "Dimensions",
       title = "2D Context (N = 854)")+
  annotate(geom = "hline",yintercept = 0.5, y = 0.5, color = "black", size = 1, linetype='dotted')+
  annotate("pointrange", x = 1, y = 1 - plotdata_sub$pct, 
           ymin = 1 - plotdata_sub$pct - plotdata_sub$CI, 
           ymax = 1- plotdata_sub$pct + plotdata_sub$CI, 
           colour = "black", size = 0.8, shape = 22, fill = "lightblue", fatten = 1)+
  theme(legend.position = "top", axis.title = element_text(size = 15), axis.text = element_text(size = 13, color = "black"),
        legend.text = element_text(size = 13))

## Warning: Ignoring unknown aesthetics: y

#ggsave("selections_2d_main.pdf",width=3.5,height=5)
#ggsave("selections_2d_main.svg",width=3.5,height=5)

Merge all in one data frame (main effect of dimensions)

tdata <- tdata_between

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3Da", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

tdata_b <- tdata

tdata <- tdata_within

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3Db", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

tdata_w <- tdata

tdata <- tdata_2d

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

tdata_2 <- tdata

tdata <- tdata_manip

# declare factors and their levels 
#tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

tdata_man <- tdata

tdata_man$Side_initial<- c("3D manip.")
tdata_man <- subset(tdata_man, select = c(1,3,4:10,12:13))

colnames(tdata_man)[2] <- "Dimensions"

# combined data frame 
total <- rbind(tdata_b, tdata_w, tdata_man, tdata_2)

total$Dimensions <- factor(total$Dimensions, levels = c("3Da", "3Db", "3D manip.", "2D"), labels = c("3Da", "3Db", "3Dc", "2D"))

# create a summary dataset that also contains the percentages
plotdata_total <- total %>%
  group_by(Dimensions, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions'. You can override using the `.groups` argument.

4.5 Plot all in one

library(scales)
theme_set(theme_light(base_size = 10, base_family = "Poppins"))

g<- ggplot(plotdata, 
       aes(x = Dimensions,
           y = pct,
           fill = selection_rec)) +
  geom_bar(stat = "identity",
           position = "fill") +
  scale_y_continuous(limits = seq(0, 2),
                     breaks = seq(0, 1, .25),
                     expand = c(0,0),
                     label = percent) +
  coord_cartesian(xlim =c(1, 4), ylim = c(0, 1.4))+
  #coord_cartesian(clip = "off")+
  geom_text(aes(label = lbl), 
            size = 4, 
            position = position_stack(vjust = 0.5)) +
  scale_fill_brewer(palette = "Pastel1") +
  labs(y = "Percentage", 
       fill = "Selec. Obj.",
       x = "Test condition",
       title = "Subjects' Selections in \n3D vs. 2D Contexts (N = 3430)")+
  #annotate(geom = "hline",yintercept = 0.5, y = 0.5, color = "black", size = 1, linetype='dotted')+
  annotate("pointrange", x = c(1,2,3,4), y = 1 - plotdata_sub$pct, 
           ymin = 1 - plotdata_sub$pct - plotdata_sub$CI, 
           ymax = 1- plotdata_sub$pct + plotdata_sub$CI, 
           colour = "black", size = 0.8, shape = 22, fill = "lightblue", fatten = 1)+
  #annotate("text", x = 1.25, y = Inf, label = "p < .001", size = 4, vjust = 1.6)+
  #annotate("text", x = 2.35, y = Inf, label = "p = .09", size = 4, vjust = 4)+
  theme(legend.position = "top", axis.title = element_text(size = 10), axis.text = element_text(size = 13, color = "black"),
        legend.text = element_text(size = 10),legend.title = element_text(size = 11))+
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank())

g

#ggsave("selections_Dim.pdf",width=4,height=5)
#ggsave("selections_Dim.svg",width=6,height=4)

5 Testing the proportions against chance

5.1 Experiment 1a

tdata <- tdata_between

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_between <- tdata %>%
  group_by(Dimensions, Transformation, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions', 'Transformation'. You can override using the `.groups` argument.

plotdata <- plotdata_between
ind <- seq(1, nrow(plotdata), by=2)

plotdata_sub <- plotdata[ind, ]

Binomial-Tests against Chance (50%)

for (i in plotdata_sub$n){
  print(binom.test(i, 122, p = 0.5, alternative = "two.sided"))
}

## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 37, number of trials = 122, p-value = 1.649e-05
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2233437 0.3930317
## sample estimates:
## probability of success 
##              0.3032787 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 33, number of trials = 122, p-value = 4.04e-07
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1940711 0.3583898
## sample estimates:
## probability of success 
##              0.2704918 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 21, number of trials = 122, p-value = 9.678e-14
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1098244 0.2510049
## sample estimates:
## probability of success 
##              0.1721311 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 30, number of trials = 122, p-value = 1.647e-08
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1724670 0.3320671
## sample estimates:
## probability of success 
##              0.2459016 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 26, number of trials = 122, p-value = 1.261e-10
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1441863 0.2964618
## sample estimates:
## probability of success 
##              0.2131148 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 28, number of trials = 122, p-value = 1.577e-09
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1582472 0.3143412
## sample estimates:
## probability of success 
##              0.2295082 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 72, number of trials = 122, p-value = 0.05682
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.4974962 0.6783489
## sample estimates:
## probability of success 
##              0.5901639

