Example data for analysis

readme.md

Sample output

Raw data with linear fit per subject*condition

Scaled by subject

Data dictionary

• subject: Subject ID
• color: Color of stimulus. Values: red, green, blue.
• shape: Shape of stimulus. Values: circle, triangle.
• size: Size of stimulus. Values: small, large
• response: Dependent variable

ANOVA output

Type III Analysis of Variance Table with Kenward-Roger's method
                 Sum Sq Mean Sq NumDF DenDF  F value    Pr(>F)    
color            162.89   81.45     2     8  77.4008 5.831e-06 ***
size             689.89  689.89     1     4 655.6223 1.382e-05 ***
shape            778.51  778.51     1     4 739.8398 1.086e-05 ***
color:size         0.87    0.43     2     8   0.4126    0.6753    
color:shape        3.85    1.92     2     8   1.8277    0.2219    
size:shape       662.96  662.96     1     4 630.0301 1.496e-05 ***
color:size:shape   0.91    0.45     2     8   0.4308    0.6642    

generate graph analyze.R

library(tidyverse)
library(lmerTest)

# subject count
COUNT = 5

set.seed(8675309)

# generate a unique intercept per subject
data = tibble(
  subject = paste0("S", 1:COUNT),
  intercept = rnorm(COUNT, 0, 2)
) %>% 
  # fully cross with all combinations of factors
  expand_grid(
    color = factor(c("red", "green", "blue"), levels=c("red", "green", "blue")),
    shape = c("circle", "triangle"),
    size = factor(c("small", "large"), levels=c("small", "large")),
    # repeat each condition
    rep = 1:50
  ) %>% 
  # simulate noisy responses
  mutate(response = intercept + (color=="blue")/2 + (shape=="triangle") * (size=="large")*2 + rnorm(n()))

# typically trials are in shuffled order grouped by subject
data = data %>% 
  split(.$subject) %>% 
  map( ~sample_frac(.) ) %>% 
  bind_rows()
  
# output
data %>% 
  select(-intercept, -rep) %>% 
  mutate(response = round(response, 3)) %>% 
  write_csv("~/dummydata3_factor.csv")

#raw data
ggplot(data) +
  aes(x=size, y=response, color=color, group=paste(subject, shape, color)) +
  geom_point(size=2, alpha=0.5, aes(shape=shape)) +
  geom_smooth(se=FALSE, method="lm", aes(linetype=shape), alpha=0.5) +
  facet_grid(. ~ shape) +
  theme_classic(16)

# scaled by subject
data %>% 
  mutate(.by = subject, response = scale(response)) %>% 
ggplot() +
  aes(x=size, y=response, color=color, group=paste(subject, shape, color)) +
  geom_smooth(se=FALSE, method="lm", aes(linetype=shape), alpha=0.5) +
  theme_classic(16)


# model it
model = lmer(response ~ color*size*shape + 
                        (1|subject) + 
                        (1|color:subject) + (1|shape:subject) + (1|size:subject) + 
                        (1|subject:shape:color) + (1|subject:shape:size) + (1|subject:color:size) +
                        (1|subject:color:size:shape), data)
# ANOVA with df calculated by Kenward-Roger
anova(model, ddf = "Kenward-Roger")

zdata.csv