1 Results

1.1 Demographics

# demographics 
min(tdata$Age)
## [1] 18
max(tdata$Age)
## [1] 69
mean(tdata$Age)
## [1] 32.94167
sd(tdata$Age)
## [1] 12.80841

above we see: min age, max age, mean age, and sd of age.

# 1 = male, 2 = female, 3 = other
table(tdata$Sex)
## 
##  1  2 
## 46 74

1 = male, 2 = female.

# Data preparation

# reorder factor 
tdata$type_effect <- factor(tdata$type_effect, levels = c("similar", "diverse"))

# reorder factor 
tdata$target_cause <- factor(tdata$target_cause, levels = c("single", "multi"), 
                            labels = c("single-effect cause", "multiple-effects cause"))

# reorder factor 
tdata$target_effect <- factor(tdata$target_effect, levels = c("first", "second", "third"), 
                                     labels = c("first effect", "second effect", "third effect"))


# to create a chart, the data must be in long format and only contain the relevant dependent variables

# make a subset with only the relevant dvs 

tdata_sub <- subset(tdata, select = 1:6)

# recode dependent variables (to have values between 0 and 1)

tdata_sub$Value <- (tdata_sub$Value) * 0.01

2 Graphs

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
## Warning: `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.

A clear dilution effect. Effects seems to be robust against effect domains.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
## Warning: `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.

Effect also occurs for all target effects.

3 Descriptive Stats

## : single-effect cause
## : similar
##       median         mean      SE.mean CI.mean.0.95          var      std.dev 
##   0.67500000   0.65933333   0.04692359   0.09596953   0.06605471   0.25701111 
##     coef.var 
##   0.38980452 
## ------------------------------------------------------------ 
## : multiple-effects cause
## : similar
##       median         mean      SE.mean CI.mean.0.95          var      std.dev 
##   0.38500000   0.49100000   0.04366105   0.08929688   0.05718862   0.23914142 
##     coef.var 
##   0.48704974 
## ------------------------------------------------------------ 
## : single-effect cause
## : diverse
##       median         mean      SE.mean CI.mean.0.95          var      std.dev 
##   0.78000000   0.78633333   0.03255935   0.06659134   0.03180333   0.17833489 
##     coef.var 
##   0.22679299 
## ------------------------------------------------------------ 
## : multiple-effects cause
## : diverse
##       median         mean      SE.mean CI.mean.0.95          var      std.dev 
##   0.49000000   0.56500000   0.04552062   0.09310011   0.06216379   0.24932668 
##     coef.var 
##   0.44128616

4 Statistical Test

# ANOVA 

library(afex)
## ************
## Welcome to afex. For support visit: http://afex.singmann.science/
## - Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()
## - Methods for calculating p-values with mixed(): 'S', 'KR', 'LRT', and 'PB'
## - 'afex_aov' and 'mixed' objects can be passed to emmeans() for follow-up tests
## - NEWS: emmeans() for ANOVA models now uses model = 'multivariate' as default.
## - Get and set global package options with: afex_options()
## - Set orthogonal sum-to-zero contrasts globally: set_sum_contrasts()
## - For example analyses see: browseVignettes("afex")
## ************
## 
## Attache Paket: 'afex'
## Das folgende Objekt ist maskiert 'package:lme4':
## 
##     lmer
library(emmeans)

a1 <- aov_car(Value ~ target_cause*target_cause_color*type_effect*target_effect + Error(sID), tdata_sub)
## Converting to factor: target_cause_color
## Contrasts set to contr.sum for the following variables: target_cause, target_cause_color, type_effect, target_effect
a1
## Anova Table (Type 3 tests)
## 
## Response: Value
##                                                       Effect    df  MSE
## 1                                               target_cause 1, 96 0.05
## 2                                         target_cause_color 1, 96 0.05
## 3                                                type_effect 1, 96 0.05
## 4                                              target_effect 2, 96 0.05
## 5                            target_cause:target_cause_color 1, 96 0.05
## 6                                   target_cause:type_effect 1, 96 0.05
## 7                             target_cause_color:type_effect 1, 96 0.05
## 8                                 target_cause:target_effect 2, 96 0.05
## 9                           target_cause_color:target_effect 2, 96 0.05
## 10                                 type_effect:target_effect 2, 96 0.05
## 11               target_cause:target_cause_color:type_effect 1, 96 0.05
## 12             target_cause:target_cause_color:target_effect 2, 96 0.05
## 13                    target_cause:type_effect:target_effect 2, 96 0.05
## 14              target_cause_color:type_effect:target_effect 2, 96 0.05
## 15 target_cause:target_cause_color:type_effect:target_effect 2, 96 0.05
##            F  ges p.value
## 1  22.88 *** .192   <.001
## 2  14.89 *** .134   <.001
## 3     6.09 * .060    .015
## 4       0.71 .015    .494
## 5       2.33 .024    .130
## 6       0.42 .004    .517
## 7       0.26 .003    .610
## 8       0.08 .002    .924
## 9       0.66 .014    .519
## 10      0.21 .004    .815
## 11      2.30 .023    .132
## 12      0.59 .012    .556
## 13      1.03 .021    .361
## 14      1.77 .036    .176
## 15      0.34 .007    .709
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

Main effect of target cause, as predicted by theory. Also a smaller main effect for type of effect (i.e., effect domains). Figures show that effect is a bit bitter for effects from the same domain. There also was a main effect target cause color, which was not predicted. However. The following graph checks this main effect:

g <- ggplot(tdata_sub, aes(x=target_cause, y=valueJitter, color = target_cause, fill = target_cause)) +
  guides(fill=FALSE)+
  facet_grid( ~ target_cause_color)+
  #ggtitle("Subjects' causal srength ratings") +
  scale_y_continuous(limits = c(-0.05, 1.05), breaks=seq(0, 1, 0.1), expand = c(0,0)) +
  scale_x_discrete(labels=c("single-effect \n cause", "common \n case")) +
  geom_violinhalf(position=position_dodge(1), alpha = 0.2, color = NA)+
  geom_point(position=position_jitterdodge(dodge.width=0.5), alpha = 0.2) +
  stat_summary(fun.y=mean, colour="black", geom="line", group = 1, size = 1.5, linetype = "solid", alpha = 1)+
  stat_summary(fun.data = mean_cl_boot, geom = "errorbar", width = 0, size = 1, position = position_dodge(width = 0.5), color = "black") +
  stat_summary(fun.y=mean, geom="point", color = "black", shape = 22, size = 4, group=1, alpha = 1, position = position_dodge(width = 0.5))+
  stat_summary(fun.y=median, geom="point", color = "black",  shape = 3, size = 4, group=1, alpha = 1, position = position_dodge(width = 0.5))+
  labs(x = "Target Cause", y = "Causal Strength Rating") +
  scale_color_manual(name = "Entity",values=c("#3182bd", "#fc9272"))+
  scale_fill_manual(name = "Entity",values=c("#3182bd", "#fc9272"))+
  theme(legend.position = "none")+
  myTheme
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
## Warning: `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
## `fun.y` is deprecated. Use `fun` instead.
g