5.2 Experiment 1b

tdata <- tdata_within

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_within <- tdata %>%
  group_by(Dimensions, Transformation, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions', 'Transformation'. You can override using the `.groups` argument.

plotdata <- plotdata_within
ind <- seq(1, nrow(plotdata), by=2)

plotdata_sub <- plotdata[ind, ]

Binomial-Tests against Chance (50%)

for (i in plotdata_sub$n){
  print(binom.test(i, 122, p = 0.5, alternative = "two.sided"))
}

## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 43, number of trials = 122, p-value = 0.001428
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2681511 0.4441143
## sample estimates:
## probability of success 
##               0.352459 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 28, number of trials = 122, p-value = 1.577e-09
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1582472 0.3143412
## sample estimates:
## probability of success 
##              0.2295082 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 17, number of trials = 122, p-value < 2.2e-16
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.0833176 0.2137055
## sample estimates:
## probability of success 
##              0.1393443 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 9, number of trials = 122, p-value < 2.2e-16
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.03428627 0.13542190
## sample estimates:
## probability of success 
##             0.07377049 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 14, number of trials = 122, p-value < 2.2e-16
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.06417694 0.18503849
## sample estimates:
## probability of success 
##              0.1147541 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 12, number of trials = 122, p-value < 2.2e-16
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.05186499 0.16551339
## sample estimates:
## probability of success 
##             0.09836066 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 84, number of trials = 122, p-value = 3.792e-05
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.5983838 0.7692605
## sample estimates:
## probability of success 
##              0.6885246

5.3 Experiment 2 (3D with Manip.)

tdata <- tdata_manip

# declare factors and their levels 
#tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_2d <- tdata %>%
  group_by(Transformation, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Transformation'. You can override using the `.groups` argument.

plotdata <- plotdata_2d
ind <- seq(1, nrow(plotdata), by=2)

plotdata_sub <- plotdata[ind, ]

Binomial-Tests against Chance (50%)

for (i in plotdata_sub$n){
  print(binom.test(i, 124, p = 0.5, alternative = "two.sided"))
}

## 
##  Exact binomial test
## 
## data:  i and 124
## number of successes = 32, number of trials = 124, p-value = 6.528e-08
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1836902 0.3443496
## sample estimates:
## probability of success 
##              0.2580645 
## 
## 
##  Exact binomial test
## 
## data:  i and 124
## number of successes = 53, number of trials = 124, p-value = 0.1265
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.3390163 0.5193708
## sample estimates:
## probability of success 
##              0.4274194 
## 
## 
##  Exact binomial test
## 
## data:  i and 124
## number of successes = 38, number of trials = 124, p-value = 1.945e-05
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2268317 0.3955711
## sample estimates:
## probability of success 
##              0.3064516 
## 
## 
##  Exact binomial test
## 
## data:  i and 124
## number of successes = 43, number of trials = 124, p-value = 0.0008203
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2635856 0.4374698
## sample estimates:
## probability of success 
##              0.3467742 
## 
## 
##  Exact binomial test
## 
## data:  i and 124
## number of successes = 40, number of trials = 124, p-value = 9.648e-05
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2414508 0.4124115
## sample estimates:
## probability of success 
##              0.3225806 
## 
## 
##  Exact binomial test
## 
## data:  i and 124
## number of successes = 71, number of trials = 124, p-value = 0.1265
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.4806292 0.6609837
## sample estimates:
## probability of success 
##              0.5725806 
## 
## 
##  Exact binomial test
## 
## data:  i and 124
## number of successes = 62, number of trials = 124, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.4089093 0.5910907
## sample estimates:
## probability of success 
##                    0.5

5.4 Experiment 3 (2D)

tdata <- tdata_2d

# declare factors and their levels 
tdata$Dimensions <- factor(tdata$Dimensions, levels = c("3D", "2D"), labels = c("3D", "2D"))

tdata$Transformation <- factor(tdata$Transformation, levels = c("Small", "Angle", "90_rot", "180_rot", "X_sym", "Y_transl", "X_transl"), 
                               labels = c("Size", "Shape", "90-Rot.", "180-Rot.", "X-Sym.", "Y-Tran.","X-Tran."))

tdata$Side <- factor(tdata$Side, levels = c("left", "right"), labels = c("left", "right"))


# recode responses so that 1 = first, 2 = second, 3 = both
tdata$selection_rec <- c(1:length(tdata$sID))
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 1] <- "symm"
tdata$selection_rec[tdata$Side =="left" & tdata$Value == 2] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 1] <- "non-symm"
tdata$selection_rec[tdata$Side =="right" & tdata$Value == 2] <- "symm"



#tdata_strength <-  tdata_strength %>% gather(Entity, Strength, g1:g3, factor_key=TRUE)

 
tdata$selection_rec <- factor(tdata$selection_rec, levels = c("symm", "non-symm"), labels = c("Y-Symm.", "Not-Y-Symm."))

