In npalmer11/psyc7709:

knitr::opts_chunk$set(echo = TRUE)

1. Complete the 2x2 factorial lab found here https://crumplab.github.io/statisticsLab/lab-10-factorial-anova.html, up to section 10.4.8. More specifically, your task is to follow that lab exercise to load in the data, transform the data into long-format, conduct a 2x2 between subjects ANOVA, and write a short results section reporting the main effects and interaction.

library(data.table)
#all_data <- fread("https://github.com/CrumpLab/statisticsLab/raw/master/stroop_stand.csv")
all_data <- fread("data/stroop_stand.csv")


RTs <- c(as.numeric(unlist(all_data[,1])),
         as.numeric(unlist(all_data[,2])),
         as.numeric(unlist(all_data[,3])),
         as.numeric(unlist(all_data[,4]))
         )

Congruency <- rep(rep(c("Congruent","Incongruent"),each=50),2)
Posture <- rep(c("Stand","Sit"),each=100)
Subject <- rep(1:50,4)

stroop_df <- data.frame(Subject,Congruency,Posture,RTs)


library(tidyr)

stroop_long<- gather(all_data, key=Condition, value=RTs, 
                     congruent_stand, incongruent_stand,
                     congruent_sit, incongruent_sit)

new_columns <- tstrsplit(stroop_long$Condition, "_", names=c("Congruency","Posture"))
stroop_long <- cbind(stroop_long,new_columns)
stroop_long <- cbind(stroop_long,Subject=rep(1:50,4))



library(dplyr)
library(ggplot2)
library(tidyr)

plot_means <- stroop_long %>%
            group_by(Congruency,Posture) %>%
            summarise(mean_RT = mean(RTs),
                      SEM = sd(RTs)/sqrt(length(RTs)))

ggplot(plot_means, aes(x=Posture, y=mean_RT, group=Congruency, fill=Congruency))+
  geom_bar(stat="identity", position="dodge")+
  geom_errorbar(aes(ymin=mean_RT-SEM, ymax=mean_RT+SEM), 
                position=position_dodge(width=0.9),
                width=.2)+
  theme_classic()+
  coord_cartesian(ylim=c(700,1000))

• There is a significant effect of congruency. This shows us that people in the congruent task are significantly faster than the incongruent task, meaning that people respond quicker when the color and word match up versus when they do not. You can also see a difference between responses for the congruent and incongruent task depending on second variable- whether you are sitting or standing. This represents an interaction going on.

aov_out<-aov(RTs ~ Congruency*Posture, stroop_long)
summary_out<-summary(aov_out)
summary_out

1. In chapter 10 of Crump et al. (2018), there is a discussion of patterns of main effects and interactions that can occur in a 2x2 design, which represents perhaps the simplest factorial design. There are 8 possible outcomes discussed https://crumplab.github.io/statistics/more-on-factorial-designs.html#looking-at-main-effects-and-interactions. Examples of these 8 outcomes are shown in two figures, one with bar graphs, and one with line graphs. Reproduce either of these figures using ggplot2. (3 points)

library(ggplot2)

p1<- data.frame(IV1 = c("A","A","B","B"),
                IV2 = c("1","2","1","2"),
                means = c(5,5,5,5))
p2<- data.frame(IV1 = c("A","A","B","B"),
                IV2 = c("1","2","1","2"),
                means = c(10,10,5,5))
p3<- data.frame(IV1 = c("A","A","B","B"),
                IV2 = c("1","2","1","2"),
                means = c(10,13,5,2))
p4<- data.frame(IV1 = c("A","A","B","B"),
                IV2 = c("1","2","1","2"),
                means = c(5,10,10,15))
p5<- data.frame(IV1 = c("A","A","B","B"),
                IV2 = c("1","2","1","2"),
                means = c(10,18,5,7))
p6<- data.frame(IV1 = c("A","A","B","B"),
                IV2 = c("1","2","1","2"),
                means = c(10,2,10,2))
p7<- data.frame(IV1 = c("A","A","B","B"),
                IV2 = c("1","2","1","2"),
                means = c(2,12,5,9))
p8<- data.frame(IV1 = c("A","A","B","B"),
                IV2 = c("1","2","1","2"),
                means = c(5,10,10,5))
all_22s <- rbind(p1,p2,p3,p4,p5,p6,p7,p8)
type <- c(rep("~1, ~2, ~1x2",4),
          rep("1, ~2, ~1x2",4),
          rep("1, ~2, 1x2",4),
          rep("1, 2, ~1x2",4),
          rep("1, 2, 1x2",4),
          rep("~1, 2, ~1x2",4),
          rep("~1, 2, 1x2",4),
          rep("~1, ~2, 1x2",4))
type<-as.factor(type)
all_22s <- cbind(all_22s,type)
ggplot(all_22s, aes(x=IV1, y=means, group=IV2, fill=IV2))+
  geom_bar(stat="identity", position="dodge")+
  theme_classic()+
  facet_wrap(~type, nrow=2)+
  theme(legend.position = "top")

1. In the conceptual section of this lab we used an R simulation to find the family-wise type I error rate for a simple factorial design with 2 independent variables. Use an R simulation to find the family-wise type I error rate for a factorial design with 3 independent variables. (3 points)

sims <- rbinom(10000,7,.05)
length(sims [sims > 0 ])/10000

n <- 12
factorial_data <- tibble(A = factor(rep(c("L1","L2"), each = n)),
                         B = factor(rep(rep(c("L1","L2"), each = n/2),2)),
                         C = factor(rep(c("L1","L2"), n)),
                         DV = rnorm(n*2,0,1))

summary(aov(DV ~ A*B*C, data = factorial_data))

# set up tibble to save simulation values
save_sim <- tibble()

# loop to conduct i number of simulations
for(i in 1:1000){

  #simulate null data for a 2x2
  n <- 12
  factorial_data <- tibble(A = factor(rep(c("L1","L2"), each = n)),
                         B = factor(rep(rep(c("L1","L2"), each = n/2),2)),
                         C = factor(rep(c("L1","L2"), n)),
                         DV = rnorm(n*2,0,1))

  # compute ANOVA
  output <- summary(aov(DV ~ A*B*C, data = factorial_data))

  #save p-values for each effect
  sim_tibble <- tibble(p_vals = output[[1]]$`Pr(>F)`[1:7],
                       effect = c("A","B","C", "AxB", "AxC","BxC", "AxBxC"),
                       sim = rep(i,7))

  #add the saved values to the overall tibble
  save_sim <-rbind(save_sim,sim_tibble)
}

type_I_errors <- save_sim %>%
  filter(p_vals < .05) %>%
  group_by(sim) %>%
  count()

dim(type_I_errors)[1]/1000

npalmer11/psyc7709 documentation built on June 3, 2022, 7:04 a.m.