# create a summary dataset that also contains the percentages
plotdata_2d <- tdata %>%
  group_by(Dimensions, Transformation, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions', 'Transformation'. You can override using the `.groups` argument.

plotdata <- plotdata_2d
ind <- seq(1, nrow(plotdata), by=2)

plotdata_sub <- plotdata[ind, ]

Binomial-Tests against Chance (50%)

for (i in plotdata_sub$n){
  print(binom.test(i, 122, p = 0.5, alternative = "two.sided"))
}

## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 60, number of trials = 122, p-value = 0.9279
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.4001674 0.5838464
## sample estimates:
## probability of success 
##              0.4918033 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 41, number of trials = 122, p-value = 0.0003714
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2531022 0.4271979
## sample estimates:
## probability of success 
##              0.3360656 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 32, number of trials = 122, p-value = 1.449e-07
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.1868347 0.3496496
## sample estimates:
## probability of success 
##              0.2622951 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 45, number of trials = 122, p-value = 0.004801
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2833077 0.4609245
## sample estimates:
## probability of success 
##              0.3688525 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 52, number of trials = 122, p-value = 0.1234
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.3371629 0.5189628
## sample estimates:
## probability of success 
##              0.4262295 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 73, number of trials = 122, p-value = 0.03688
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.5057622 0.6860679
## sample estimates:
## probability of success 
##              0.5983607 
## 
## 
##  Exact binomial test
## 
## data:  i and 122
## number of successes = 66, number of trials = 122, p-value = 0.4153
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.4484068 0.6315242
## sample estimates:
## probability of success 
##              0.5409836

Combined:

# create a summary dataset that also contains the percentages
plotdata_total <- total %>%
  group_by(Dimensions, selection_rec) %>%
  summarize(n = n()) %>% 
  mutate(pct = n/sum(n),
         lbl = scales::percent(pct))

## `summarise()` has grouped output by 'Dimensions'. You can override using the `.groups` argument.

6 Test the contexts against each other

6.1 Test 3Da against 3Db

test3Da_3Db <- prop.test(x = c(plotdata_sub$n[1], plotdata_sub$n[2]), n = c(854, 854))
test3Da_3Db

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(plotdata_sub$n[1], plotdata_sub$n[2]) out of c(854, 854)
## X-squared = 4.5631, df = 1, p-value = 0.03267
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  0.003825503 0.089851312
## sample estimates:
##    prop 1    prop 2 
## 0.2892272 0.2423888

6.2 Test 3Da against 3D with manip

test3Da_3Dmanip <- prop.test(x = c(plotdata_sub$n[1], plotdata_sub$n[3]), n = c(854, 868))
test3Da_3Dmanip

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(plotdata_sub$n[1], plotdata_sub$n[3]) out of c(854, 868)
## X-squared = 19.238, df = 1, p-value = 1.154e-05
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.14696333 -0.05568833
## sample estimates:
##    prop 1    prop 2 
## 0.2892272 0.3905530

6.3 Test 3Db against 3D with manip

test3Db_3Dmanip <- prop.test(x = c(plotdata_sub$n[2], plotdata_sub$n[3]), n = c(854, 868))
test3Db_3Dmanip

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(plotdata_sub$n[2], plotdata_sub$n[3]) out of c(854, 868)
## X-squared = 42.96, df = 1, p-value = 5.588e-11
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.1926782 -0.1036503
## sample estimates:
##    prop 1    prop 2 
## 0.2423888 0.3905530

6.4 Test 3D with manip against 2D

test3Dmanip_2D <- prop.test(x = c(plotdata_sub$n[3], plotdata_sub$n[4]), n = c(868, 854))
test3Dmanip_2D

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(plotdata_sub$n[3], plotdata_sub$n[4]) out of c(868, 854)
## X-squared = 2.8977, df = 1, p-value = 0.08871
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.089138481  0.006075854
## sample estimates:
##    prop 1    prop 2 
## 0.3905530 0.4320843

Analysis of Exp. 1a, 1b, 2, and 3

Simon Stephan and Sarah Placi

1 Packages

2 Read in data

3 Plot Results

3.1 Plot Results of Exp. 1a

3.2 Plot Results of Exp. 1b

3.3 Plot Results of Exp. 2

3.4 Plot Results of Exp. 3

4 Main effect of Dimensions

4.1 Exp 1a

4.2 Exp. 1b

4.3 Exp. 2

4.4 Exp. 3

4.5 Plot all in one

5 Testing the proportions against chance

5.1 Experiment 1a

5.2 Experiment 1b

5.3 Experiment 2 (3D with Manip.)

5.4 Experiment 3 (2D)

6 Test the contexts against each other

6.1 Test 3Da against 3Db

6.2 Test 3Da against 3D with manip

6.3 Test 3Db against 3D with manip

6.4 Test 3D with manip against 2D